I wrote a post telling the story of the experimental editing you hear on the record. That editing is really the "main idea" of the project: more significant than the details of the tunes or the performances, I'd argue. But of course the project began with standard jazz fare: tunes, read off lead sheets, with blowing. A core of more-or-less traditional jazz, modulo my own special interests, sits within the music. I want a transparent record of how this album came to be, so as a counterpart to the post on editing, here's a reflection on the (jazz-) compositional thinking behind the 6 tunes on the album.
0. Big picture:
This record is one of a pair. Twelve tunes in total, not specifically composed for the project; rather, compiled from my list of compositions across 2021-2022 or so. Cleaving the twelve into two groups didn't take much effort; I had a clear-ish vision of the two aesthetics and the tunes sorted themselves. The vision for High Firmament: bright, Apollonian, big-C Classical, positive. The grace and elegance of both Mozart and Bird counterbalanced, as influences, the contrapuntal thickets of the editing. Clear, familiar composition supports — opens space for — density and entropy in other areas of the music.
The narrative of the album took shape once we sequenced it. High Firmament is dedicated to the "morning mindset" and so one may imagine the album as chronicling the first half of a (good) day: Wakin' up and stretchin'; Thinkin' through some mathematics, visualizin' something strange and twisty; Enjoyin; a hearty breakfast; Hikin' up to a cliff where the wind whips around and the morning sun shines into your eyes; Practicin' the fundaments of bebop; Playin' baseball with the sun right overhead, and hittin' it out of the park.
I'm a morning person. I love this stuff. I get the sense that most jazz people are night people. If that's you: don't fear the morning! It's great! Try it!
1. Stretchin' in the Mornin'
This straightforward tune has two main ingredients: 1) a wide-open, frothy meditation on F-major-7; 2) a rubato melody and form, supported by fast-moving chord changes. The two ingredients alternate in a sort of sparkly rondo. Gas and brakes; exertion and rest. Not much to say about the F-major froth. The only composition there is a suggestion of a cute little wrist-roll for piano or bass:
The tune itself starts with as bright and positive a phrase as I could come up with. The sound of moving from I to V as a secondary key area dominates Classical sonata form. "Applying a sharp" to a key brings Mozart and Haydn to my mind, every time. But this move doesn't happen much in jazz. One could argue there are not secondary key areas in jazz with the same status as their Classical counterparts; but even so, standard jazz harmony, as inherited from Tin Pan Alley, seems to lean a bit more to the flat site. So many tunes go to IV. Very few go to V and hang out there. V is usually a stop along the way, whereas IV often feels like a destination of its own. But I love the brightening effect of going to V. The other classical device in play here is the so-called "cadential 6/4," which instantly signals classical music and especially opera. The sound of jazz is the sound of the ii7 — V7. Classical music prefers ii6/5 — V6/4->5/3. (Or if you prefer, I6/4—V. Who cares?)
I'm not exactly the most extraverted bubbly guy. I can't just let a phrase like the above go, uh, uncontested. The rest of this tune slips through jazz chords, accelerating before alighting back on the tonic.
The pacing is something like twisting into a tough yoga pose and then taking a moment to breathe and relax afterwards. The voice leading in the middle section is what I call "melty:" lots of chords that are close to each other — mostly related by small downwards steps in individual voices — but that move fast so that you end up "far from home;" or in this case, back home after starting far away. (One day I will write up a precise theory of the differential calculus of voice leading — that is to say, quantifying rate of harmonic change as a ratio of distance traveled to time. The only tricky part is defining the proper notion of distance in harmonic space. But it's not that hard.) At first glance, it may seem foolish to attempt to improvise on changes blasting by so fast, especially without a consistent pulse. But the proximity of the voice leading picks up that slack; most of the notes of a given chord work or nearly work over the previous chord and the next. And "smearing the changes" is indeed one of the lovely sounds of jazz. This is just to say it's easier and lower-stakes to blow over this tune than the lead sheet would betray. Plus, confident rhythmic phrasing will pull the rhythm section along. If your ears are open, you'll never get too far off.
