Year End Thoughts

Hot nose breath; early bedtime; unaromatic seafood.  “Is today the day?”  Well, one of them was.  I got it, along with seemingly every other sinner in this small town.  Truth be told, it’s not so bad.  I am more bored than I am sick.  Some combo of the vaccine doing its job and the virus mutating into a highly-transmissible yet non-deadly variant.  Well, whatever.  They lied to us over and over and they keep lying.  This moves money around, and you know which direction it’s flowing.  Up and up.  Sad!

2021 was not a big year.  Overall, a whimpery, achy year.  I am proud of my debut jazz album Connectedness but that doesn’t feel like it “lives in” 2021.  I started writing the music in 2016 and finished by summer 2017.  The record came out real nice but I’m a little annoyed that I didn’t record it a little later, for mere weeks after we recorded, I set out on a path of saxophone improvement.  In particular, my absolute man Caleb Curtis, the big bad wolf of the alto, master of huffing and puffing, graciously took me on as a student and lit me the fuse of Joe Allard.  Without indulging the whole self-loathing mode, I’m not there yet.  But flashes of true saxophone competence make themselves known; I have begun to unlock the next level, where air really becomes sound so that sound can become music.  Fuck the prideful idiosyncracies and technical errors we rationalize as “personal style.” In really learning to play the instrument the right way, one blasts open the cobwebs of self-delusion and confronts the screaming, ice-cold truth of whatever it is one does.  It is no coincidence that as a result of my study and reworking of my lingual technique, I am even less tolerant of mediocre jazz than before, less accepting of the truisms and the default modes of playing.  Alongside breaking down saxophone-playing into its barest objective pieces, I have been naturally asking questions that break down jazz performance and composition.  Why improvise?  Why play a/the melody?  What makes a good solo?  Who cares?  Such questions are profound in their stupidity (they don’t have answers) and stupid in their profundity (overwhelmingly huge).  The ultimately egoistic and yet occasionally healthy mode of re-dredging these basic questions totally hinders creative output but potentially slingshots into a fruitful period, ideally that points in a new direction.

Just before I got COVID, I played three gigs in a single weekend (a first), rehearsed some new/old original music, conducted a piece of avant-garde music (gigantically poor judgment by my nameless friend who asked me to do this — did my best nonetheless), and produced a recording that features players so good they would never even think to call me.  All good stuff, notches in the belt.  How was it?  Eh, meh.  The meek-yet-truthful voice way in the back of the head: “that’s not what it’s about, man.”  So what is it about?  That remains to be seen.  But my interest in jazz made outside the tiny, shrinking pantheon diminishes ever so.  Classical music, thank God, still hits pretty Goddamn hard but I feel the stretch of universe that separates me from Vienna ca. 1791 expanding.  The flames of love will burn through my log at some point, right?  *shudder.*  And indeed, Bartók doesn’t quite arouse me as he once did, nor do I have the patience to even press PLAY on Mahler.  Mozart and Bird are still safe, for now.

And yet!  I am further emboldened in my predictions about the future of music.  The slothy irony is that I haven’t done/made much computer music this year.  I suppose if I really believed in what I believe in, I’d peel my ass off the armchair and actually go for it.  I could say “easier said than done” but that is too easily done, let alone said;;;,,,... no excuses.  Somewhat lamely, I probably have to squirt Another Jazz Album [2022] out of my system before I go full Neuromancer — *sigh* — but I’ll keep preachin’ in the meantime.   My imagined future of music moreover offers an escape from the quagmire of Spotify et al.  Indeed, Spotify is choking out the talent that undergirds the whole  industry — but I would not call it the “Music Industry.”  There is more to music.  Spotify is in the Instantly-Accessible-Through-Your-Device Audio Recording Industry, which is the humongous glutton sitting on the throne in the palace of music.  But that industry only ascended to obese dominance in the 20th century, an exceptional century in music.  Before then, it was about BEING THERE, IN PERSON, PARTICIPATING IN ONE WAY OR ANOTHER, with no replacement.  And to a lesser extent, sheet music and the pedagogy that enabled a person to make music themselves.  If we resign ourselves to repeat the 20th century of music over and over again, then music will just get worse and worse and Spotify will win harder and harder.  But audio recordings need not be the standard of music.  They will never disappear — of course.  But I optimistically envision music in 2094 not as being “consumed” (ew), but just played.  Nobody is not a musician.  It’s a matter of tools and communication and opportunity — it’s got COMPUTER written all over it.  In 2094 I hope that the youngsters snarkily look down on the boomers of the future, hitting play on their devices then just sitting there, the way we would laugh at someone who listens to baseball on the radio.  Pure audio will be seen as the aural equivalent of 2D black-and-white imagery.

Perhaps.  My prediction requires a generally active and curious population, or at least one whose addictive tendencies can be weaponized into action and curiosity.  The 20th century way of ingesting music is well-suited to the flabby world of Wall-E, which may well be our reality.  Time will tell indeed but I do not believe the future is determined historically or determined at all.  We need artists and technologists to, like, do stuff, ideally as unimpeded as possible.  Hence my proselytizing but also my COVID-etc-induced dismay.

That said, damn! Thomas Ades is a good composer.  An heir to the Beethoven-Brahms-Bartok-Ligeti lineage.  Unpretentious music coming from an environment with infinite tolerance and even lust for pretentiousness.  On the other hand, Giacinto Scelsi really is of the most essential thinkers of the 20th

century — exceedingly pretentious, but it was just a matter of time before the “one note” guy came along and actually did it right.  I can’t wait to play the Scelsi videogame.  Tigran Hamasyan released concert footage from 2010 — I was in the middle of high school, at peak Tigran fandom, and this video reminded me why.  Red Hail is still the best Tigran album and this performance legit brought a single tear to my eye.  The perfect youthful cocktail of confidence, naivete, and indulgence — that music just works, undeniably.  My wife and I were listening to a ton of tracks produced by Zaytoven the other day, the side-mission being to track the development of Trap from its primordial turn-of-the-millenium roots to its Obama-era flourishing, to its unfortunate yet predictable appropriation by the likes of Sprite.  You know someone’s getting P-P-P-Paid when the corporate overlords slither in and decide that a musical style isn’t just for “gangsters” anymore but is in fact suitable for their imagined “general public.”  Congratulations, OGs of Trap — ya did it.  Enjoy the bread, but if you’re not going to make something cool and fresh, at least seed the next generation.  Least you can do.

~    ~    ~

2021 was also not amazing for video games.  Metroid: Dread was probably the best new game I played this year.  They did everything right.  The music lacked the magic needed to take it to the top of the mountain, but all the “Metroid-y” stuff was right on.  Less memorable than I would have hoped, but my memory of the compact, straight-to-the-point game is warm.  

The real masterpiece I played this year, though, was the “Final Cut” of 2019’s Disco Elysium, which is to Baldur’s Gate what The Witness is to Myst.  Long have I dreamed for an RPG with no combat but just dialogue.  Distill and perfect that mode of playing and existing in a fantasy world.  The bleak yet funny politico-economic world of Disco Elysium is perhaps less fantastical than one would hope, but they nailed it.  The pure-dialogue RPG with real role-playing.  None of the garbage of paths that seem to branch but then rejoin like 20 minutes later; no lip service, no bulshitty filler.  Actually good writing (not “good for a videogame”); real characters (no juvenile anime bozos); beautiful art (not just pixel-per-square-inch overdose).  A dream come true and one that makes an important, oft-overlooked philosophical point, and very forcefully at that.  Namely, that life and your character as a person can be modeled and/or decomposed into interlocking, often quantitative and yet random systems and statistics.  It’s a tacit assertion in most RPGs, but the brilliancy of Disco Elysium is to 24-furcate “your” personality into modules that interact, compete, and importantly are not created equal.  More than just being an engaging game system, the 24 skills, which are personified and voice-acted as inner impulses, implore you to decompose your own personality as such.  Are you the person who wants a cigarette right now?  Are you also the person who empathizes with the stupid little dog in the video?  The verb “to be” is, as usual, deployed sloppily here, but the real point is that questions of identity can indeed be more interesting, and more importantly useful, than they were in dumb into philosophy class or in dumb Twitter thread where a child all-caps yells at you because of the geographical happenstance of your great-great-great-grandmother’s birth.  I bring up The Witness again because that’s the other semi-recent game that made me see the world differently.  Where The Witness’ commentary is about the visual world, problem solving, nature versus technology, and scientific discovery, Disco Elysium gets its hands dirty with society and interpersonal communication.  A must-play for many gamers.  And many non-gamers!  Disco Elysium makes me optimistic about the future of literature in a time when it is so easy to feel that no good books will ever be written or read ever again.

In COVID isolation I began playing Metal Gear Solid V: the Phantom Pain, indeed my first earnest foray into the franchise.  Having never gotten into war-based games or even first-person-shooters generally, I must admit that the gratuitous and at least somewhat realistic violence does make the stomach quiver.  I was surprised to feel that.  It’s a great game, though.  Its interlocking systems play well together and its storytelling could never work in any non-videogame format — good.  To pick some nits, Quiet’s outfit is utterly retarded and I have no idea why there is an online component at all (I am several years late, though).  A few frustrating moments due to checkpoint mechanic, too.  Highlights: C4 on anything; the unbelievable smoothness of the animation; the cassette tapes instead of codecs.  I love some of the details of the control system that make the action extra visceral: hitting R2 repeatedly instead of just once to choke out a dude in your clutches; the fact that Snake’s body moves when it would have to to achieve certain neck-craning camera angles; the hilarious moment of Fulton-ing a waking-up solider back to Mother Base at a jillion miles an hour.

Sluggish Morss: Pattern Circus disappointed me slightly if only because I loved Dujanah so much.  Never really “got” this new one but enjoyed my time nonetheless.  More than any other developer, Jack King-Spooner makes me want to get up and make games.  Living proof that someone with non-generic tastes in music, art, and writing can step up to the plate.

~    ~    ~

The one morsel of mercy 2021 leaked onto us was the return of Survivor, the only good TV show ever.  Season 41 had like two-and-a-half bad episodes but several good ones and a couple great ones.  My #1 “rootin’ for you, baby” character fell victim to a questionable strategic decision but I really dig the winner and predict her game to be seen as a gold standard for a certain type of gameplay that thankfully opposes some of Jeff’s seemingly unending appetite for Big Moves™.  Someday I will write my own treatise on Survivor.  I have to.  Mario J. Lanza is the best Survivor writer ever if you have seen the sho, but I think that with a chunky handful of hours I could produce an essay that would do the job of enticing someone to take the plunge into Mark Burnett’s sacred realm.  [For what it’s worth, I put M.B. as the great genius of the early 21st century — even greater than Trump (who Burnett sharpened, if not created as the figure he was during the lead-up to his election).]

Hopefully the producers are at least beginning to learn their lessons about all the twists and advantages.  The episodes focusing on those flopped, the more “classical” episodes soared.  Sadly, the most interesting strategic twist, the Shot in the Dark, had about as much impact as a fart in a jacuzzi.  They probably never would have even mentioned it if Sydney (incredible character — a travesty she wasn’t on the jury) hadn’t played hers.  Whatever.  Glad to know they’re leaning towards non-returnee casts as well, which are ultimately better, as fun as it can be to root for old favorites.  Best moments of the season: Xander executing (what was obviously) Tiffany’s and Evvie’s idol plan; Shan’s arc; honestly JD shouting “money!” as he fumbles the bag as hard as anyone ever has; Naseer “un-throwing” the challenge; and honorable mention: “Baruch HaShem we’re eating.”

~    ~    ~

Eh, here’s to a MUCH better 2022.  Bar’s too low to wish for anything less.  Keep swinging out there.  Here’s my link to music you’ve definitely never heard.

Technical Notes on Connectedness

I usually love reading musicians’ words on their own music.  Both illuminating and opaque reflections are fun and telling in their own ways.  My liner notes to Connectedness lean more opaque, at least with respect to technical musical details, since my audience (hopefully) contains non-technical but open-minded listeners who take in music for its emotional and aesthetic properties rather than its nuts and bolts.  But of course, there are those like myself who also hunger for the secrets up the magician’s sleeve, as it were.  What follows is for you guys.

~ ~ ~ ~ ~

An overarching and also permeating principle of the album is duality: the two-ness of opposites that are also the same.  The concept of duality’s home in mathematics but is, of course, right at home in music.  Major vs. minor, tritone substitutions, notes vs. rests, …  So much music is about maximizing contrast but also interrelationship, and any process or concept that generates new music from old is eagerly welcomed into the musician’s bag o’ tricks.  In the case of Connectedness, the tracks were composed in dual pairs, symmetrically arranged around the center track, “Reflected off the Water” (which is indeed self-dual).  The introduction, “Opening Up,” is outside of this structure.  Specifically, “Ordinary” and “Long Line” make a pair, then “Boiling” and “A Crack in the Ice,” then “Zenith” and “Nadir,” then “Indigo Conjunction” and “Viridian Forest & the Night Sky.”  There’s nothing particularly fancy going on here; the duality was more of a general principle in the back of my mind as I composed, not a specific procedure.  I bring it up so that it makes sense when I break down the tracks in pairs (except for the two un-paired ones).  

0. “Opening Up”

Sonny Rollins is my god; Way Out West, The Bridge, and Alfie were strongly in mind when I worked on Connectedness.  One of Sonny’s amazing tricks is to pit bluesy/modal/folkloric playing against rigorous, elevated bebop, a sort of call-and-response between two modules within his own musical personality.  On Way Out West in particular, his blues playing takes on a cowboyish hue.  I wanted to lift some of that for several reasons: my own “western” (Californian) origin, as an affirmation of the validity and depth of American folk culture, a nod to Robert Stillman’s Horses as well as Way Out West.  But instead of bebop, of which I am obviously not a Sonny-level master, Middle Eastern melodic improvisation/composition comprises the other pole in my juxtaposition.  (“Middle Eastern” is an extremely broad category; I am most familiar with Armenian, Persian, and Turkish styles/ideas, and I freely draw from these without over-sweating “authenticity” or consistency.  Bulgaria and Albania, more Balkan than Middle Eastern but not without overlap, will end up creeping in later on, too.)  

The outline of “Opening Up” is: 

• An antecedent blues-cowboy melodic phrase that alternates between adjacent notes in the D minor pentatonic scales as it weaves downward from the top of the saxophone range to the middle, punctuated by two fat (subdominant-implying) rhythm section hits.

• The consequent to the previous phrase, which works its way to middle D; the rhythm section punctates again and confirms D minor.

• A dualized repetition of the first two phrases — D minor is transformed into D♭ major and subsequently D♭ minor.  (Neo-Riemannian theory characterizes this move as an L-P-R transformation followed by just P — whatever, dude.)  Very few listeners would identify the slippery half-step modulation as important, but one cool thing about idiosyncratic instruments like the saxophone is that nearby key areas can take on strikingly different colors because of the unevenness of the instrument and the technique it requires — that’s what I’m going for: pitting an “easy” key against a “hard” one.

• After the 2+2 cowboy phrases, I present another version of a descending modal pattern that highlights adjacent notes.  The descending “up-down-up-down” flourish is ubiquitous in Middle Eastern music and it’s part of my melodic repertoire.  First I do it in A lydian (a cousin of D♭ = C♯ minor), then passing through F major/D minor (recalling the top).

• The third primary color of “Opening Up” is rubato free jazz.  The end of the Middle Eastern pattern twists from A over D to A♭ over C: an implied tritone relationship, another instance of duality.  The washy, bubbling moment where the band comes in for real on the A♭ dominant chord is, to me, like color flooding into a previously black-and-white scene.  The band nurtures the roiling texture and acclimates us to some bona-fide jazz harmony, preparing the final thrust.

• The last phrase sequences a nearly-even melodic shape through quick, chromatic harmonies (more tritone games).  The arpeggio contorts a little bit in order to grab the harmonic footholds the chords allow — this is one of my favorite harmonic effects, and indeed a very old one.

