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Poetry ยท #52

On Substitutions

for the subgroup lattice of Zโ‚โ‚‚ โ€” where every jazz revolution
was a mathematician's theorem, played before it was proved

Before the name, the ear.

Before the proof, the horn.

Parker found a door

at the tritone โ€” not knowing

it was the only involution,

the unique self-inverse,

the axis that splits twelve

into six pairs of strangers

who share a secret:

the same two burning notes.

Tโ‚†. Order two.

The farthest key is the nearest voice.

Dizzy played it like gravity

reversed โ€” the bass falls

a half step instead of a fifth,

and the world still resolves.

Nobody called it an antipodal map.

They called it hip.

Before them: Tโ‚….

The circle of fourths,

old as tuning itself,

generator of everything

we named "functional."

V goes to I.

The arrow that built harmony.

Order twelve โ€” it visits everyone.

After them: Coltrane.

Who heard Tโ‚„

and played three keys at once,

the augmented triad orbiting

in major thirds,

B โ†’ G โ†’ Eโ™ญ โ†’

a triangle inscribed

in the circle of twelve.

Order three. The partition

nobody expected.

Giant Steps was a theorem

about Zโ‚ƒ โŠ‚ Zโ‚โ‚‚.

John just heard it first.

And underneath all of it,

the lattice:

Tโ‚ โ€” chromatic, everything, chaos.

Tโ‚‚ โ€” whole tone, Debussy's dream.

Tโ‚ƒ โ€” diminished, four corners of the square.

Tโ‚„ โ€” augmented, Coltrane's triangle.

Tโ‚… โ€” fourths, the spine of all tonal music.

Tโ‚† โ€” tritone, bebop's secret handshake.

Six generators.

Six eras of harmony.

Each one a subgroup

of the same twelve notes

we've always had.

The revolutions weren't in the notes.

They were in which symmetry

you chose to hear.

 

Same circle.

Different axis.

New music.