2. Toroid
Don't sleep on Mozart's slow movements. A lot of famous slow classical music is heavy on gravitas and the epic, icebergulous sounds of e.g. Mahler. But few musical moods are quite so tasty as an andanteor adagio that doesn't take itself too seriously. The strawberries-and-cream of the ballroomy second movement sandwiched between two vivacious dances. Of particular gustatory delight are the fast bits of the slow music: the delicate little flurries that bubble out of the harmonies, the hemidemisemiquavers that tickle you with a feather. Coleman Hawkins, a guy who surely met people who met people from the eighteenth century, has an appetite for little flurries too. One can go back even further, to Couperin, for the pinnacle of ornamentation. None of us can even hold a candle to his conception of ornamentation, but it doesn't stop up from trying.
Big fan of the sound of piano and saxophone getting through the second half of that phrase semi-together. It's all about poise, more so than strict accuracy. The most fun rhythmic feature of this tune comes again from Classical music: the two halves of the form are punctuated with little cadenzi, time-freeze breathers between the stately plod of the harmonic motion. You can think of the candenzi as unshackled elaborations on the idea of the ornaments that happen over the pulse (as in m.3 above). The big-picture tonal strategy of Toroid is to take inspiration from its namesake and twist around the circle of fifths. The opening chord, G, is IV of D, the tonal center of the first twelve bars, up through:
That last chord is one of my favorites, and certainly part of my "sound:" V7 but with I in the bass, an ambivalent almost-resolution that opens the door rather than closing. Indeed, that chord allows a sneaky lean towards a brighter key: the next four bars point towards A major and indeed land on A. But that A turns out to be the IV of E, just as the opening G was IV of D. The last phrase of the form is an abridged version of the first phrase, up a whole step. That last phrase ends on B7, the V7 of E, setting up the toroidal twist that brings us back to the top (G as IV of D). B7 is awfully close to D7 — those two chords are equally spaced around the D#-F#-A-C diminished axis — and indeed, in jazz, playing something like B7 over D7 is not only allowed, but encouraged. You "pick up" the flat-9 and the 13: salt and sugar. Bottom line: yes, B7 does a great job leading back to G. The two most scrumptious moments in the harmony of Toroid perch the melody a minor ninth over an important note in the chord:
B over A#.
And, from the Coda,
E over D#.
Speaking of which, the Coda is a half-beautiful, half-humorous statement that compresses the main form's tonal moves and equivocates between E major and D major.
3. Maple
I have written a handful of tunes with the same basic format as Maple: long, medium-swing forms with standard but meandering harmony. Think Cedar Walton or Benny Golson. No individual harmonic moment in Maple rocks any boat. It's an AABA' form. The only experimental ingredient is the on-the-fly tempo-switching. We discontinuously switch between two tempos, a few metronome-notches apart, as part of the form. The main hook of the tune is always slow, and everything else is fast.
That main hook relies on one of the oldest tricks in the book: tonal chord changes over a pedal.
File this one in "if it ain't broke, don't fix it."
The rest of the tune exploits the natural closeness of four-note-chords related to each other by minor third. The four members of tonic axis F-D-B-Ab all send representatives over the course of the tune. If you prefer not to think in terms of symmetries but rather individual tonal moves, chain together parallel and relative minors/majors for the same effect: ||: F-d-D-b-B-g#-Ab-f :|| (And of course, it's a bit boring and on-the-nose to stick exactly to that plan. Much classier to jump around and stretch the formula.) That's about it: the tempo-switch game plus the corresponding gas-and-brakes of pedalling versus twisting through key areas. A long form — a bit tricky to pace — but otherwise not hard.
4. Zephyr Point
This one's as bright and boisterous as I could make it, and as self-conciously Mozartian as anything on the record gets (except for a truly idiotic deleted "saxophone-concerto" tune whose score you may request for 0.001 BTC). The tempo marking is "galant swing." Whereas we feel and guess approximate tempo changes on Maple, the trick at the heart of Zephyr Point is a proportional relationship between two tempos. The opening gambit teases that relationship:
Bars 3 and 4 are notated wrong. The top line should be whole notes and the bottom line should be quarters, but writing it this way "feels better" (and could be corrected with an admittedly clunky 'half tempo' marking). I repeat the same mistake throughout.
If you're asking yourself, "what in the gosh-darn heck is that 3 doing in that denominator," first things first: settle down. It is legal, I swear.