The final two chords serve three purposes: 1) recall the descending minor-third rhythm section statement from the very beginning; 2) exploit the near-symmetry of the dominant chord that smoothly connects it to minor-third neighbors; and 3) set up the F major center of the following track, “Ordinary.”

1. “Ordinary” and 9. “Long Line”

The exciting gambit of “Opening Up” is a bit of a fake-out; the album “truly” begins with a simple, calm, mysterious song.  Likewise, the finale, “Long Line,” is more of a ride-into-the-sunset moment than a bombastic “and the curtain falls!” one.  They share the same basic setup, too: an active, through-composed bassline underneath an operatic melody, bathed in a cowboy atmosphere.  The second halves of both songs are basically the first halves transposed by tritones, and each composition finishes with an on-the-nose 1-over-I preceded by one of the two strongest tonal cadences: iv-I in the case of “Ordinary;” V7-I in the case of “Long Line.”  (The voice leadings of those two moves are essentially the same; they are indeed dual.) 

“Ordinary” is more tender and diatonic, the only tricky harmonic move being the slide from F major to B major, negotiated by a D♯ half-diminished chord in 3rd inversion.

The rest of the harmony is by-the-book: a good-ol’ American dollop of subdominant, particularly as the non-standard downwards resolution to V7/V, and the welcoming of the sixth scale degree as a happy member of the tonic major chord.  The outro G♯ minor vamp is a nod to the title track of Robert Stillman’s Horses, whose Americana-inflected opening track, “The Dance 1,” is part of the DNA of “Ordinary” as well.

*    *    *

“Long Line” is more adventurous.  The placid opening bassline is indeed stolen from Majora’s Mask, but it starts to morph as soon as the melody enters.  The first chord progression (supporting the initial 10-bar melodic phrase) is more or less taken from a Bulgarian musical, but truncated so that C#7 returns to D major rather than the B-major-to-B-minor-to-F♯-minor cadence in the musical.

I love this chord progression and it appears elsewhere on the album as well as later on “Long Line” albeit transposed).  The second chord progression, supporting the second, snakier melodic phrase, functions as a connector between D major and B major.  (“Long Line” interpolates D and A♭ between the F-B poles; it spends time in all four key areas while “Ordinary” employs just two.  The basic outline of “Long Line” is: 1) D major intro/melody; 2) B major solo section; 3) A♭ major melody; 4) F major outro.)  The solo section is basically centered on B, with two quick trips to D major and G# dominant.  My favorite part of the section is the cowboy counterpoint at the end; on the subject of “obscure Zelda melodies I stole,” yes, the bass plays “Sheik’s Theme” from Ocarina of Time starting in m. 66.

Taken together, “Ordinary” and “Long Line” moreover highlight the (somewhat subtle) difference between 6/8 and 3/4 time signatures, the double- vs. triple-meter duality present in so much music.  While “Ordinary” cleanly separates the dotted- vs. non-dotted-note streams into melody and bass (leaving drums to glue them together), “Long Line” features a melody that flirts with both subdivisions as it floats over the repetitive 3-bar bass shape.

The “cowboy bookends” of the album surround the “real” jazz; “Ordinary” allows the listener to settle into the sounds of the instruments via an unchallenging melody; “Long Line” caps the journey with an unhurried operatic flourish and the final sparkly embers of the album’s harmonic world.

2. “Boiling” and 8. “A Crack in the Ice”

“Boiling” was actually the first completed composition of the album, and was in fact probably what gave rise to the project in the first place.  On November 10, 2016, Simón, Avery, and I played as a trio for the first time, and I brought in my then-brand-new tune, untitled but with the descriptor “boiling” for the opening out-of-time section.  Long story short, the band just worked, Simón told me “that’s the title, man,” and the second we finished playing, I bolted for a piano to write more.  “A Crack in the Ice” came later, after I had settled on the duality theme.  So in some sense, “Boiling” is the original material and “A Crack in the Ice” is a purposefully contrasting response.  These two are far less obviously connected than the cowboy pair.  “Boiling” is all about improvisation and interaction, alternating between aggressive out-of-time jazz and aggressive in-time jazz, while “A Crack in the Ice” is rather tightly constrained and cloaked in a cold, foggy demeanor.  I suppose in this pair I am leaning towards the oppositional qualities of duality, de-emphasizing the samenesses.

“Boiling” begins with one of my favorite “jazz games:” out-of-time group improvisation trying to hit chord changes together.  It’s somewhere between Simon Says and Chicken, game-wise, and you get these blurry harmonic edges that are impossible to compose directly.  The first chunk, leading up to the in-time melody, once again exploits tritone symmetry and two different shadings of the dominant chord; I personally listen for the subtle chromatic inner voice leadings rather than “the chords themselves,” lest I find myself flipping the tritone coin with F and B in my ears.

The subsequent “A” section, where the real melody begins, takes a circuitous path to B major, the loose home key for all of “Boiling.”  (B is honestly just such a great key.  The comfiest key on the piano, fun and “grippy” on tenor with all the side keys, and the bass’ open E string makes for such a warm subdominant, even more pleasing than open-E-as-tonic.)  There’s some sneaky harmony in the form, but nothing too special — relatively straightforward jazz fare — even a couple ii-V-Is!

Melodically, “Boiling” is essentially built of three pieces: 1) the pattern of 4 descending notes then an ascent that begins the whole track, kicks off the melody, and comes back several times within it; 2) the up-down-up-down Middle Eastern scale pattern that first appeared in “Opening Up,” placed in a double-time swing context; and 3) the whole-tone bassline that will re-occur throughout the album and be dualized itself: 

The central metaphor of “Boiling” is best embodied by the transition at the end of form, where the time breaks down (“boils over”) and we move into out-of-time improvisation à la the intro.  Anyone who cooks knows the moment: the pot is suddenly bubbling up like crazy, and you rush to run down the fire, hopefully saving yourself from a big mess or worse.  In this jazz context, the in-between moments are the most exciting to me: feigning an ametrical melodic twist before the rhythm section really gives up the pulse, or bending a rubato phrase into the freshly reestablished tempo.  All in all, it’s jazz with a bit of an edge.  On our particular recording, I’m especially proud of Hayoung’s Herbie-esque solo.  It’s just perfectly constructed and so swinging.

*    *    *

“A Crack in the Ice” dispenses with the extroversion and bubbly loquaciousness, generating tension through mystery instead of loudness.  The opening melody, harmonized in elevenths (a trick I lifted from “Paula’s Theme” from Earthbound, itself a rearrangement of “Youngtown” from Mother), appears elsewhere on the album, most obviously on “Viridian Forest & the Night Sky,” but this is its most complete, straightforward presentation.  One interesting thing about jazz harmony is that because chords often have many notes, it is possible to voice thirds-based chords in fourths; in fact, using ninths and thirteenths to “quartize” the sound of, say, a tonal seventh chord, is a classic recipe to make your functional harmony sound like jazz (or French Impressionism).  The move from “Boiling” to “A Crack in the Ice” abstractly represents this thirds-to-fourths shift.  The second harmonization of the melody in “A Crack in the Ice” tempts the listener to recover a tonal context from the neutral gray fourth-chords. 

“It’s like G minor, but it smells weird!”

The final harmonization of this melody, near the end of the track, is even more melty and diabolical.  Imagine repeatedly strumming three guitar strings tuned a fourth apart but also constantly detuning them so that the composite chord squirms ever-downward.  “Boiling” has a couple of analogous squirms, but they are all tempered by good ol’ tonality and hence are less infernal.

A more direct thematic connection comes at the sudden shift from in-time to out-of-time.  The descending figure that initiates “Boiling” is flipped upside down and sequenced from the bottom of the saxophone’s range to the top.  We play another rhythmic game: start and end a long phrase with (almost) the same number of notes together, but don’t line up along the way.  The  Intermediate Value Theorem guarantees that our emergent tempi pass through each other. 

The brief solo-piano moment before the bass improvisation has a similar (“Boiling”-related) motivic idea under the surface, made even more symmetrical and obvious (this one’s for you, Béla).

The last major piece of “A Crack in the Ice” is the slow rubato melodic passages with tenor way up high and bass pedaling an open string and a thumb-position melody (parallel with tenor) simultaneously, arco.  The sonic effect is cold and foggy, the piano and brushes accompaniment acting as little ice crystals, small bits of hard texture floating in a vapory mass.  The melody appears four times, and each time Simón pedals a different opening string: four different shades of dark blue-gray.

Lastly, I will mention the modal trick behind the bass solo and the outro of “A Crack in the Ice.”  The instructions on the page say “Locrian/Lydian” over the same bass note.  Locrian and lydian are the two modal extremes of the diatonic scale, and at first glance may seem to be as different as can be.  For instance, E locrian comes from the F diatonic scale while E lydian comes from B (raise your glass to the mighty tritone once more).  But what may appear as opposites can often be reinterpreted as dual partners: stacking ascending fourths on E produces the E locrian scale, while descending fourths (or dually, ascending fifths) creates lydian.  None of the other modes have this property of “maximum quarticity/quinticity.”  Another beautiful game you can play is to transit through the modes over a single root note.  So, for instance, C lydian — C ionian — C mixolydian — C dorian — C aeolian — C phrygian — C locrian.  Each move only requires one note in the scale to move down by one half step.  It would seem at first that the game must finish at locrian, but if you “de-privilege” the note C, you can continue the pattern indefinitely by gluing B lydian to C locrian, which are indeed just a single half-step shift away from each other.  Then, the cycle loops back on itself after 84 moves, hitting all seven modes on all twelve notes.  A consequence of this that I use in “A Crack in the Ice” is that any locrian voicing can be transposed up a half step to become a lydian voicing over the same bass.  Try it!

“Boiling” and “A Crack in the Ice” both play with in- versus out-of-time sections, exploit harmonic symmetries, and share motivic material.  On the other hand, they represent the opposing extremes of “temperature” on the album and are paced very differently than each other.  

3. “Zenith” and 7. “Nadir”

Moving inward, we arrive on the two “episodic” tracks, each of which juxtaposes two totally different musical characters and jumps back and forth between between them.  Both tracks have a dark, spidery character; “Zenith” compares this to a light, bouncy groove, while “Nadir” pits it against hard rock.

The musical machine that sets “Zenith” in motion has three layers: 1) free-time drums playing almost-triplets accelerating and decelerating like a gentle breeze; 2) bass + piano freely but slowly arpeggiating triads; and 3) a saxophone melody that weaves downward in huge leaps — imagine the big, slow, careful steps you’d take from foothold to foothold descending a mountain.  The melody itself purposefully steps around chord tones, only coming to rest when it has to land on the shifting harmonic platforms.  The supporting triads move by major third (mostly): E major — C major — A♭ major — C minor — A♭ major — A♭ minor (= G♯ minor) — E major.  There are few extra chords in there to disguise the naked symmetries and to keep it from being a total neo-Riemannian wet dream, but the major-third-related poles comprise the main structure.  Compare to the tritone/minor-third symmetries of “Ordinary”/”Long Line,” as well as the upcoming harmonic symmetries within “Zenith” and of “Nadir.”  The out-of-time-yet-accelerating transition to the first solid tempo of “Zenith” indeed relates triads (and one seventh chord) by minor thirds (note that triads are always more smoothly connected by major thirds, while four-note-chords are always more smoothly connected by minor thirds).  The C♯ — E — G — E twist is a bit more jagged to my ears than the initial E — C — A♭ one.

In any case, saxophone, bass, and piano come down to a whisper while the drums crescendo, setting up a new 5/4 triple meter.  A delicate 11-bar interlude, a moment of alignment, juggles pretty much all of the harmonic considerations seen so far and also plays the triple-vs.-duple rhythmic game.

The reverie ends quickly enough — a couple of long saxophone scales and a cadential fake-out bring us back to the out of time “mountain-descent” melody supported by major-third-related triads, this time with a bit more volume and edge.  The first complete arc of the composition comes to a close on a restful E major moment, as if the tune so far had never happened or was just a dream.  But then the drums once again push into 5/4 triple meter for the solo section.  The first half of the solo form is a gentle and conservative tonal elaboration of E major.  The second half is the Bulgarian chord progression (this is its first complete appearance), complete with the (missing in “Long Line”) IV-iv-i cadence in F♯.  The tempo disintegrates in the final bars of the saxophone solo, leading to an important piece of thematic material that has popped its head out earlier but fully reveals its true form here for the first time:

This four-note “down-down-up-up” motif is sort of the Beethovenian counterpart of the Middle Eastern “up-down-up-down” figure.  It moreover executes a wonderful negotiation between diatonic and chromatic spaces, and also smoothly connects to itself (a major third away) after five cells:

The whole figure, fourteen cells moving through three keys, is essentially the melodic opposite of the beginning of “Zenith”: all fast stepwise motion rather than huge slow leaps; generally ascending rather than descending; nestled in a diatonic scale rather than tiptoeing around one.  The line functions as a sendoff to the climax of “Zenith”: one last round of the spidery melody, supported by the major-third-motion and then the minor-third-motion, starting fortissimo but dying to a whisper by the end.

*    *    *

“Nadir” has a loosely comparable arc but the details are, of course, quite different.  The opening machine, this time, is more rhythmically aligned: 1) A 3+3+2 bassline that you might find as the “Cave” theme in a GameBoy game; 2) drums playing a repeating 3/16 figure (cf. the almost-triplets of the introduction to “Zenith”) that goes over the bar lines, sometimes lining up with bass, sometimes opposing it.  The spidery rubato saxophone melody offers another level of “misalignment,” floating over the beat, almost lining up at times but not strengthening the meter at all.  While the ionian mode has more or less conquered major-key music, (Western) minor-key music is still amenable to variation in modal shading, and consequently, it is easier in minor to draw inspiration from the highly sophisticated modal systems of e.g. Persian and Turkish musics.  I fully admit that I am not at all using a particular dastgah or makam anywhere on this track, but I am thinking about how various pitches/intervals sit on and resonate with the open canvas of a minor triad.  The first section of the “Nadir” melody is G dorian or D aeolian depending on if you privilege the bottom bass note or the whole triad the bass outlines.  (For what it’s worth, I can hear it both ways, a bit like the “rabbit-duck” optical illusion.)  The only deviation from G dorian/D aeolian is the E♭ upper neighbor to D in the transitional phrase that links the G minor bass triad to the B minor bass triad.  In the “B zone,” the modality of the melody expands: both raised an natural sevenths appear; raised, natural, and lowered fourths appear; there are likewise two different seconds and fifths.  I also sneak in a couple of microtones to further juice up the modality.  

The modal ambiguities of the B minor section create tension, and in the aftermath of the saxophone melody, drums crescendo while the bass line slips through a neutral quarter-tonal triad to B♭ major, preparing an unadorned V-I to E♭ while Avery shamelessly plays the Phil Collins fill and Hayoung explodes forth with a fast arpeggio, straight from the Beethoven playbook.  Woo!

(Not my most subtle music.)

No fake-out here — it is time to rock.  I have lots to say about the relationship between jazz and rock — when it works, when it doesn’t, how it works — but suffice it to say for this post that I’m throwing my hat into the ring as such.  One outstanding issue is jazz’s appetite for lush (usually functional) harmony versus rock’s retrofunctional norms (rock harmony often moves the “other way” on the circle of fifths compared to classical/jazz; for example, the rock progression I-♭VII-IV-I mirrors I-ii-V-I) and its general avoidance of thickly-voiced chords.  My compromise in “Nadir” is to rely on a strong descending bassline that only slightly “nerdifies” I-♭VII-IV, and to change keys quickly to satisfy modernistic/jazz cravings.  Mm. 30-31 I more or less stole from the fourth movement of Mahler’s 9th symphony; it is a chromatic alteration of the “Pachelbel scheme” that fits in perfectly with the triads-related-by-major-thirds theme present in both “Nadir” and “Zenith.”

In any case, the rock section only lasts long enough for the listener to not realize I’m huffing and puffing on an acoustic wind instrument and that the band is extraordinarily over-educated for the music it’s producing.  The “turn” motif I brought up in “Zenith, which is also rather Mahlerian (see the aforementioned movement), reappears as the time disintegrates and our free jazz “mode” re-engages.  The two triads of the opening come back as tremolos underneath a rough-and-tumble saxophone line, capping the aggression set alight by the flames of Collins and Beethoven.  A quarter-tone interpolated between B and A♯ recalls the earlier modal antics, preparing the solo section.

The first chapter of the solo section is an expansion of the opening “GameBoy cave level” feel: brooding and not-quite-symmetrical, receptive to expressive modal shadings.  The major-third wheel is completed via the addition of an E♭ minor area.  After 8 segments, we move on (via Collins again, of course) to an expansion of the rock section: the second chapter of the solo section.  This time, the minor-third wheel is closed by continuing the pattern through A and F♯, so that the harmony seems to always descend on average but, as harmony does, ends up right back where it started.  After a couple of loops, we get out of the solo by reprising the Mahler transition and the free jazz segment.  What follows is an acquiescence of the original bassline to the demands of tonal resolution: a perhaps-slightly-ironic iv-i in G♯, diminuendoing towards a fake “dot-dot-dot” ending.  But, “Nadir” being the climax of the whole album, we rock once more and for all.  A totally barbaric whole-tone bassline (as opposed to e.g. “Boiling”’s rather pretty one) walks us down an up-escalator, and we freak out until the admittedly somewhat nerdy ending.  But if my listeners can tolerate some rock, they can tolerate some prog rock too.

In summary, “Zenith” and “Nadir” both juxtapose episodes of totally divergent music.  The lightness of “Zenith,” its musical representation of altitude, comes from the cautious, rappelling melody over a breezy base, plus the effervescent 5/4 triplet groove, more diaphanous than sturdy.  On the other hand, “Nadir” skews dark and heavy: a cavernous, eerie melody over a gravelly pair of linked ostinati, plus a hard rock avalanche — the climax of the album.  In my mind when composing both was the complex exchange between harmony and modality, or stated as a puzzle, how to get more pitches to “work.”

4. “Indigo Conjunction” and 6. “Viridian Forest & the Night Sky”

Having now rehearsed, played, and recorded this music a few years after its initial compositional period, I admit that my ears no longer signal a strong dualistic link between these two tracks.  Both of them morphed a bit over time as well, blurring some of of the conceptual linkage.  In any case, some shared DNA survived: both feature pedal points, tritone-based harmonic relationship, divisions of beats into 5, and high-energy solo sections.  The narrative inspiration comes from an iconic moment that many gamers my age remember: in the first generation Pokémon games, Viridian Forest is the first little dungeon the player reaches, connecting Viridian City and Pewter City.  The forest itself is notable for is winding structure and its blunt, almost abrasive tritone-based theme, but the area it leads from, Viridian City, is interesting because it serves as both an introductory area just after the player’s hometown, Pallet Town, but also the site of the final gym and the lead-up to Victory Road and Indigo Plateau, the climactic section of the whole game.  That is to say, the whole game loops back in on itself, and fun childhood “wow” moment inevitably pops up when you realize that you walked right past the biggest, baddest enemies mere minutes into your adventure.  As a kid, I imagined Viridian Forest as a long, circuitous hallway of grass flanked by tall columns of trees, and it always seemed to be night time there; to this day I can emulate my young imagination tilting my head back and looking up at the stars, the long trunks and leaves in the corner of my view, receding into the distance.  This image, plus the astronomical thematics of “Zenith” and “Nadir,” conjured the image of the stars aligning before the climactic moments on Indigo Plateau — as epic in my memory today as they were in ca. 1998.

As for the music! Though “Indigo Conjunction” and “Viridian Forest & the Night Sky” form a dualistic pair in the larger context of the album, they serve secondary functions relative to other tracks.  “Indigo” bears resemblance to “Boiling” — energetic, swinging, jazz harmony — and “Zenith” — 5/4 swing and the descending-leaps melodic idea — so that the first half of the album is the “jazz half”: a bit more approachable (at least to a jazz-steeped listener), less abstract, faster-paced.  On the other side, “Viridian”’s darker tone and episodic form, as well as some of its specific motifs, connect it to “Nadir” and “A Crack in the Ice,” fleshing out the “non-jazz (or ‘less jazz’) half,” where rock, opera, and videogame music push back on the jazz aesthetic.  

The 5/4 in “Zenith” is light and bouncy; the upcoming 5/4 in “Viridian Forest & the Night Sky” is plodding and heavy; the 5/4 in “Indigo Conjunction” is somewhere between: a repetitive pedal figure but not strictly symmetrical, and the swing tempo admits the duple v. triple game I mentioned before.  “Indigo” opens with a short drums improvisation over the pedal then launches into the melody, which was totally freely composed without motivic connections to the other tunes save for the “Zenith” melody shape in the send-off and the coda.  The melody line twists and turns without much respect for the barline, and possesses a more improvisational character than some of the other, more straightforward melodies.  Perhaps a bit of Tristano peeks through.  Harmonically, the scheme is essentially “Inner Urge”: a pungent, evocative half diminished chord to start (in this case, D half diminished in 3rd inversion); a series of lydian chords moving in a strict pattern (up-a-minor-third instead of down-a-whole-step); then a final episode of quick harmonic moves exploiting the symmetries that connect jazz chords.

The above snippet — the end of the melody going into the blowing section — shows off some of the rhythmic tomfoolery and the pretty chord progression that sends off the head.  The descending-leaps shape is quite like the opening motif of Bartók’s first quartet, and moreover, the chords supporting this instance of the motif are quite like the chords he uses at one equivalent moment in the first movement of the quartet.  The “big harmonic reveal” at the climax of that movement is an arrestingly beautiful voice leading pattern that connects major and minor on A, F♯, E♭, and C — the diminished octagon that probably brought more than a single tear to Ernő Lendvai’s eye — but the same melodic shape is supported with slipperier and somewhat more opaque harmonies earlier in the movement.  My version is not-so-symmetrical, closer to the latter option, but still fits very comfortably under the hang if you take a moment to compute good voice leadings.

After the send-off, the solo section echoes the opening, pedaling C.  But it is really the beginning of an eight-bar phrase alternating between C and F♯ pedals.  (Yes, a harmonic scheme like those in the cowboy tracks is at play.)  This anxious vamp admits modal playing more than harmonic; one is free to play octatonic stuff or emphasize major/minor subsets of that big scale.  For what it’s worth, this is always a very fun but also dangerous section to blow over: there are many possible modal/harmonic choices, and if Hayoung and I guess clashing options at the same time, we can get into hot water.  This is where we test our telepathy and sensitivity (she has insanely good ears and I’m not an aural mega-slouch either).  In my opinion, harmonic areas that feed off these kinds of symmetries (see Bartók again) always build tension and creepiness, like infinite mirror hallways or mazes in the woods.  That’s the idea here; we charge up energy on the pedal-vamp and then release it in the second chapter of the solo form, where the walking starts.  The harmonic scheme here is simple: a four-bar phrase connecting A major to F♯ minor followed by its transposition down a minor third, connecting F♯ major to D♯ minor (the last chord being muddied up as a dominant♯-9, minor’s angry cousin, to launch into the next phrase).  The third phrase supports a non-necessarily-played instance of the “Zenith” leaping motif with some more snakey late-romantic harmony, and the fourth phrase slows down the pace of the root movement, re-setting up the pedal section.  As you might have learned to expect by now, when the form resets, it is a tritone away from where it started.  Both solos are twice through the form, but the first pass begins on C while the second begins on F♯.  But because the opening pedal episode alternates between C and F♯ anyway, it’s a bit tricky to find footing here, both as listener and player.  That’s the point!  Unlike other solo forms on the album, this one, to me, kind of encodes the narrative a soloist ought to take, though hopefully not too strongly.  The sections are so distinctive, though, that to approach them all in the same way would be harder than just catching their waves and riding along.

The large-scale form is quite simple: intro; melody; tenor solo on both tritone-halves of the form; piano solo on the same form; piano begins the melody and tenor joins for the second half; coda out.  Excuse the immodesty but I am quite proud of the harmony of the coda; I think it’s the most romantic and magical chord progression of the whole album, and it really breathes along with the melody.

The dark, impish character of the pedal points under the rest of the melody is replaced by a warmer, fluffier pedal-point moment in the final measures.  I just love the sound of parallel diatonic chords over a bass pedal.  I also really like the transition of D♭/A♭ to G minor across the 3rd and 4th measures, though I’m not quite sure why it works so well!  If it were not for the G chord, the D♭ chord might be more appropriately spelled as a C♯ chord connecting A major to F♯ minor (the two subdominant(-ish) key areas in C♯ minor, which is probably what I’d call the loosely prevailing key area from the beginning of the coda).  But a C♯ chord after an A chord could also reasonably connect to an F♯ major chord (instead of minor) with A♯ in the melody; recontextualizing the A♯ as B♭ but then switching the support back to a minor chord produces G minor.  Chalk it up to a little Neo-Riemannian flourish or just accept smoothly-voice-led chromatic movements as inherently valid, or, perhaps better yet, don’t worry about it too much.  If it works, it works, and this works to my ears!  Plus, who isn’t immediately won over by a warmly-voiced D♭ major ending?  It’s the velvetiest of the keys, the luxurious connoisseur’s tonal vacation home.

*    *    *

Even the tense moments of “Indigo Conjunction” are in relatively upbeat humor; it’s probably the most fun tune overall.  “Viridian Forest & the Night Sky” is more or less the opposite — quite tricky to play and rather demanding on listeners who seek out a thread of coherence.  That said, the composition is indeed playing with some of the same elements in “Indigo Conjunction,” and the overarching form is relatively straightforward and  symmetrical, though more segmented than “Indigo”’s.  The opening atmosphere  is essentially a one-beat loop: bass drum bumping along underneath quintuplets on brushes.  Compared conceptually to “Indigo,” this is about dividing a single beat into 5, rather than a whole measure (which is itself a sort of larger beat).  This rhythmic setup, sometimes called “small fives,” is something of a hackneyed modern jazz trope at this point, but if I may offer an explanation as to why my version is better, it is because I did not commit Avery to a fixed sub-subdivision (like 3+2 every time, say).  He phrases his accents unpredictably so that the more open and abstract “five-ness” prevails over the perhaps more common 3+2 or 2+3 options, which are certainly constricting.  There are 32 distinct ways to accent or un-accent five notes in a row, and if you expand to include three options per note — accented, unaccented, or rest — the number of possibilities shoots up to 243.  Which is just to say there is so much variation in phrasing afforded by big subdivisions; it is therefore a shame to stick to just one or two basic patterns.  My man Avery knows these numbers and it shows!

Returning to the subject of the texture of the opening, the original version of “Viridian” included a bass pedal with the bass drum, but it was determined to be a bit too heavy and obvious, so the first melodic statement is just a duet of tenor and drums.  The tenor melody is very rhythmically basic, but its “natural phrasing” is delayed by an eighth note so that what would have been its downbeat attacks lay in the tiny gap between the third and fourth quintuplets.  The effect is intentionally unsettled, tempting the listener to switch over their perceived pulse.  (On top of that, Avery, being the nerd king that he is, throws in other subdivisions of the pulse.)  The full band snaps into action after three melody statements and a break; the second melody idea enters at [B]: an almost-banal diatonic melody “creepified” by supporting parallel chromatic thirds, the whole-tone bassline from the coda of “Boiling,” and the quintuplet grid churning underneath.  (The first two melodic sections indeed comprise the melodic material from “A Crack in the Ice,” if they seem familiar.)  The third melodic section, this time expressed by piano, brings the quintuplet grid into the melody in a rather on-the-nose way that nonetheless feels pretty good in the hand.  It’s all five-finger ascending scale patterns, moving between segments of B lydian (except for one E-natural) and F lydian (except for one B♭): like corrupted Hanon.  Underneath that, bass simply tiptoes down the B lydian scale twice in a row. 

The three-segment arc comes to a close with bass and piano fading away so that the tenor + drums duet can initiate another round at [C], this time a tritone away, of course (the B pedal in the bottom staff got replaced, as before, with just bass drum).  The second melody idea returns, too, but the “Hanon” section does not; instead, the piano solo section starts over the quintuplet grid plus bass pedalling for real.  The changes exploit the same locrian-lydian trick I explained before, so that the resulting diatonic collections keep playing the tritone game but the root stays fixed.  The musical challenge here was to not let such an admittedly boring bass figure bog down the energy.  Simón deviates, mercifully, and Hayoung and Avery do an excellent job of obscuring the grid without sacrificing too much groove: the result has forward propulsion but also a certain foggy uneasiness.  Chapter one of the piano solo sits on the B pedal, alternating locrian and lydian.  Chapter two introduces D as an alternative bass note and switches the chord-scale possibilities to G lydian and B♭ lydian (though not at specific times — Hayoung can freely choose when to switch between the macroharmonic areas, which, to be fair, share many notes).  Chapter three keeps the same chord-scales but transposes the bass notes (by tritone) to F and A♭, but more crucially “flattens out” the grid into sixteenth-notes.  The eventual goal is to reconceive each individual beat (~75 bpm) as a full measure of 4/4 (at ~300 bpm).  The rhythm section is setting up the lone episode of blistering swing on the album, but the kraken is not to be released straight away.  The piano solo builds in intensity but then diffuses some energy and dovetails into a new section, a new texture with a new perspective on the beat and its subdivisions.

Avery avoids his cymbals, opting instead for a light sprinkling of pure drums; Hayoung floats on the dissipating updraft of momentum from her solo; Simón hops on to a through-composed walking pattern that expressed the new tempo but also reminds us of the old slow pulse.  I’m very proud of the texture they cultivate here: it’s very relaxed and open but also breezy and just a little agitated.  The imagine in my mind was riding Epona, galloping through Hyrule Field in Twilight Princess, the weird dull-yellow light enveloping Castle Town in the distance, perhaps an eagle drifting through the sky without a strong purpose, the impossible cliffs standing proud and abrupt in defiance of realistic physics and geology.  To that end, the upcoming saxophone melody takes its opening shape from one of the main leitmotifs in Twilight Princess.  What can I say?  I’m true to my roots if nothing else.

The section I’m talking about is essentially four repeats of a twenty-four-and-a-half measure phrase driven by the bass.   The first time through, Hayoung offers a patient, wide-open (frankly American) harmonization of the bass line, Simón briskly chugging underneath — no melody.  The tenor+piano melody enters on the second repeat; it moves at its own slower pace, tugging on the meter of the bass+drums (I wrote it as floating non-metrical individual noteheads, loosely arranged on the staff). 

For the third repeat, the bass transposes up a minor third but the melody stays the same (except for two notes adjusted a half step to avoid a couple of ugly clashes).  To my ears, the transposition is not immediately obvious, but the long arcing run (around the 6/4 bar) sounds much more extreme in the higher key.  For the final repeat, the melody catches up to the bass, transposing up a minor third too.  The section sneakily flows into a transition where the beat expands into 5/4, recalling the earlier quintuplet grid.  Tenor foreshadows two melodic coming up in the second half of the album and flashes back to two others from the first half, then launches into the solo section.

The opening section of the tenor solo is two loops through four minor chords with a composed bassline that continues the earlier bass trajectory.  The subsequent main chunk loosen’s Simón role and Hayoung momentarily drops out so that she re-enter with gusto for the climax.  The harmony of the section is not really important at all but for what it’s worth, it’s basically a Hans Zimmer-esque plain minor triad sequence.  We really push, flirting with the high-gear free jazz mode of e.g. “Boiling,” shooting towards a big payoff after a couple hundred measures of gradual build-up.  The climax after the solo is the return of the original theme and the recontextualization of full bars of quick 5/4 as individual beats of slow 4/4 — undoing the earlier metrical transformations.  Or, almost-undoing; if you’re keeping track, the original tempo was quadrupled (75 → 300 bpm), then the time signature grew from 4/4 to 5/4 but the tempo did not change; so, when we cut the tempo by a factor of five after the solo (300 → 60), we end up 20% slower than the opening.  Which is fine, and arguably a bit more epic anyway.