Math time: 2 measures of 4/4 comes out to eight quarter notes or two whole notes. (Typesetting fractions in Squarespace will kill me — forgive the one-linedness.) You can see the equivalence via the equation
2 * 4 / 4 = 2 * 1 / 1,
both in the format
(number of bars) * (beats per bar) / (size of each beat).
3 bars of 2/3 is the same amount of time, equivalent to the length of a breve. What is the meaning of the 3 on the bottom? Third notes? Yes. A third note is equivalent to a half-note-triplet, which divides a whole note into three equal pieces. 6 third notes, 2 in each bar times 3 bars, comes out to the same amount of time as two whole notes.
3 * 2 / 3 = 2 * 4 / 4 = 2 * 1 / 1.
In the notated example, the top line is equivalent to three notes in the space of 2 full-length 4/4 bars, i.e. whole-note triplets. The bottom line is filled in with 12 sixth notes, each of which is equivalent to a quarter note triplet. Because this weird division still lines up with the original pulse, a drummer could play through those bars in 4/4 and pop out the other side unscathed. We break that pattern in the next phrase.
This cheeky pair of phrases toys with the above ideas. The 5/6 bar does not line up with the original pulse — you "lose a triplet." But the 6/6 bar is equivalent to a 4/4 bar populated with 6 quarter note triplets. I'll be the first to admit that it's hard to stay slick when you're blowing over this sort of thing. The real puzzle is to what degree you commit to the tuplets as being in a new tempo, so that you swing in that tempo. In the context of the whole tune, these flashes of a slower, triplet-based tempo can be seen as premonitions of a more definitive switch, in the [B] section:
The standout bar is m. 22, which I originally wrote as bar of 4/4 + 2/4 (and indeed, that's how Kayvon plays it). The effect is essentially the opposite of what happens in the [A] section. The duplet tempo flashes in amidst the context of the triplet tempo: th converse of [A]. The [C] section explores the faster side of the otherwise slower-feeling triplet tempo, ending with a merciful finisher: a quick fermata and a rubato phrase to let us re-align.
3/4 and 9/12 are equivalent.
That realignment opportunity is important. All too often, you come across challenging jazz compositions that never relent, that seem to take some masculine pride in bucking off rhythm sections and soloists alike. Fuck that! Leave the jazz school tuplet-measuring contests behind. Throw everyone a bone. Or two!
We blow over this form with no modifications. Hard but not impossible! In fact, not as hard as I'd've expected. My improvisation goal was to highlight the Classical flavor of "high bebop" a la Bird, Bud, and Brownie. Max Roach was in my ears. The harmony is nothing too special. Once again I tonicize V in order to conjure the Classical spirit. [A] works its way from G to D; B minor is the pivot point (or maybe E minor uh idk). [B] is mostly in D but turns back towards G at the end. [C] implies G at first but reveals that G to be VI on the way to F#: V in B minor, which gives way to secondary chords surrounding D major. A year-and-a-half later I can still giggle at a legitimate claim to a diminished second, E-flat to D#, in the snakey voiceleading near the end:
Yum! Pedantry!
5. Plucky
This bebop blues is a point of pride because it's one of very few of my tunes that has been played without my presence. I'm not going to quit my day job just yet, but several unpaid sessions in Brooklyn have graced Plucky with their blessings, just sayin'...
Charlie Parker is one of the greatest jazz composers ever. Obviously. But unlike Duke and his children Mingus and Monk, he didn't write original changes or song forms or any large-scale compositions. It's just short, perfect, bouncy bebop heads. Potato chips and chocolate, not a veggie in sight. Bird and Miles represent a spectrum in early high-bebop composition. Whereas Miles is an abstract and harmonic composer, prone to long, sinewy lines, Bird's tunes just pop off the page, short phrase after short phrase, like a boxer jabbing and weaving around the beat. My own study leads me to identify the following primary features of Bird-as-composer:
Short phrases of irregular rhythms (no long streams of eighth notes).
Syncopation, especially of a 3-against-2 type (clap dotted quarters along to any Bird head).
Occasional but not frequent moments of strange harmony, subverting or extending the changes. Major sevenths on dominant chords, tritone substitutions, or other weird superimpositions.