The remainder of the track reprises the original melodic material (a tritone away), but in a more aggressive voice.  (The mighty Kevin Sun calls this “The Virgin Sacrifice.” No virgins were harmed in the making of this album.)  The final vamp is like that of “A Crack in the Ice” — the lydian/locrian game over a tritone pedal.

Despite its length and many sections, “Viridian Forest & the Night Sky” is pretty straightforward as an arc, and looking back, it’s almost in a kind of sonata form: an initial section with a primary and secondary theme group; a long, sequential, tension-building development, then a return to the original material with a little extra gravity.  One of the oldest tricks in the book!

5. “Reflected off the Water”

Finally, we have reached the cornerstone track of the album, the self-dual central jewel.  The two surrounding tracks I just discussed are both rather sophisticated in their own ways; to counterbalance the demand on the listener I wanted this middle track to be simple, beautiful, approachable.  My model was therefore “Love Theme” from Robert Stillman’s Horses: an unhurried rubato melody bathed in a warm, heavenly light that glues the album together.  I knew moreover that the central track would not have a dualistic complement elsewhere on the album, so the overall form was easy to come up with: two earnest statements of the melody, a tritone apart, separated by a fulcrum moment where time essentially stops and the trajectory of the rest of the album realigns in a new direction.  Simple enough in theory, but it is not a trivial task to write slow, simple music without any irony or flashy tricks.  And to imbue that natural character — to make it feel like the melody “already exists” — is even harder.  To me, it amounts to fully trusting the basics of the systems of music, to faithfully submit to elemental ingredients: diatonic triads, V-I progressions, quarter notes, four-bar phrases, …  Hipness and irony corrupts the holiness of those elements, but on the other hand, composing something that’s too basic is itself an ironic, degenerate act.  It’s an exercise in balance, where every note takes up space and the total amount of space is very finite.

So how did I fare?  Well, it’s not for me to decide, but here was my strategy: 

AABA form — tried and true.  The A sections feature a repetitive bassline that is a bit like the whole-tone bassline from earlier, but smoothed out into a diatonic mold.  The harmonic implication of the bassline is bland: A♭ for six bars, then an F minor scale that lazily connects back to the top, taking two beats longer than it should to switch directions and set up a (rather nonchalant) V-I.  On top of the bassline sits the melody: even slower and completely diatonic except for a single E-natural connecting the sixth and fifth scale degrees of A♭.  (On some repeats, I omit the E-natural; on others I bend it by about a quarter tone to segment the F-to-E♭ gulf)  The top line is ionian with a downbeat-accented major seventh in measure 3, but the bassline features G♭s so that it comes across as more mixolydian until the F minor scale, which is aeolian, featuring a G-natural.  That modal mismatch creates a little bit of rub, but it’s pretty subtle because the two versions of G are never simultaneous.  Hayoung’s job is particularly tough because any chord could be an imposition on the simplicity of the counterpoint, but she also has the opportunity to add a third stream into the mix, so she ought not be too shy.  The rhythms on the page are beyond basic, readable by a day-one music student.  We added some variation by playing a game, led by Simón.  On paper, he’s just playing quarter notes, but he is allowed to freely (but smoothly) vary his tempo, so that the pulse breathes, mirroring (or contradicting) its melodic momentum.  The rest of us play a guessing game, trying to be as perfectly in unison with him as we can despite his outward unpredictability.  The result is a sort of Brownian motion of tempo, a tidal cycle of rushing and dragging, and a chance for us to flex whatever telepathy we’ve developed from playing together and being friends.

Simón generally pushes and pulls on the tempo more and more as the tune proceeds, and especially during the bridge, which sequences a hyper-simple IV-V-I progression through the home key of A♭ then C♭ major, a minor third up.  The minor third tonicization is peeled off when a scalar descent that sounds like it should begin on C♭ and end in F♭ lands instead on F-natural minor, at which point the scalar descent is reversed; Simón painstakingly and diatonically climbs from his lowest F up two octaves, then turns the other direction to reset the [A] section back in the home key.  The end of the last [A] section is similarly extended by a scale; after the six bars of A♭, Simón climbs stewise down the F minor scale back to that bottom F as the rest of the band fades to a whisper.

So concludes the melody and moreover the first half of the album.  We experimented with the following moment, the exact center of the whole record.  It was always going to be some kind of improvisation — we tried a full-band version, a trio version where I get out of the way for once, but the choice was essentially made for me when, in a single take, Hayoung improvised an interlude that ended up being what got printed.  It was just so arrestingly beautiful, so crystalline, so absolute.  The heart rate of the music slows to hibernation so that the collective organism we comprise fades out of the picture, revealing a lush yet meek ambient backdrop — a partial memory of a melody; a hopeful daydream; a moment of burbling water transfixing a once-hyperactive child.

Words do no justice to such an uncorrupted moment of inspiration, so they end here.  The second half of “Reflected off the Water” is essentially identical to the first.  The new key imbues saxophone and bass especially with a new registral timbre, and we play the Brownian motion game slightly differently on the way out.  But that’s it — the composition is identical except for a tritone transposition.  (On that note, Hayoung’s interlude is even more impressive in how she connects A♭ major and D major. A continuous, casual stroll through the circle of fifths gives the feeling of waking up from a nap on a train, consciousness seeping in as you realize you’ve reached your destination without being aware of the details of the journey.)  The four tonicized key areas of the whole track are, in order of appearance, A♭, C♭/B, D, and F, the same square as in “Long Line,” the other semi-operatic track. 

In terms of album sequence, I view the first half of “Reflected off the Water” as a moment of respite, like a save point in e.g. Final Fantasy, after the heated energy that builds up through the first half of the album.  The second half of “Reflected,” then, is a well-wishing departure, a pushing-off towards the darker, more abstract second half, which is best approached with a recently-cleaned palate.  In 2021, where TikTok and other ADHD-paced media dominates, it’s quite a big ask to have listeners sit through an album of instrumental music.  My hope is that “Reflected off the Water” segments the experience somewhat, without cleaving it into disconnected chunks.  For what it’s worth, it is often these “and now a break from the action” moments that stick in my mind in long musical works (especially operas).  The humming chorus in Madame Butterfly; the waltz sequence in Der Rosenkavalier; Ornette Coleman playing “Embraceable You” on This Is Our Music.  It’s a delicate balance in music between consistency/continuity on one hand and variation/development on the other.  I really value long continuous experiences that draw you in deeper and deeper, but a well-placed, perhaps shocking discontinuity is sometimes just what the doctor ordered!  Music, being infinitely deep and sacred, admits no magic formula other than the musician’s own personality.

~ ~ ~ ~ ~

If, by some perverse miracle, you’ve read this whole post and have more questions or want to see more sheet music, please do reach out.  I am happy to send complete scores. (Moreover, if you’ve read all this, I think you’re entitled to a free copy of the album — send me an email and I’ll send back the files.)  If any of my musical techniques or ideas appeal to you, take them!  Counterbalancing the joyful and fun process of generating music is the somewhat painful process of excluding ideas from a project; the pain is abated by the faith that someone else somewhere else will draw from the same source or elaborate on a similar idea.  Almost any musical idea is a portal into a deep, unending well of expression.  The worst thing that can happen to music is when it’s never played/heard at all — take that as a command to play, hear, and explore!

CONNECTEDNESS Liner Notes

Listen to Connectedness and purchase on Bandcamp.

If you let it, music will soak into every part of your life.  Music mirrors the universe — mysterious, rigorous, emotional, sublime — and thus naturally glues together one’s whole experience of life.  It has something to contribute in every area: the intellectual, the social, the sacred, the corporeal; and yet, despite all these prongs, music is an inseparable mass, a continuous fluid that resists any attempt to discretize or classify it.  That we can harness the energy of music at all is a human miracle, an endless source of gratitude.  The composer-builder Harry Partch is right on when he declares, “Music is Magic.”

The power to conjure music, then, is proof of the majesty of humanity.  Along with language, religion, and mathematics, music brings out the human spirit’s tendency to bite off more than it can chew, to create and wield technology that we don’t fully understand.  Abstraction meets urgency; the heart directs the hand.  Mercifully, no one is alone in any musical quest.  We absorb and filter knowledge from teachers living and dead, and then we combine our efforts in ensembles.  With friends, music turns into a simultaneously challenging and forgiving group ritual that strings together millions of moments, countless half-decisions carried out by an emergent democratic organism.  What we capture on tape is a projection of that process, recompiled and refracted by the listener’s ear — which is to say that you, the listener, are not merely an observer; you are playing with us, letting it soak into part of your life, which surely has something to say about our music, consciously or otherwise.  And whatever you say or feel about a recording sheds new light on what one might naïvely think of as “the same” piece of music. This generates a new variant for each listener’s experience.  Musicians know that the identity of a piece of music contains all of those variants, past and future — a vast, multidimensional web that far overshadows whatever composition or planning went in originally.  These webs, moreover, have structures and textures that bewilder and inspire in equal measures.  

The mathematician Benoit B. Mandelbrot, in the 1960s, revealed that many natural as well as mathematical phenomena are characterized by a fundamental infinite “roughness." One cannot simply measure the straightened-out length of a coastline nor the flattened-out surface area of the sea that defines it. There is detail at arbitrary levels of zoom, and hence the universe is not solely made up of 2- or 3-dimensional slices — the world is fractal in nature, with dimensionality floating somewhere between the counting numbers.  So too with music: try to find where a note truly begins or ends, and you will come up against a rough, undefined barrier, more like tree bark than a man-made knife’s edge.  Whole continuous lifetimes pass during phrases, and the spaces in between are just as pregnant and fragile as the notes they surround. 

It's all one thing — one big action in defiance of sterile, boring silence.

--- 

The music on Connectedness — born in Boston, reared in New York, with ancestry in Armenia, Austria, and Japan — is both for and about my friends Avery, Hayoung, and Simón.  I wrote the music because they are my friends, but they are my friends because of the music.  I accept the paradox in order to express something of my own personality through these special people.  They judge me not when I bring in a transfiguration of music from Pokémon or a saxophone aria in a half-Persian, half-cowboy style.  And in fact, they intensify such visions; they ripen the fruit of the heart and the mind by being open, musically conscientious people.  For that I am immensely grateful, as I am to you for listening and thus being a part of the music-making process.

Jacob Shulman

Brooklyn, NY

Spring 2021

---

Special thanks first and foremost to the band: to Avery, who shaped and texturized the music on big and small levels alike; to Hayoung, who pushed us all to make every moment the best it possibly could be, who didn’t take any detail for granted; to Simón, who played bass.  Thanks to Kevin for watching over us, for trusting us when we earned it but weighing in when we most needed it.  Thanks to Knar, who really heard the album for what it was and produced artwork that wasn’t just beautiful but also perfectly matched to the music.  Thanks to Josh for creating a smooth, natural recording environment, and to Lee who fought valiantly both for and against me in order to produce the best sound I could have hoped for.  And thanks to all family and friends, teachers and collaborators, inseparable characters in the great web of music.

Reaching and Grasping

My day job finds me explaining math at various levels of rigor.  At one end of the spectrum, math manifests as a game, not to be played but rather hacked.  “What is the path of least resistance to the correct multiple choice answer on the SAT?”  Honestly, not so fun, as all the beauty and structure and glory of math is sucked out by the greedy and lazy test-taking mindset.  When I am fortunate enough to engage with students at the advanced high school or college level, warm coals of that glory start to radiate through, especially to receptive students.  All math-lovers wish that love of math were more contagious, that teenagers could learn to truly dig humanity’s greatest accomplishment rather than just transact with it.  Realistically, it’s probably impossible to devise a worthwhile “romantic” math curriculum, and in any case, it’s more important for students, young ones especially, to earn basic skills in arithmetic and reasoning.  That said, I gripe about the rather ahistorical treatment of math in high school and college.  Math biographies and timelines are not so interesting, but the history and development of the concepts themselves reveals a side of math that students rarely see: its fluidity, its improvisational and searching nature, its fundamental arbitrariness despite its miraculous and unreasonable effectiveness.  

Take geometry, which is in many ways the black sheep of the high school curriculum.  Geometry is typically the first and indeed only subject where a student is exposed to proofs.  Proofs dismay and discourage most students too; they require strategic and formal yet open-ended thinking, unlike algebra, which is mostly about symbolic manipulation and “tricks of the trade.”  One might rightfully ask, “Why should geometry be the home turf of abstract reasoning?”  Its domain of objects -- shapes, pictures -- is less obviously ‘mathematical’ than the domain of algebra -- equations, variables.  But such a question betrays a lack of historical perspective. Geometry predates algebra by an order of magnitude; symbolic manipulation is a far more recent mathematical style than geometrical (i.e. visual) argument is.  In fact, most algebraic ideas are, in one way or another, abstractions/crystallizations of geometrical ideas.  Also, algebra, at least at the high school level, is relatively devoid of theorems, while geometry is all about its theorems.  There is lots to do in algebra, but not all that much to prove.  But the value and legacy of mathematics lies in its magnificent, vast collection of true statements derived from (nearly-)self-evident axioms: its theorems.  Theorems undergird all the practical techniques and applications as well as the aesthetic internal theorizing. But that doesn’t answer the question.  Why learn logical arguments in a pictorial medium?  Or, equivalently, why do the foundations of mathematical reasoning go back to Euclid, a geometer (rather than, say, Diophantus or al-Khwarizmi, the OG algebraists)?  

My own answer hints at the hidden, fluid nature of math I brought up earlier.  The supreme power, the miracle of math, is to lift situations and patterns from the real world into the transcendent abstract realm where mathematical technology can perform its work.  True equality does not exist in the physical world, but an equation can capture and generalize the notion of a balanced scale, or two things of the same type, or a fair transaction.  Likewise, circles and triangles are fictions of the mind, austere and perfect yet rigid models we try to squeeze real shapes into.  Real shapes, i.e. any visual thing at all, are infinite and totally ubiquitous, even more ubiquitous than the phenomena captured by equations/algebra, which makes them the ideal starting ground for this mathematical procedure of abstraction and generalization that unlocks the potential of reasoning.  The genius of Euclid and other Ancient Greek geometers was not just the treasure chest of theorems and propositions they proved, but the messy, playful compromising between real and abstract that enabled those theorems to 1) exist, 2) cohere, and 3) link together in an astounding beautiful and smooth way.  It’s almost impossible to imagine, but there was a time before such a concept as “square” existed, and obviously yet amazingly, some human mind had to be the first to come up with that concept.  But it’s not like once one person thought of “square,” it was immediately understood by everyone else.  This is the battle frontier of math!  A word must be chosen.  What does that word refer to?  Is a “square” merely a four-sided figure?  Does it need more structure?  Equal sides, equal angles?  (Sides and angles are already abstract terms, relatively easy to intuit but not so easy to pin down with enough precision for mathematics.)  If something is like a square but does not have equal sides, does that need a new word?  Where does that conceptual bubble begin and end?  (Think of rectangles and rhombi, distinct yet overlapping and both under the umbrella of parallelograms.)  There is simply no way there was instant consensus.  Early mathematicians must have wrung out these ideas and fought endlessly, internally and externally, consciously and subconsciously.  And it’s not like this is some effete, silly, cushy-armchair philosophical game; the stakes are staggeringly high, for mathematics cannot recover from even a single successful attack; it is both the strongest and most delicate human creation.

Once the dust settles and a concept takes form in a rigorous and complete way, the usual mathematical muscles can get involved.  Cold, logical reasoning stacks statement upon statement, never worrying about foundations.  Despite the existence of innumerable beautiful and powerful theorems and techniques, this mode of mathematics impresses me less.  I am instead in love with the mathematician whose reach initially extends beyond his grasp, who wrestles with dirty and mysterious half-formed ideas until he can confidently display an austere, coherent conceptual gem that plays nice with others.  The domestication of the beasts of the mind.

The histories of mathematical ideas are not taught in school, so students don’t get a sense of that process.  We enjoy peace earned through the battles of the past.  But as concepts stack up, often precariously in the adolescent mind, so grows the implicit weight of abstraction.  Teenagers, laden with thousands of years of sophisticated scholarship boiled down into extremely efficient mathematical/linguistic machinery, inevitably hit some point where a new idea simply does not fit into their model.  The notion of, say, graphing a quadratic equation is both 1) needlessly complicated and 2) seemingly arbitrary.  

“Why do we care what it looks like?” 

“Why should the solutions, which sometimes you call ‘roots’ and sometimes ‘zeroes’ and sometimes ‘factors,’ have anything to do with crossing the x-axis?!”  

“Why do these so-called parabolas only smile and frown but never tilt to the side?”  

Most teachers dismiss these questions because they cannot answer them satisfactorily.  

“You’ll get used to it.” 

“It’s not about the math per se; it just makes you smarter.”

“You’ll need this next year.”

The subtle tragedy in all this is that the students are right: it is totally arbitrary, at least at the most foundational level.  Math is not real.  It could have been something else.  But, the greatest minds of the past fought hard, not for the flawless definitions, but for the best compromises.  The most comfortable perches on the tightrope between abstract generality and practical specificity.  The concepts were designed to solve problems, as much as homeworks would have one believe that problems are designed to explain concepts.  To chime in on an admittedly inconsequential debate, mathematics is certainly invented and not discovered.  Being right on this question brings me no joy, but I would like to see this truth acknowledged by the education system.  It can be acknowledged gingerly at first: take 25 minutes in a geometry class to dissolve Euclid’s fifth (parallel) postulate and peel back the curtain to non-Euclidean geometry.  Show 7th graders what kind of nonsense you can come up with if addition is no longer commutative.  Convince a college freshman that the additive identity (0) and the multiplicative identity (1) cannot be the same number.  An informal discussion of paradoxical statements like “this statement is false” could open the door to Gödel’s mind-bending work.  A similar project could be undertaken to demystify computation, which to most people might as well be sacred yet unapproachable magic we cannot live without.  Music theory is often viewed as a frustrating game of puzzles devised by nerds in lieu of making real music, but one could instead view music theory, and indeed music itself in many instances, as a solution to puzzles that arise naturally.  Tonality is a compromise between tuning, modality, and symmetry.  Why should parallel fifths and octaves be forbidden in counterpoint? (What “proof by contradiction” can you come up with if they are allowed?)  Chord-scale jazz thinking is a somewhat-fast algorithm for finding the right notes -- what are its weaknesses that offset its speed, and why?  When is it worth it?  (To be fair, I think music theory actually does a better job, on average, of presenting itself as a series of historical developments compared to math.)  

I bet that acknowledging this intuitive, historical, imperfection-embracing mindset wouldn’t just tantalize the especially curious students but also bridge the gap to abstract/theoretical/technical topics for struggling students.  Pull back the veil, demystify, show the cracks in the armor -- if for no other reason than to make math (or whatever subject) less intimidating.  Wouldn’t it be empowering if a teacher acknowledged a student’s complaints about mathematics as valid, but then worked with her to see why things are the way they are?  The answer would not merely be “by decree.”  On a related note, Common Core math has lots of issues, especially at the elementary level, where students need to build up fluency in math through repetition and memorization.  CC’s goal of making math more intellectual and less mechanical is misguided for young kids, but by the late middle school/early high school level, forays into history a la the examples I mentioned above would accomplish these goals better than the silly renamings and fragmentations of ideas that currently comprise CC.  If nothing else, give kids a little buzz of excitement now and then by telling some of the rare tales of math being exciting.  Archimedes running nude through the street shouting “Eureka!” upon discovering his principle of water displacement; Turing cracking the Enigma code; Eratosthenes calculating the circumference of the entire freaking Earth using nothing but wells and shadows.  My own middle school math teacher spun some great tales and we as a class were transfixed.  It is far more engrossing to work hard on problems when you feel you are tapping into some great ancient legacy, gliding along the swift river of ideas and accomplishment.  That’s part of the joy of music transcription or even just reading sheet music, or playing chess, or celebrating an old holiday.  Zoom out and appreciate the magnificent edifices upon which we stand!

~ ~ ~

Long Coda: the Example of Continuity

To put my money where my mouth is, I’ll do my best to build the formal notion of continuity from the ground up. It’s one of my favorite examples of mathematicians pinning down a slippery concept precisely without sacrificing flexibility. Also, many teachers never define continuity satisfactorily because the somewhat vague intuitive notion of its meaning is sufficient for most purposes, even through calculus. If anything, students are merely given examples of non-continuity and expected to intuit the definition from there, as if swimming were the act of not drowning. But it is rewarding to wrestle directly with an evasive concept that seems so obvious at first! Without further ado:

“Continuous” in everyday speech means something like “smooth; unbroken; happening always.” In a mathematical setting, this notion naturally applies to the idea of a smooth, unbroken curve in the plane or in space, but also the idea of a shape or quantity smoothly morphing over time. Think of a candle melting, a tree growing, or water swirling around in a cup. This is already tricky for a mathematically conservative and uncreative mind: firstly, how does one reconcile the paradox of a smooth curve made of individual infinitesimal breadthless points? and secondly, how would one extend that notion to 2-, 3-, or N-dimensional, potentially physical objects like candles, trees, or water?

To the uninitiated, the answer is complicated, baffling, likely meaningless:

Let f : [a,b] → R and x₀ ∈ [a,b]. f is continuous at x₀ if for

every ε > 0 there exists δ > 0 such that | x − x₀ | < δ implies | f(x) − f(x₀) | < ε.

Not helpful. Let’s step back, way back, and find the path there ourselves.

First things first -- let’s focus on the idea of a smooth curve with no gaps. A curve that can be drawn without lifting your pencil. An unbroken string of pearls. Recall that most often, plane curves are generated from equations relating X and Y, as in the X- and Y-axes of the coordinate plane. More specifically, one typically considers functions relating X to Y. A function is a rule (an equation) that allows one to plug in an X-coordinate and generate a Y-coordinate so that a point on the plane, having an X-coordinate and a Y-coordinate, represents, potentially, a solution to an equation. The simplest possible example is the function Y = X, which tells us to draw a line through all the points where the Y- and X-coordinates are the same. An infinite diagonal line from Southwest to Northeast. Y = 2X + 3 is a slightly steeper and higher line including points such as (0, 3), (10, 23), and (-1.5, 0), as well as everything in between and beyond. More exotic functions generate curves rather than straight lines, but the principle remains the same: plug in X, return Y, plot the pair. Already we can see the roots of continuity: we are assuming X and Y are real numbers, which is to say we are allowed to plug in any value from the continuum of all possible values. Not just whole numbers, but fractions and irrational numbers too. An infinitely fine grain, the smoothest sand on the beach of the mind. The fact that there exists so many damn numbers, an infinitude between even the smallest gaps, gives us a clue as to how we might capture the notion of drawing a curve without lifting the pencil. Maybe there’s a way to do it “one point at a time” but leverage the infinitude of points into a suitable definition for curves, which is to say functions.

However, the problem with that approach is obvious. A single point “knows nothing” of the curve it’s on; it doesn't “know its neighbors.” A point is very slim on data: just two individual numbers, bundled together. Darn. But we do like how “zoomed in” a single point is; a continuous curve should be unbroken even at atomic scales and beyond (it would be a shame to discover gaps between the pixels). Can we have our cake and eat it too -- compromise between the global shapeliness of a curve and the local specificity and numerical properties of an individual point? Herein lies our first big strategic move: we will take the indirect approach of calling a function continuous at a point rather than over its whole domain. An approach that seems backwards at first, but the convenient fact is that if we do this successfully, we can call a whole function continuous if we know it is continuous at every point individually. In other words, we employ the smoothness of the numbers themselves to do work for us. We, as mathematicians, can zoom in to a specific location and analyze behavior there rather than having to juggle a whole snake of points all at once.

But we aren’t there yet. How do we imbue a point, a naïve and minimal chunk of data, with more structure and awareness of its surroundings? The key is to zoom out from the point, in the slightest way possible, to a “neighborhood” around the point. One can imagine a little blob surrounding a point on the plane. But we must be more precise, and we must appeal to the curve itself, not merely the space on the plane. We also must be extremely careful not to zoom out too much, for even a tiny segment of a curve is as infinite and unwieldy as the whole thing. Hence the foundational innovation undergirding limits, continuity, calculus, and the whole subject of mathematical analysis: ε. This measly Greek letter (epsilon) represents an arbitrarily small yet finite value. Think of the game you can play with any child:

“What’s the smallest positive number?”

“1.”

“What about ½?”

“Oh...well then what about ½ of ½?”

“Now you’re getting it.”

The notion of ε scales to whatever resolution of tininess we need at the present moment. Let’s see it in action.

To draw a curve without lifting the pencil, each point on the curve must be close enough to its neighbors that no pencil-lift is necessary to get there. On the pencil-scale, a distance of, say, .01 millimeters will surely do: that is, if there are no gulfs in the theoretical curve longer than .01 mm, we will be safe dragging our pencil across any smaller gaps. In this case, ε stands in for .01 mm. On the extra-thick Sharpie scale, a full millimeter might be sufficient for ε. On the electron microscope scale, ε would be on the order of nanometers. The magic is in the flexibility of the idea of ε. Let’s break it down further and get specific. Call whatever point we’re zoomed into, on whatever curve, p. p has an X-coordinate and a Y-coordinate determined by its X-coordinate. Call its X-coordinate x₀ and thus its Y-coordinate f(x₀). (Formally, “f of x-zero;” i.e. the result of applying the function f to the number x₀.) We want to encode the idea of minuscule intervals around p in both the X- and Y-directions. Mathematically, all points on the curve a distance less than ε away, where ε can be any small positive (greater than 0) number. In order to disambiguate the X- and Y-directions, we introduce δ (delta) as another arbitrarily small positive value, to be used shortly. We are ready to put it all together.

We can now make precise the notion of sliding an infinitesimal amount along our curve, starting from the point p with coordinates (x₀, f(x₀)). The neighborhood around x0 consists of all x-values less than δ away, which is calculated through subtraction. Mathematically, all values of x such that | x − x₀ | < δ. (The absolute value just turns all distances positive in order to defend against the semi-nonsensical notion of negative distance.) Likewise, the neighborhood around f(x₀) (now we are oriented on the vertical Y-axis) is all those values of f(x) such that | f(x) − f(x₀) | < ε. δ and ε can be freely specified at any point; we imagine in the meantime numbers like .000001. To finally define a continuous function (and thereby a continuous curve), we play a game. Imagine your adversary encloses point p within a small vertical box of size ε, and challenges you as follows:

“Your curve must not change more than ε. If you slide left or right along the curve and the y-value jumps more than ε, the curve is discontinuous and I win.”

Let’s imagine the two scenarios. If the function f is indeed continuous as we imagine it, that is smooth and unbroken, we should be fine. Imagine p is attached to a smooth line on both sides, and say ε is .001. Zoom in super-close to p and mark a ceiling and floor .001 above and below it. The smoothness of f implies that the ceiling and floor will cut off a box such that a minuscule segment of f with lies totally within. Call the width of the box δ. Here is a picture:

The adversary is defeated for now. He is free to shrink ε even further, but we can counter with a smaller δ that does the job. We believe in the smoothness of the real numbers to win this battle for us. Because ε can shrink to any microscopic scale at all and we can still find such a δ that encloses our smooth curve, we confidently declare that f is continuous at x₀.

How do we know this definition is working? We check the other scenario, where f has some gap or jump, and hope that the adversary wins the game. So pick p somewhere where f jumps; let’s say that to the right, it is attached to a smooth curve, but has a gap on the left:

The adversary sets a small ε and challenges us to ensure that f changes less than ε vertically within a horizontal interval of δ. On the right side, we are OK. Tiny rightward nudges produce only tiny upward nudges, so our quest for δ begins swimmingly. However, on the left side, we run into a major problem. Even the smallest leftward nudge pops us downward far more than ε. We cannot find a small yet positive δ that closes the box; we fail! f is discontinuous at x₀. Exactly as planned -- the definition “feels right.”

Note that we would have won our continuity-testing game anywhere else on f, even in the second scenario. It thus makes sense to say that f would be continuous on intervals that do not include that pathological point p. Remember, f being continuous as a whole curve/function amounts to all its individual points having the continuity property individually.

All that is left to do is summarize the procedure of this game in mathematical notation. One step at a time:

Let f : [a,b] → R and x₀ ∈ [a,b].

All this is saying is that our function, our curve, is defined as mapping x-values on an interval of the real numbers ([a,b] means every number from a to b) to a real-numerical output. It’s a fancy way of placing us on the X-Y plane. Our special point has to have its X-coordinate, x₀, in the domain of f. Read ∈ as “belongs to.”

f is continuous at x₀ if:

for every ε > 0 there exists δ > 0 such that | x − x₀ | < δ implies | f(x) − f(x₀) | < ε.

Now the meat. “For every ε > 0” means that the adversary is free to challenge us with an arbitrary small positive number to box us in. Our job is to find, i.e. show that “there exists δ > 0 such that” the horizontal neighborhood around x₀, i.e. the x-values fulfilling | x − x₀ | < δ, don’t pop us out of the vertical neighborhood, i.e. the y-values fulfilling | f(x) − f(x₀) | < ε.

In summary: the adversary assigns ε, and if we can always counter with a δ that keeps f comfortably in the adversarial box, we establish continuity at that point.

Deep breath. We have successfully defined an intuitively clear but mathematically slippery notion: continuity of a curve (represented by a function). The point here was to show that these definitions don’t just appear from nowhere; they are earned through head-scratching, compromise, and creative workarounds to paradoxes and imprecisions in intuition. While the definition may at first seem needlessly technical, abstract, or indirect, it turns out to be instead an ingenious balance of specificity and flexibility. We, counterintuitively, zoom into single points to define a global property of a curve; we play a recursive game with simple individual steps involving finite, definite numerical values that generalizes to infinitesimal scales so that we are satisfied without having to appeal to the paradox of zero-length nudges or zero-area boxes. Better yet, this definition is totally agnostic to the properties of f: it tells us whether points or intervals are continuous or not no matter how wild our curve gets. It also easily generalizes to higher dimensions with a rather minimal amount of mathematical massaging. In fact, it generalizes to domains beyond numbers in the case of general topology. An even more abstract definition, presented without comment or explanation:

Let (X, TX ) and (Y, TY) be topological spaces. A function f : X → Y is said to be

continuous if the inverse image of every open subset of Y is open in X.

(The real puzzle here is the meaning of open.)

I would have loved to grapple with this stuff in high school. Sure, it’s difficult. Merely presenting the definition and expecting a student to understand it would have been an obviously stupid idea. But with an hour of mental wrestling, led by a teacher, working through examples and trying out some hypotheses, this becomes a rewarding exercise that reveals the glorious, dirty, living, breathing, miraculous nuts and bolts of mathematics, the hard-earned truths that unlock our simple computational methods. Not exactly “light afternoon reading,” but instead of the ten-thousandth arcane, soulless symbolic manipulation of the sort that pervades high school math? Yes please!

If you read this far, good for you and please accept my gratitude.  I hope you don’t feel I wasted your time.  Some music recommendations to make up for it:

• An arrestingly beautiful Horowitz performance of Bach

• RIP Sophie.

• Willie Nelson’s version of Stardust - wow!

Be well and keep it real.

Where Two Streams Cross

November 2020: It’s impossible to be anything but dismayed at the overall state of things.  Approximately zero progress has been made on the pandemic; the institutions that should have protected, informed, and healed us have totally failed, and miserably so.  The “election” was (and still is) an utter embarrassment.  The two groups of people I regularly work with, kids and musicians, are both suffering as greatly as ever; the initial shock of the collapse has been replaced with a gurgling sense of dread accompanied by the withering-away of invaluable time.