So there's the homework assignment that generated Plucky. The 5/4 time signature was to lock myself into a challenge of stretching bebop vocabulary into odd time signatures, whose checkerboards of strong and weak beats threaten to buck you if you're not careful. A slight adjustment to bebop blues changes that I first heard on Gerkin for Perkin (ew) off Study in Brown: resolve to bII major in the ninth bar before twisting back to I in the eleventh. In bebop, the eighth bar of a blues is often biii to bVI, interpolating a chromatic ii-V between iii and ii. I prolong that out-of-key chromatic move by resolving the middle ii-V. In D, that means sandwiching Fm7—Bb7—Eb between F# and E minor chords (I actually use E7 instead of E minor 7 to intensify the feeling of a dial spinning through the circle).
But this tune ain't about harmony. It's about emulating the crunchy, push-and-pull bounce of a bird head. 3-beat units fit differently over 5/4 than they do over 4/4, but in a way, they don't. In particular, a 3-beat phrase puts you "1 beat behind" a 4/4 pulse, and a doubly-long 6-beat phrase puts you "1 beat ahead" of 5/4. Similar effect relative to the strong-beat-weak-beat checkerboard. Plucky also plays with, lightly, the triplet-as-new-tempo idea that Zephyr Point fleshes out.
Lastly, the bassline rubs against the melody in spots, cracking open a window to some future blossoming of contrapuntal bebop. ELEW is on that mission — take it away, man.
6. Hometown Hero
The set closes with a triumphant and cheeky tune that juxtaposes the heavy and the light, but both with a positive attitude. Shedding light on this tune feels a bit like explaining jokes, but oh well... Many clave-esque rhythms can be loosely described as "fit in as many 3s as you can, then correct for the meter." For instance, 3 + 3 + 3 + 4 = 16; shuffle those 3s around and you get four variations on a tasty syncopation over 4/4. That's the trick of the first half of [A].
The melody floats to obfuscate the trick, which otherwise may have come across as harsh on account of the seconds in the piano voicing. Back to our formula for a moment.
3 + 3 + 3 + 4 = (3 + 3) + (3 + 4) = 6 + 7.
3 + 4 = 7 fits over one time signature better than all others: 7. Duh! The joke of the second half of the [A] is to make 7 feel like the regular, symmetrical pulse as opposed to the asymmetrical 4 in the first half.
Humor notwithstanding, that section is a lot of fun to play over, especially for drums and saxophone. It's heavy and syncopated but not without lilt and bounce. But that heaviness evaporates at the gossamer [B] section:
Those held chords look ugly, I know, but they too are the result of a simple trick. The first chord is all seven notes of the D major scale. The bass moves diatonically down, swapping one pair of notes in that seven-note collection. To illustrate, from the first bar of [B] to the second, bass moves from D to C#, so the C# in the chord moves to D. Then bass moves from C# to B, so the B in the chord moves to C#, preserving the macroharmony. The result is a light-blue glassy blur of the diatonic scale. That little moment of slow harmony sublimates into a faux-Classical piano-bass duet, sitting on a cloud, finishing off the scale descent in the bass. (Consult the discussion of Zephyr Point if the 5/6 time signature disturbs you.) The last two bars, like a splash of cold water on the face, re-enliven the tempo and reinstate the heavy syncopation. Nothing like a cannonball to truncate a daydream. And that's the form. All that's left is the long Coda after the head out. The cold-water-splash doesn't land this time; instead, the triplet time signature remains through the end of the piece and we enter a less-ironic-than-you-might-think episode: dollar-store Brahms in the key of middle school: B-flat.
Not notated: the clarinet figure that sits on top of the tenor melody. But come on, it's, like, the major scale.
The second-to-last joke is to stack more triplets on the triplets, in the bass. Math puzzle: how would you describe the values of those notes relative to the original 4/4 pulse? Rev up those denominators!
The ending of the whole album: oblique and uncertain — just how I like it — a drum solo on shaky ground. Whereas earlier, 7 represented a symmetrical alignment of hits, now it returns to its usual unstable character. One cannot help but giggle at a 3:7 polyrhythm in 7/3 time. Your gut tells you they should cancel out...but the ear says otherwise.
~ ~ ~
Email me for sheet music if you want it. Read the corresponding post for Ferment Below here.
Happy Pi Day.