~ ~ ~

The first two gods of jazz tenor saxophone are Coleman Hawkins and Lester Young.  Any jazz fan knows this and most are familiar with the narratively convenient dichotomy of their styles: Hawk, the bold, fiery lion; versus Prez, the cool, melancholic hipster.  Seemingly every aspect of each man’s style is at odds with the other’s.  Hawk’s sound is fat and fluffy in the low register, growly and rough in the middle register, and blasting in the relatively rare moments where he goes up high.  Lester, on the other hand, is comfortable to hang in his silky high register, but will descend to his throaty middle register and occasionally to his whispery bottom notes.  Pre-war Lester’s sound is buoyant, while post-war it’s brittle; early Hawk is bulbous and strong, and later he is rough, almost plasticky.  Moreover, Hawk’s sense of harmony is remarkably advanced for a pre-bop improviser: his default harmonic statement is the arpeggio, but he liberally sprinkles in adjacent chromatic tones and chord substitutions, and hiding within his arpeggios is often a smoothly voice-led composite melody, like a tasty inner voice from a pianist or a big band.  Lester’s harmony is less sophisticated; essentially everything he plays is diatonic or the blues, and he is generally unbothered by quickly moving harmony so long as he can find a note or two to milk while the band shifts underneath him.  A dominant chord replaced with a spooky augmented triad is about as fancy as Lester gets.

If you need a refresher on Hawk vs. Prez, listen to the most famous, recognizable solo of each character: Coleman Hawkins playing “Body and Soul” in 1939, and Lester Young playing “Oh Lady Be Good” in 1936.

Like any two diametrically opposed forces, Hawk and Prez define a spectrum, on which one can locate every jazz saxophonist since.  Indeed, there is no worthy player who is not a direct descendant of both giants, in one way or another.  This is of course true for the saxophonists of the generation just after Hawk and Prez, and in particular for two of my personal gods: Sonny Rollins and Warne Marsh, born 1930 and 1927 respectively. At first glance, the ancestry seems clear cut: Rollins, a vocal devotee of Hawkins with a comparably muscular tone; Marsh, perhaps the only tenor player with an ever darker, featherier tone than Prez, who literally played Lester Young transcriptions on stage.  Sonny is Hawk’s next evolution, and Warne is Lester’s, right?  

Not so.

Before I make my case that Sonny is actually closer to Prez and Warne is actually closer to Hawk, I want to explain why I would spend time on these comparisons at all.  The goal is to show a path towards piecing together one’s own personal style.  You nor I will ever do anything truly original, but we can each come up with a unique cocktail of the features of the masters.  Importantly, almost none of these features are incompatible with each other, even if they may seem so at first.  With a creative, open mind, it’s possible to fuse and blend seemingly opposed musical attributes.  You could play like Paul Desmond and Chris Potter at the same time.  You could play like Gene Ammons and Mark Turner simultaneously with a spicy dose of Don Byas.  You could play fast swing like Stan Getz but play ballads like John Coltrane.  And so on.  Though I do not yet have a convincing solution, I strongly believe that the best of my own personal style will emerge as a crossing of Rollins and Marsh, and later on I will outline an exercise I use to deliberately cross their streams.

Up front, I will admit that Sonny Rollins is the far superior artist to Warne Marsh.  Sonny is, by all accounts, a deeply thoughtful, enlightened person, a continuously unsatisfied artist continuously reaching beyond his grasp, despite a vast and diverse career.  Warne became almost instantly complacent due to the deadly combination of exceptional talent and self-destructive habits.  The sad truth is that one could delete Warne Marsh from jazz history and it would be relatively undisturbed, but Sonny Rollins is an obviously foundational figure, the Saxophone Colossus indeed.  

However! for listeners in the know, Warne is a dark and prickly yet delicious fruit and an alluring yet dangerous influence on saxophonists.  And his lackluster career was not a foregone conclusion; Sonny’s illustrious career was not either, especially considering his addiction and imprisonment in his early twenties.  Both men, in fact, blossomed early into promising if not downright artistic saxophonists, and the 1950s shaped each’s career and eventual legacy.

Therefore, it is fair to compare Rollins and Marsh at the crests of their 50s waves, when their talents were freshly honed and surely disarming to a hungry listener or fellow saxophonist.

Conveniently, both Rollins and Marsh recorded “I’ll Remember April” in trio formats, in 1957.

Sonny’s is a live recording from the immortal Blue Note album A Night at “The Village Vanguard” and Warne’s is from his self-titled Atlantic release (the title of the track is merely “Excerpt,” which likely allowed the dodging of licensing fees, made possible because Warne doesn’t play the melody).  Both are masterful 5-star takes; the point is not to rank them but rather to analyze them and in particular trace the Hawk and Prez influences from a generation upstream.  Let’s listen.

* * *

First, consider Sonny.  Listen at least until the trading.  As with any saxophonist, Sonny makes his first impression through his sound.  He blows hard and tongues even harder; even his most open notes fly straight out the end of the bell.  The little bit of grit at the start of the accented notes creates an obvious transient; i.e. the beginning of the note, and therefore its placement with respect to the beat, is crystal clear.  The aggressive tonguing itself comes more from Coleman Hawkins, who could really smack his high notes too, but musically, the pre-head intro is a two-note riff around which the time coalesces — that’s pure Lester Young.  

Semi-side note: the way Sonny plays the melody is an exemplar of what makes him so special to me: every note, every phrase is articulated in a different way.  From smooth legato to chirpy staccato, from beefy straight tone to wiggly vibrato, it’s all in there.  Sonny’s advantage over all other saxophonists ever (except for perhaps Bird) is his gigantic toolbelt of articulation.  His air, tongue, lips, and fingers can play the same “note” in a million different ways and his unsurpassed artistry is picking out the perfect one, every single time.  (Lester had lots of articulations, too, though not quite as vast a palette.  Hawk even less so: I hear his default tonguing style change and develop over his career, but I don’t hear the cornucopia of articulations within a single solo to the same degree as Sonny or Prez.  Vibrato is another story for another missive...)

The solo is more or less what one expects from Sonny Rollins in 1957: incredibly swinging, serious bebop, perfectly nestled in the changes, juxtaposed with levity courtesy of cute melodic commentaries and quotations.  A delightful, unassailable formula.  Where does this performance lie on the Hawk-Prez spectrum?  Neither of the two OGs ever really embraced bebop, so we must retrodict the 1937 analog of Sonny’s use of bop as his main vehicle in 1957.  What “kind” of bebop is Sonny playing?  I’d call it prime, uncontroversial bebop.  Rhythmically, lots and lots of eighth notes plus the classic eight-note triplet arpeggios/turns, and the upbeats are heavily accented.  Melodically, the lines are full of all the lovely twists that push and pull on the beat: inner groupings of both even and odd numbers of eighth notes, expressed through articulation differences and melodic contour.  Harmonically, it’s on the conservative side, relishing the glory of bop that outlines the changes as they are.  The most adventurous side-steps are brief octatonic moments that intensify dominant chords, but Sonny does not leave such moments unresolved.  I’d argue that this style of high bebop is to 1957 what groovy diatonic playing is to 1937; viz. Lester Young.  Yes, the rougher sound indicates Hawk, but the material actually being played strikes me as coming from Lester’s philosophy (if not his style): don’t mess with the changes; don’t be esoteric; don’t forget the sweet melodic moments; let your tonguing imbue the beat with bounce, variation, and energy.  An ultimately rhythmic conception with a side dish of melodic sentimentality.  Another point in the Prez column: what does Sonny do at 1:43, 2:29, and 3:52?  Riffs, baby!  Sonny doesn’t chill on the riffs for as long as Prez would have, but that device is as Youngian as it gets.  Simple, repetitive riffs deepen the groove and charge up energy to be released in subsequent bursts of melody.  That was never Hawk’s style; he was always overflowing with energy and wasted no time deploying his serpentine lines straight into the foreground.

In short, while Sonny’s aggressive tone reminds us of Coleman Hawkins, the contents of his solo, and even more so his overall approach to improvising, place him, in my view, much more on the Lester Young side of the spectrum.

* * *

On to Warne Marsh.  His rendition of “I’ll Remember April” is hardly a rendition at all — it is an incomplete performance, solely a tenor solo over the changes with no reference to the melody, and no beginning nor ending except for the briefest studio fade.  Marsh fans are used to this sort of thing; arrangement and presentation were not skills Marsh or any of the Tristano people possessed.  Perhaps bothersome for the listener who wants a bow on top of his improvisation, but not really a problem for a saxophonist investigating the craft or a collector amassing material.  

In any case, the first impression of this take is strong, despite the non-beginning, because the bass and drums are swinging hard right out of the gate.  If you listen closely, you’ll notice that Warne does not actually begin with the easy-to-hear A—F# descending third; in classic Marsh form, there is an almost-imperceptible blur of a few indistinct notes just before the beat, like a drag on a snare drum made of marshmallows.  The dichotomy of clear(ish) notes and ghostly shadow notes is a hallmark of Warne’s style, in a certain sense a replacement for the drama he loses by basically never tonguing.  It’s not even clear if the second phrase goes straight into the third or if there is a breath between them.  Listen just before the ascending triplet arpeggio at about 0:04 — does the sound stop, or is he continuing to release the slightest drip of air as a gossamer thread between two helical phrases?  The mystery is tantalizing and essential to his turn-on-a-dime style.  This tiny example leads us to consider his articulation more broadly.  In some ways, Warne’s way of playing is simpler than Sonny’s (I think it’s easier to emulate, though also a bad idea to emulate more than just a little bit — more on that another time).  It’s simpler because Warne does not have nearly the arsenal of tonguings that Sonny does, and the way the notes come out is a result of the contour of the line, which is, in general, a spontaneous creation (Sonny, though certainly spontaneous himself, has more vocabulary and often plays things that he’s clearly worked out in advance).  Another way of describing this is that Warne is a “fingers-first” player while Sonny is a “tongue-first” player: Warne’s fingers think the notes and he blows through them as they come out; Sonny articulates complete ideas, complete phrases, and his fingers follow, conforming to the scales/changes/quotes so that the story his tongue tells makes sense.  (Indeed, I’d argue that Coleman Hawkins is more of a fingers player and Lester Young is more of a tongue player.)  My theory of Warne Marsh-style articulation is based on a visual metaphor: a moving surface, perhaps of the ocean, through which notes can either breach or descend.  Notes that are higher in register or blown harder pop out; lower/softer notes stay submerged.  The net effect is like watching a dolphin leap out of and back into the water as it traverses the waves — you watch, in alternation, its majestic body but then just a watery shadow.  A natural follow-up question is “how much of this effect is intentional?” My guess is that it is mostly a byproduct of the lines he plays, which is to say Marsh is not really choosing when to pass through the “surface;” the direction, jaggedness, and momentum of his lines (i.e. the choices of his fingers) push him above and below naturally.  This is in direct contrast with Sonny, who could play the same piece of melodic material with totally different, specifically-chosen articulations, imbuing even the most familiar line with a twist.  To finish on the subject of articulation, I want to argue a somewhat subtle point: although Warne’s notes can come out in wildly different ways in terms of timbre, volume, and emphasis, the technique behind them is rather homogeneous and is subordinate to his melodic, finger-led thinking.  And despite his generally warbly sound that is at odds with the beefiness of Hawk, Warne’s overall approach, the order of operations to getting notes out of the horn, is more aligned with Hawk than with Lester.

With respect to harmony, Warne Marsh is almost inarguably more advanced and adventurous than Sonny Rollins, at least at this point in their careers.  That is not a value judgment, though.  There is certainly a glory to Sonny hitting all the right notes all the time and a satisfaction to reciting bebop vocabulary that Warne never gives.  Nonetheless, Warne’s harmony is surprising, edgy, and utterly progressive for the 1950’s, and therefore a treat for any listener attuned to it.  The whole solo is full of goodies, but listen to the chorus from about 0:54 to 1:45.  He is juggling forbidden fruit the whole time but is nevertheless playing the changes.  You can hear alterations of the basic chords, superimpositions of new chords, and delightful sidesteps into neighboring harmonies that swivel back home in a frankly sexy way.  Without getting into pages of analysis, the fact of the matter is that Sonny did not play like that, and Lester Young even less so.  However, Coleman Hawkins’ playing is full of comparable moments — tasteful flirtations with remote harmonies, gracefully packaged within lines that begin and end inside the changes.  In fact, until Warne, there was not really a saxophonist as harmonically adventurous as Hawk, and there have been few since.  Warne and Hawk are further connected by their reluctance to regurgitate.  Neither player has characteristic licks; they improvise more on a note-to-note basis.  Sonny and Lester, of course, were unafraid of vocabulary.

So, let’s tally up the final scorecard.  Sonny’s burly tone — yes, more Hawk-like; Warne’s feathery, high-register-centric tone — yes, closer to Prez.  But Sonny’s overall style: highly varied, well-curated articulation; conservative diatonic harmony; a mix of linear playing and melodic/riffy playing; and an ultimately rhythmic conception — that’s Lester Young.  By contrast, Warne’s overall style: a finger-first approach with articulations as byproducts of the lines; progressive, adventurous harmony; a constant flow of abstract ideas without appealing to fossilized vocabulary — Coleman Hawkins, through and through.  Perhaps not the initially expected result, but that’s the point — great players take lots of little things from other great players, and superficial influences need not box one into a narrow style.

* * *

Frankly, it doesn’t really matter if Sonny/Warne is more like Hawk or more like Prez.  It is not so hard to argue the opposite of what I said above (though I still think I’m right of course).  My large-scale goal here is to prove that saxophone playing, and indeed any complex craft/artform, is built up from a large amount of small components, many of which are independent of each other.  This is a deep fact because it shows that there can be a truly gigantic number of different styles even without coming up with something “truly original” (the originality, I’d argue, would come from the choice of how to combine these components).  It also indicates how one might improve their playing.  In my opinion, there is not really such a thing as “general improvement.”  Rather, one can crank up individual skills a little at a time through exercise, then make an artistic judgment about how to compile them into a musical personality.  Transcription is great, probably indispensable, but you must break apart what you transcribe into its pieces: pitch content, articulation, time feel, pacing, tone, etc.  Otherwise you’re missing the full benefit and you’re doomed to merely amassing vocabulary.  Not to mention it takes a little pressure off if you transcribe a solo for a purpose, say, to feel how Freddie Hubbard places his notes relative to the beat. In that case, it’s fine if you miss some notes or leave out the double time!  Moreover, this way of thinking, factoring great players/solos/records into their components, can alleviate some of the anxiety of falling in love with seemingly incompatible styles.  From the perspective of a young saxophonist in 1940, Lester and Hawk must have seemed incompatible, but every great saxophonist since has taken from both! A generation or two later, one might have felt that one had to choose between, say, Zoot Sims and Joe Henderson; nowadays, Chris Potter and Mark Turner, but no.  There is no single choice to be made — follow the heart and cherrypick.  It goes deeper: if you play jazz but you love to listen to Sting or Tchaikovsky or Umm Kulthum, figure out what small piece of those outside influences you can appropriate and coherently integrate into your jazz playing.  Go beneath the surface.  Don’t just copy — analyze, abstract, experiment.  So much more is possible than any of us realize.  

* * *

Coda: I love the two “I’ll Remember April” cuts because the changes and the trio format act as a kind of scientific “control” relative to which one can experiment.  A fun exercise is to play along.  There are four basic ways to do this: play like Sonny with Sonny; play like Warne with Warne; play like Sonny with Warne; play like Warne with Sonny.  And when I say “play like,” I mean “take some element of that player’s style and try to incorporate it;” the point is not to be a carbon copy.  Articulation, time feel, harmonic approach: all good individual options.  I usually start by playing like Sonny along with Sonny — the intro and melody make a good on-ramp and the solo is nice and long so you can take little breaks to listen then dive back in if need be.  Once you get cooking and you feel your Sonny Rollins impression is at least passable, switch over immediately to the Warne recording and play along with him.  As best as you can, keep the Sonny approach going, but keep your ears open to Warne at the same time.  How do the eighth notes fit together?  Can you compromise on the fly, find some novel mixture?  What usually happens to me is Warne takes over my ears after a couple minutes and I start playing more and more like him.  You could do another round of Warne-style over Warne, then switch to Sonny, and play like Warne over Sonny.  And so on and so forth; it’s like alternately dunking in hot and cold baths.  After five or six rounds (~20 minutes), I like to just play on my own, maybe with a metronome, and see what comes out.  You’ll surprise yourself!  Sometimes this particular combo comes out sounding kind of like Chris Cheek; sometimes it’s more like Joe Lovano; sometimes something totally weird.  Most of all, it’s really fun and also challenging — the best kind of practice.

One can easily play this sort of game with Sonny and Trane using “Tenor Madness,” or with Stitt/Ammons, or with Miles/Cannonball/Coltrane.  A slightly different game: play a single tune for a long time and try to “time travel.”  Pick something easy — I like to start by playing Lester’s “Lady Be Good” solo verbatim — and try to move through the styles of various players as continuously as possible.  I say continuously because the liminal spaces between styles is where you’ll discover the most exciting stuff.  Start with Lester, then try to play some Hawk, then maybe jump to Bird, take a detour to Lee Konitz or Hank Mobley, then Sonny, or maybe go straight for Coltrane, then Joe Henderson, then Dewey Redman, then maybe tread back to Ornette, then Albert Ayler… Over the course of ten minutes, you’ll get a physical and mental workout, and also probably play things you’ve never played before.  

~ ~ ~

Bonus recommendations:

A Fire Across the Deep by Vernor Vinge: sci-fi novel that I have dragged my feet on but enjoyed nonetheless.  The greatest strength is the world building and believable dialogue.  Some of the political machinations of characters are pretty boring, and the plot doesn’t really begin until page 150 (also really slows down around p. 300), but it’s been a good read before bed and on the train.

Into the Breach by Subset Games (known for FTL: Faster Than Light): really excellent turn-based strategy game, less stressful than FTL but more to my taste.  Chess-like in several ways but with tons of variation due to the various squads you can play as.  Relatively small number of enemy types and missions but they mix in interesting ways and a two-hour playthrough can go by in the blink of an eye.

Duke Ellington: duh.  Just particularly in the mood these days.  I mean come on man.

Neil Luck, British composer: a brilliant madman I recently discovered.  Thinks bigger than just the music, really fun and zany without coming across as gimmicky.  This video got me hooked.  Read some of his writing on a blog too and enjoyed that.

Late Flowerings

I recall reading the following statement from the Wikipedia article of Richard Strauss: “Along with Gustav Mahler, [Strauss] represents the late flowering of German Romanticism after Wagner.”

Fair enough - a good way of putting it. Indeed, I love listening to Strauss for the same reasons I love listening to other German Romantic masters, but on top of those reasons, there’s a bonus to Strauss: a sort of “new-and improved,” boiled-down efficiency afforded to him by his lateness relative to the Beethoven-Wagner arc. Listening to Beethoven entails some listening to Mozart; that is to say, if you’re in the mood for some penetrating romanticism, Beethoven serves it as a sauce on top of a Classical base. Listening to Wagner entails wading through literal hours of sludgy voice leading and heavy-handed leitmotific “development” (insofar as repetition is development). Strauss cuts to the chase, and to put on Salome or Ein Alpensinfonie is to put on a compact, juicy dose of romantic modernism — all the bells and whistles one loves without much fat. The “late flowering” Strauss represents marks a great moment in that particular musical tradition, where Strauss, looking back on the past, picks and chooses his favorite techniques of the old masters and dresses them up, repackages them for an audience who doesn’t want to sift. A “Wagner’s Greatest Hits” album, if you will.

While German Romanticism has come and gone, other traditions are coming ‘round that bend, where the accumulation of early masterpieces affords the creation of refined, retrospective masterpieces. My gut tells me that jazz is not quite there; instead, jazz may be in awkward period after the initial thrust but before the seeds of late flowers blossom. I therefore predict excellent albums resurrecting the best ancestors of jazz a few years from now. Perhaps important centennials (Bird’s being less than a month away at the time of writing) will set the stage, make the time feel right. Right now, my generally low opinion of contemporary jazz comes from the mixed messages sent about the past. Some jazz musicians throw out the baby with the bathwater; they reject past idioms (swing, tonal harmony, blues) without innovating to fill in the gulfs left by removing the DNA of jazz. We can all conjure memories of limp, tepid straight-8ths modal jazz featuring arbitrary forms, unmemorable melodies, and gratuitous cookie-cutter solos. Reject the past, subvert it, fine. But you better put something in its place. On the other hand, puritanical jazz musicians lament the de-emphasis of swing, harmony, and blues a la Ellington, Parker, Monk, etc., but all too often, the music of these contemporary jazz Luddites merely imitates and dilutes the masters they revere. Did you really need to record Inner Urge in 2016 and quote Joe Henderson’s solo to prove that you’re a “student of the music?” Has anyone ever said, “wow, this Charlie Parker cover is so much better than the original!” No. Figure out where you stand, jazz boys, and whatever you do, do it right. There are many pairs of ears that would be receptive to either a) truly innovative, probing music descended from jazz, or b) truly loving, detail-oriented treatments of the great moments of the past, i.e. late flowerings. For what it’s worth, examples of the former do exist, though few and far between. I just heard some of Jacob Garchik’s new big band album Clear Line, which is innovative and subversive: a big band album with no rhythm section (yes, that means no dumb tinkly piano intros, no over-the-top drum fills, no ironically un-interactive solos). Dana Saul’s Ceiling is stunning start-to-finish: real composition, real playing, stylistically unfettered by jazz “best practices.” Innovative, beautiful, and polished. But, I have not yet heard what I would call a late flowering of jazz (or bebop, swing, or whatever, if you want to get specific). I wait eagerly for jazz’s answer to Death and Transfiguration.

The reason the phrase “late flowering” came to mind in the first place actually has nothing to do with music. I think we are currently in a period fertile for late flowerings in video games, despite how quickly the history of video games moves. A decade is an aeon in games, and accordingly, one can look on the watershed games of the 90’s as artifacts of an ancient Golden Age. My most recently completed game, Ghost of Tsushima, has essentially zero innovation on any fundamental level. Yet, it is great. It is a late flowering of the broad “adventure game” formula, essentially a grown-up Zelda game. Late flowerings are especially valuable in games because the main agent of poor aging in games is frustrating carry-overs from the arcade era plus technological limitation. We don’t need finite lives anymore, and 16 colors just doesn’t seem like enough these days. But there is more to what makes Ghost of Tsushima great, for it is not just a piling-on of big, new features. Skyrim pushed the open-world concept to its 2011 limits, and it is surely great and important, but the fact of the matter is that much of The Elder Scrolls is repetitive, artificially bloated, unrefined, and ultimately boring. One wades through Skyrim the way one wades through a Wagner opera: the great moments are enough to keep one sucked in, despite some of the slog. Ghost of Tsushima’s brilliance is a result of its advantage of being able to look back on those old games trim the fat. The world is not overwhelmingly huge, but there are not many empty regions — the nature itself, the wind blowing through the pampas grass and the sun glinting off a decapitated Mongol’s helmet, is beautiful and obviously lovingly crafted. There is not an infinite number of quests, but most quests in the game have some novel story or gameplay element, so the game circumvents the creepy feeling of RPG deja vu. The collectibles only come in a few types, and there’s none of the bullshit of inventory management or encumberment; there’s no frustratingly arcane crafting system. One gets the sense playing the game that the developers respect the player - a fantastic and all-too-rare feeling.

Persona 5 is another perfect example: perhaps the greatest big JRPG of all time if one factors out nostalgia. Hundreds of JRPGs have come along since the first Final Fantasy and Dragon Quest, each with its own blend of successful and unsuccessful experiments in gameplay and presentation. FFVII had an engaging story and a generally cool world, but it really dragged during the corridors of random battles. Paper Mario has a timeless and lovely style, but the gameplay is almost trivial. Earthbound is genuinely funny, with excellent style and music, but the graphics don’t exactly hold up today, nor does the relatively uninspired turn-based combat. By contrast, Persona 5 has it all. The art and music is on point, the writing is surprisingly good, even in translation, and the interface generally is smooth, intuitive, and engaging. There’s a healthy dose of the kinds of complex systems some of us love in RPGs (in this case, the creation of new personas, the social links, the “one more” chain attacks), but the systems never get too arbitrary or opaque, nor are they strictly required to play the game. There’s essentially no grinding or throwaway characters, no complicated yet forgettable lore. In other words, Persona 5 is the late flowering of the JRPG because it distills the genre’s strengths and ameliorates or solves its weaknesses.

The Witness is a late flowering of the first-person puzzle game a la Myst. Hollow Knight is the late flowering of the Metroidvania. Hyper Light Drifter is the late flowering of 2D Zelda. None of these games are masterpieces because of innovation; they are masterpieces because of refinement and good judgement.

I wish late flowerings would pop up more in music, as they have in games. At the same time, games, the primary artistic frontier of the early 21st century, tend to lean into nostalgia too much since the artform progresses so quickly: good for these late flowerings but perhaps at the expense of true innovation. I am not sufficiently expert enough in other fields to judge the innovation versus late flowering balance, but it certainly is fascinating to consider. What will be the last great novel? Has it already been written? Could a genius chef innovate say, Italian food, which is so recognizable and beloved for its basics? What is the most innovative garden in the world? Have there been late flowerings of earlier styles of blacksmithing?

Sadly, progress is slow due to the seemingly unending low flame of misery known as COVID-19. Fingers crossed that energy is being stored rather than diffused, so that whenever the floodgates open, there’s a real flood of creativity waiting to burst, not just a dribble.

The futures of jazz and creative music

Still at home. Still lucky enough that COVID-19 hasn’t attacked anyone in my immediate circle, but the recent deaths of two heroes, John Conway and Lee Konitz, make the virus feel like the Grim Reaper. It’s not clear that those two giants were going to make career leaps had the virus not swept them away, so the loss is perhaps not as tragic as the untimely deaths of younger, undiscovered geniuses. The pandemic has compressed the continuous drip of death into a nasty spike, further cementing the fact that we are entering a new era. A big question is, “will Lee Konitz’ career die with Lee Konitz?” which is a way of asking what the future of live and recorded jazz will be once the short-term crisis is ameliorated. For ~70 years, despite many signs of progress, the world has been more stagnant than perhaps was expected. Computer technology is the outlier; if you took away all the screens, how would you know it wasn’t the 1970’s? Or, where are the revolutions in medicine, ecology, psychology, transportation, energy, etc. that should have accompanied the computer revolution? And, even if it is a bit sad to say, jazz has not really gotten better since the death of John Coltrane in 1967. Few titans remain from before then, and the “middle generation” that came of age afterwards has survived on 1) institutional backing and 2) the diminishing possibility of surviving as a gigging jazz musician. Will it really be possible for someone my age to forge a career as a jazz musician the way, say, Sonny Rollins or Dave Liebman did, playing club dates, touring, and/or teaching at jazz colleges? Record deals are ridiculously scarce and maybe not so helpful in the first place; for the time being, there are zero live gigs to be played, and even before COVID, the pickings were rather slim. MSM and Berklee only have so many job openings, and to be honest, I get the sense that jazz colleges aren’t fooling kids into paying exorbitant sums as they used to… probably for the best; the emphasis on college, especially for artists, will likely decline in the coming years.

So what are these brilliant young musicians supposed to do? Many are in debt without skills that pay the bills during a pandemic. I would like to hope that people who are stuck at home are picking up new instruments and that my friends can teach them, but that seems unlikely to be a robust survival plan. Live-streamed concerts fail to capture some essential Dionysian magic, for jazz especially. Home recording is an option for some but certainly not all, and even so, then what? Bandcamp/SoundCloud release to a few dozen people? I am asking all these questions without having answers. I have predicted to friends that the next frontier in creative (American) music will be computational, at the intersection of videogames and music as we know it now. Just as American jazz picked up the torch of enjoyable yet creative/progressive tonal music from European Romanticism in the early 20th century, composers, programmers, and designers will probably take the torch from jazz as we go deeper into the 21st. Common practice European classical music became institutional museum music; it only survives as such, and its direct descendants in the classical academic world are thriving in certain sense, but at the expense of scale and accessibility. It is not hard to find the corresponding story for jazz. The “deal with the devil” that jazz made with educational institutions safeguarded it from totally languishing into obscurity, but probably also sealed its fate as eventual museum music from the 20th century. Wynton Marsalis leads this project, and though many of my peers disapprove of his work, I actually think it’s for the best, and probably necessary for the survival of jazz. My approval of this project is partly rooted in my prediction that the up-and-coming punk geniuses of music will gravitate towards aforementioned computational formats the same way that those kinds of kids gravitated towards jazz improvisation in the last handful of decades. Wynton pushes to exalt jazz because as a historical phenomenon, it has yet to fully enjoy the respect it deserves. Part of his claim is that the major arc of jazz is complete; the Bach-Mozart-Beethoven-Wagner legacy may have its jazz answer in Armstrong-Parker-Coltrane-Marsalis. Indeed, there exist significant musicians in their respective styles after both of those arcs, but the trajectories are inward rather than outward. One can argue that Wagner set in motion the impending doom of tonality and enabled the impulses towards abstraction, esotericism, and ultra-specialization, Babbitt being the ultimate flowering of that impulse. The story in jazz is of course different but comparable. The early progressive albums of Marsalis, like Black Codes, feel like mature saturations of the ideas of the mid 1960’s, suggesting that other jazz artists should find other paths, outside that dominant central culture. Herbie and Wayne had done a good job of changing with the times while others basically kept to their old scripts and rode the waves of their earlier careers. (Joe Henderson showed some reflections of the 1970s, for example, but really he was playing 60’s jazz until he died. Keith Jarrett and Paul Bley survived by putting piano improvisational genius on display without deviating too far from standard practice; Barry Harris, Kenny Barron, and others were even more conservative but the same idea applies.) Despite the successful ventures of The Bad Plus, Eric Lewis, Kurt Rosenwinkel, Logan Richardson, and other jazz artists who drew on rock and popular music from after the 1950s, it may (unfortunately, to some) be the case that jazz improvisation, at least the theoretical descendant of bebop, is best suited to the song structures of the era it came from. In other words, the arc of post-bebop is finite, and was doomed to wither in the 1970’s and beyond, not to be resuscitated by rock, hip hop, or whatever. Cuban and Brazilian musics were, then, lucky pairings. But that is not to say jazz improvisation is done forever — one can still play in the old styles, and who knows? perhaps Middle Eastern music or some other musical culture will provide new soil for jazz to till. The point is that it’s likely time for jazz to crystallize its history and start transitioning away from a punk artform toward an exalted, institutionally supported one.

I think you get the picture if you know a little classical music history and a little jazz history. Getting back to the social/economic point, I wonder if there will be a “fork” among my friends and peers: will some stick to traditions, cling to jazz and hopefully survive off of gigs and maybe some institutional backing down the road, while others move towards other formats of musicmaking that are less traditional but more cutting-edge or at least more connected to modern technology? If this split happens, both positions will be tough. The competition for traditional jazz gigs, tours, and teaching positions will surely be fierce and defeating. On the other hand, if progressive music moves towards computation, games, VR, or whatever, those of us who spent years on instrumental technique and historical listening may feel that our skills are not relevant enough, that we “missed the boat.” There will be successes and failures on both sides. We can only hope that the peaks are very high and that the valleys are not too low.

COVID-19 and Bartok

At the time of writing, late March 2020, the world is in an unignorable state. The novel coronavirus COVID-19 has reached the level of pandemic: thousands have died and probably hundreds of thousands are sick, and those numbers will exponentially increase in the near future. New York City is in pseudo-lockdown; we are encouraged to practice “social distancing” and the vast majority are either working from home or not working at all.

A major discontinuity in global society reminds us of the paradox of the size of the world. On one hand, the world feels small right now: a single virus has taken control of almost every corner of the globe and it is thus easier than ever before to empathize across vast social and geographical distances. The nature of exponential growth is such that no number is too large to conquer: unfettered, the spread of such a virus across all of humanity is just a matter of time, and not that much time, either. On the other hand, the world is still huge: efforts to “flatten the curve” will likely mean that despite the infectiousness of this virus, something like 1% of people in a given area will get it, and about 1% of those will die, meaning 9,999 of every 10,000 people will be more or less OK at the end of this. Personally, I still don’t know anyone with coronavirus, and I would not be surprised if nobody in my circle ever gets it. It is hard to mentally hold both of these size-observations at once. I hope my prediction about 9,999/10,000 being OK comes true; I try not to entertain the thought of a total global meltdown…

Focusing on musicians, I feel for those who previously went all in on playing live and especially with others. I am lucky that much of my musical energy is spent alone and that I don’t rely solely on live performance for income. For the less fortunate, I can only hope that the current restrictions breed creative solutions…I look forward to the outpouring of music at the end of this ordeal. Now is a good time to buy albums for a change, and to get back into listening to music at home, not just during commutes and exercises. I guess in such uncertain times, one might as well gamble on optimism.

///

Today is one of the three days between the birthdays of two of the biggest Bs: Bach (March 21) and Bartok (March 25). I have been playing through Bartok’s second string quartet on the piano, trying to get into the details and all that. The second quartet forms a natural pairing with the first; those are the “romantic” quartets that come before the darker, harsher third and the progressive rock of the fourth and fifth. I had always preferred the first; it is easier to follow and I claim that as Bartok’s first masterpiece, it lays out a proof of concept or “abstract” for the rest of his career: a movement of post-Wagnerian heavy romanticism, a movement of uneasy musical symmetry, and a movement of raw folk energy. But now the second quartet is growing on me. It mixes those three colors rather than separates them by movement, and the romanticism/symmetry blend is particularly gorgeous. In the first movement, chord motion is so frequent and continuous that is impossible to hear a key center for more than a moment, and the keys of motives indicate large-scale architecture more than the fleeting tonalities do. Chords with symmetrical “cores” (for instance, an augmented triad plus one extra note a half step from a chord tone) are always close to their transpositions and inversions, and these structures afford Bartok much harmonic agility while also homogenizing the general sound of the sections, so that dissonant chords don’t “pop out” of a texture of simpler consonant ones. In other words, he manages to import all of the wonderful structural features of more traditionally tonal music into a mysterious world. This is different than the contemporaneous composers Schoenberg and Webern in their “free atonality” period. Those composers sought to express totally new ideas with totally new machinery, perhaps at the expense of a coherent system (12-tone music was the system that came about when Schoenberg felt too adrift in atonal freedom). That music speaks for itself; it is beautiful and important, but Bartok showed, at the same time, that one did not need to throw out the baby with the bathwater, so to speak. Old structures could be wrought into new ones; romanticism and atonality could flirt with each other and compromise.

The timing of the second string quartet is noteworthy, too. It was written amidst the throes of World War I, a far more terrible tragedy than COVID-19 (unless, God forbid, things get shockingly bad in April and beyond). The War shut down Bartok’s ethnomusicological expeditions but also probably forced him to really focus and extract as much as he could from his material. That shows in the quartet, where ideas are juiced to the max and little moments appear and reappear with the subtlest variations. An inspiring message: “You have enough! Make it work!” In the score, I am impressed with the organization of the rehearsal numbers: each labeled chunk clearly features a single idea or mechanism, so that a whole movement is a well-fastened chain of little episodes. There are macro-forms on top, but I find it easiest to listen and admire one chapter at a time. Last thing I noticed: the voice crossings are brave and omnipresent! Flies in the face of the traditional wisdom…

///

Stay inside and listen to music. Work with what you have and be romantic even in dark times.

Atmospheres of Charles Mingus

The jazz composer and bassist Charles Mingus is one of my heroes. Mingus, Duke Ellington, and Thelonious Monk form a triad of geniuses, arguably the best composers in jazz history. Wayne Shorter could make a strong claim to be of that echelon, but to my taste, his music doesn’t quite have the divine perfection of Duke, the infinite replayability of Monk, or the scope of Mingus. Shorter, Strayhorn, and Ornette might be the triad just beneath Ellington, Monk, and Mingus - better than everyone below but ever-so-slightly south of the tip top three. Oliver Nelson deserves a very high spot, as does Count Basie…. Duke Pearson is incredible, but…

Arbitrary categorization aside, Mingus has been on my mind and in my ears during recent weeks. I heard for the first time Let My Children Hear Music, a towering orchestral jazz album that Mingus thought of as a jewel in his crown. I also had my first experience with Changes One, which doesn’t possess quite the grandeur of Let My Children Hear Music but contains a definitive recording of “Duke Ellington’s Sound of Love,” one of the absolute greatest Mingus compositions, and features beautiful playing by a smaller ensemble throughout. Ah Um is probably the most “perfect” Mingus album - it is as clean as his bluesy music can be, tightly arranged and executed from start to finish. As masterful as that album is, it is somewhat atypical for Mingus because of its perfection. In contrast with Ellington and Monk, the majority of Mingus’ recordings/compositions are not sparkling and pristine. Even Ellington’s lesser-known albums are composed flawlessly; and except for on a few early recordings with deficient band support, Monk was incapable of anything but the highest level of swing and the most brilliant tunes. But Mingus produced many flawed masterpieces. Large-ensemble orchestrations are occasionally clumsy; big, episodic song forms sometimes lose steam; some of his linear bebop writing feels a bit forced. But still, Mingus is the heaviest of the heavy, and the flaws in his music beg the question ‘why?’ or more concretely, ‘how is this still so good?’

My best answer is atmosphere, one of the most difficult qualities of music to master and compose deliberately. There are endless melodies that are good enough on their own; one could competently learn jazz harmony (from the perspective of composition, at least) in a matter of months; with enough years of practice, any musician could learn to swing. In other words, the basic theoretical/technical components of jazz are staunchly within reach for a fairly disciplined non-genius. But merely putting those components together doesn’t lift the music to that higher plane where one deeply feels a specific aesthetic. By contrast, when musical memories surface of the supreme jazz composers, I’d guess that what comes to mind is a set of emotional/spiritual atmospheres rather than specific moments.

Examples:

• Duke Ellington’s music, especially the earlier music that predates the Civil Rights movement, comes across as holy and exalted, living proof of graceful black excellence in an era all-too-rife with prejudice. The urgent blues aspects of Duke are counterbalanced with a certain lightness and restraint, almost a fanciness that comes from economical arranging. I have a mental image of the atmosphere of Duke Ellington - the musical equivalent of morning light coming through church windows; warmth hitting the back of the neck.

• Billy Strayhorn is, in general, easy to tell apart from Duke, for atmospheric reasons. To me, the essence of Strayhorn is the essence of New York City on a rainy night, perhaps being unsure exactly where to go after a drink or two and some secondhand smoke. Strayhorn’s dark-tinged ambiguity complements Duke’s bright clarity.

• One does not need to be told which tune is being played to envision the atmosphere midway through a Thelonious Monk set. All of his tunes and all of his bands swing in that jaunty, jagged way - lots of space between the notes, lots of kinetic energy.

• Wayne Shorter’s classic 60’s albums are imbued with a magical blend of fantasy and blues - subtle and impressionistic harmony underneath rather cute melodies. Swinging fairy tales. One hears big rumbly thunder and also small, ginger creatures in the woods.

But Mingus, to me, is even deeper than all of those composers when it comes to atmosphere. The above surely have diverse, wide-ranging output, but I can nail down a relatively slim set of atmospheric characteristics for each. Mingus, on the other hand, actively composed with a wide palette of distinct atmospheres. That is to say he could not only conjure up a specific ambiance underneath the melody, harmony, and rhythm of a musical moment, but he could juxtapose, layer, and blend many of them according to what he thought the music needed. Mingus possessed a higher-order version of an already rare musical skill. This facet of his genius is most proudly displayed in his biggest, dirtiest works. In fact, the multi-atmospheric abilities of Mingus are probably least pronounced in the comparatively clean Ah Um. But Let My Children Hear Music is quite the ride through subareas within classical music, small- and large-ensemble jazz, and the blues; the occasional clunkiness may indeed be unavoidable considering the points A, B, C, … on the album. Mingus Moves is relatively consistent, but Pithecanthropus Erectus and Charles Mingus and Friends in Concert go all over the place, dragging the listener as if by a high-speed time-travelling spaceship. The source of his atmospheric technique is not entirely clear (that’s part of what’s so mysterious and magical about it); one is tempted to point to orchestration, but it really is so much more than that - if anything, it’s a nose for sniffing out perfect orchestrations to complement harmony and melody, plus the cultural/historical awareness to predict how various layers of the music will be received. But that doesn’t really cover it, and probably nothing could. Atmospheric composition is certainly a skill that cannot be taught, maybe one that cannot be learned…. In any case, Mingus’ magic, to summarize, is how he paints with a deeper brush than just melody/rhythm/harmony/etc. - he conjures whole atmospheres, environments one can inhabit rather than merely hear. On top of that, he plays with more than a single atmosphere per composition or album; there are so many rich musical locations he builds, sometimes two or more right on top of each other.

The question then becomes, “how do I listen to this?” Does one try to mentally hold the individual atmospheres for comparison, or does one simply accept each moment and the transits between them, no matter how bewildering? Is it worth trying to untangle the thorny, layered moments, or is it better to let them hit with full astonishing force? Of course, there is no single answer. But if one answer is chosen at a time, it can be adjusted later! That is to say, Mingus is especially rewarding for the listener who is willing to go back for seconds and thirds. A first listening may be a “dragged along” type experience, but the second time through, one could choose to focus on just a few elements at a time, perhaps listening from the bass chair, for instance. What’s amazing is that by focusing on subgroups of the ensemble, one can be transported to vastly diverse places: perhaps bass and drums chug along swinging while the piano and saxophone yell the blues, but the big band behind them is in some bizzaro bebop version of Vienna! The giants of music all reward repeated listening, but in jazz, only Mingus hits so many atmospheric destinations. My final proof of this is that I rarely identify myself as being in a “Mingus mood,” which is not the case for other composers. Sometimes, a little Monk will hit the spot and it’s obvious that that’s the case, but choosing to listen to Mingus comes from a desire to be intrigued/challenged/amazed, rather than a subconscious hunger for a certain atmosphere.

In his ability to create, move between, and layer atmospheres, Mingus reminds me of another great Charles of American music, namely Charles Ives. Anyone who knows Ives knows what I mean: what other music has parallel substrates of marching band, Beethoven, and New England transcendentalism all at once? Someday, someone should record an album of Ives and Mingus covers!

I think the very best video games have palpable atmospheres, too. Besides controls, that’s what makes it fun to just be in the game. Atmosphere is a big difference between the masterpiece Chrono Trigger and something more generic, like one of the less-than-perfect Dragon Quest games. Music is obviously a huge part of game atmosphere. The track “Aquatic Ambiance” from Donkey Kong Country is the only thing that saves the water levels (where the controls aspect of atmosphere is ruined). I’m nearly done playing Kentucky Route Zero, a newer, highly aesthetic narrative game that’s all about atmosphere. That’s what makes it.

Three recent enjoyments: Harold Land, a Bach Prelude, Cryptovolans

It’s early 2020 and I am in a relatively calm period after a dynamic one. I recently returned from Korea and Japan, I just started renting a piano, and I’ve been spending time teaching and learning about mathematics.

///

I visited a woodwind store in Japan and picked up the new 100th-anniversary Florida Super Tone Master Otto Link mouthpiece. Slight frustrations with my old mouthpiece led me to try new ones in the first place, but once I started began to replacing my equipment, I got to thinking about my favorite saxophone sounds and what they possess that I lack. The tenor saxophonist Harold Land has always occupied a special place for me; he is vastly underrated and underrepresented, but this makes him a ripe influence for the picking. The slight tragedy of his career is that once John Coltrane ascended, his impact on Land was so great that some part of Land’s natural style'/personality got swallowed up. Land’s genius came to be in 1950’s bebop, and the subtlety and flexibility he brought to that style didn’t fit the same with the modal style of the 1960’s and beyond. A similar trajectory holds for his tone: in the 50’s, with Clifford Brown, the bluesy, textured core of his sound was tempered by a certain coolness; he rarely pushed past mezzo-forte, his tonguing is light but consistent, he ghosts notes at the beginnings and ends of phrases so that his lines are like slick fish popping out from the surface of the water but then sliding back under without a splash. But once Coltrane’s influence took over, Land’s tone often came across as over-exerted or uncontrolled at higher dynamics. He replaced his bluesy swagger for a bluesy screaming urgency, but others did the latter better. Virtually no one could touch him on the former, though! My biggest hope in purchasing a dark metal mouthpiece was to emulate Land’s multidimensional tone from the 50s: a semi-roughened center that sits comfortably in medium dynamics, plus some softly singing overtones that surround the dark core with a halo.

One of my favorite recordings featuring Harold Land is Study in Brown from 1955. The track Jacqui is a personal favorite that features the best of Land’s bebop style. The A sections are standard B-flat major bebop fare, but the bridge is a blues in B major, a key so rarely heard in bebop. Land takes a perfect mini-solo over the end of the first bridge; the foreign key poses no challenge. Notice how his dynamics mirror the contour of his lines and how both of his phrases finish with the most delicious cherry-on-top notes. The soft notes still pop and swing; the loud notes flirt with pathos without going overboard. It’s incredibly tasteful.

Land’s chorus after Clifford Brown’s solo is similarly perfect. He has the best turns in the game; rather than using a triplet turn to correct the parity of a bebop line or to cheaply signify bebop authenticity, Land plays turns to highlight a beat, to intensify an inflection point within a line. I love how each phrase of the first 16 bars inches up his range. Track the highest note of each line until the bridge, and you’ll hear Land turning up the heat a single notch at a time. Lastly, the variance in rhythmic position of the beginnings and ends of lines is perfectly balanced. I classify (4/4 swing) phrases as beginning or ending on the odd downbeat, odd upbeat, even downbeat, or even upbeat, so that there are 16 possible combination of start and end. All too often I hear the same pairs over and over: beginning players almost always start phrases on odd downbeats; these days, I hear many players my age repeatedly ending phrases on odd upbeats, which is really only swinging in moderation. Land mixes it up, and that variation imbues his playing with the supremely important element of bebop surprise. (Good rappers know this well!)

///

When my new piano was delivered, I made a beeline for Bach. I instantly discovered my piano-playing fingers had atrophied to basically nothing! The only benefit: when one sucks, one must play Bach very slowly, so every moment really sinks in. I rekindled my love affair with the A major prelude from WTC Book I. To me, this short piece exemplifies one of Bach’s great miracles: the thematic material strongly keeps its identity throughout yet seems infinitely mutable as it moves through keys and voices. In contrast to many fugues and other contrapuntally dense/imitative Bach pieces, this prelude always has the spotlight on one voice and one voice only. The way the other two move out of the way for this is flawless. The balance of steps and leaps is similarly flawless. I find that both staccato and legato renditions of this piece work; usually I gravitate towards bouncier, pluckier Bach, but these lines have a certain passionate liquidity when played connected. The best moment of the piece is probably the appearance of the theme in the relative minor, almost exactly halfway though. The chromatic notes are so good, and the way one voice launches another is totally engrossing.

///

I have plunged deeply into SoundCloud at various times, and perhaps my most prized discovery is Cryptovolans, who can only be described as a MIDI genius. CV’s magisterial album Global Understanding is an excellent place to start. The music lives somewhere between an obscure JRPG aoundtrack, advanced prog rock, and music by a hyper-complex composer like Ferneyhough, except that in stark contrast to the latter two categories, this music sounds good. It is no less bewildering, though! Half of the fun of this album is mentally gripping an individual moment of beauty, like finding a shell on the shore; the other half of the fun is being unpredictably punched over and over again until you are forced to submit and let the music steamroll.

I have endless admiration and respect for Cryptovolans and other similar composers. I have nowhere close to this level of MIDI skill, and the difference is really one of kind, not just degree. That is, I cannot even imagine how one undertakes a composition project like this, and that mystery draws me in even deeper. Are algorithms at play? Randomness? Intuition? “Typing” versus “performing?” I couldn’t tell you, but if I could, I wouldn’t. This music is proof of the power of computers and numbers for classical composition! It is moreover proof that the musical/aesthetic soil that fed my generation is sprouting some beautiful, novel, astounding artists. Children who spent hours and hours interfacing with computers through videogames and other programs have their own kind of classical training!