Nine tones,
not twelve.

Take the octave. Cut it into nine equal pieces instead of twelve. Each step is 133⅓ cents; the ratio between neighbours is the ninth root of two, 1.080059739.

That is the whole definition, and almost everything interesting follows from one accident of arithmetic. Twelve divides by four into three. Nine divides by three into three. Both systems therefore contain the same three-way division of the octave — the augmented triad, four hundred cents a step. Three pitches sit in exactly the same place in both worlds.

Everything else moves. Six of the twelve familiar keys must be bent; three are abandoned altogether. Those three shared pitches are the only ground on which a nine-tone player and a piano can ever agree — which makes them the door between the two systems, and the natural foundation for anything written for both.

How the first one was made

In 1997 the idea was turned into numbers for the first time. Nine of the twelve keys on a Kurzweil were kept; six of those were detuned by 33⅓ or 66⅔ cents; three were silenced. The conversion from hertz to cents — "something like turning miles into meters," as Francisco put it — was computed at Michigan State that December and printed out beside the keyboard.

That printout was the first instrument. Anyone with a synthesiser that accepts fine tuning can repeat it this afternoon.

The nine tones, in the pure form

Each octave doubles. A second reference, A = 440 Hz, is used when playing alongside conventional instruments — multiply every figure above by 0.97778.

Francisco Mora Catlett was born in Washington and raised in Mexico City, the son of the sculptor and printmaker Elizabeth Catlett and the muralist Francisco Mora. He travelled the spaceways with Sun Ra from 1973 to 1980, assembled Afro Horn in Detroit, founded AACE Records, and played in Carl Craig's Innerzone Orchestra.

The nine-tone system belongs to that Detroit seam where jazz meets electronic music, and it was arrived at by a route no textbook would sanction.

I had heard the scales of Julián Carrillo. He divided the octave into 13 equal parts and composed music, retuned instruments and other instruments to play his scales. Harry Partch worked on equal divisions of 32 notes, and created instruments as well.Francisco Mora Catlett

In the 1970s he led a Detroit band of electronic and acoustic music called Parsec 9 — named for the number the tuning is built on, and the earliest surviving trace of the idea. It rested on the observation that any number multiplied by nine has digits summing back to nine. A circle has 360 degrees; three plus six plus zero is nine. Concert pitch A = 440 sums to eight, so the new system is tuned to A = 450, which sums to nine.

None of that is mathematics, and it does not need to be. It is a generative constraint, of exactly the kind that produced Partch's forty-three tones and Carrillo's thirteen. What it generated is a real, coherent, playable tuning that almost nobody was using — and one genuinely load-bearing insight about the augmented triad that a music theorist would have been pleased to find.

Nothing was written down for twenty years. In 1997, at Michigan State — where Francisco taught percussion out of the traditions of the African presence in the Americas, and where Dale Joachim was taking a doctorate in electrical engineering — he handed the problem over. Within a month it had a table of frequencies, a retuned synthesiser, and four recordings.

Cutting the octave into equal parts other than twelve is not an avant-garde gesture. It is a long-standing practice in African instrument making, and the instruments that carry it are struck.

The Buganda court xylophone of Uganda, the amadinda — twelve keys, three players interlocking — is tuned to an approximately equidistant five-fold division of the octave, steps of about 240 cents. Gerhard Kubik measured it repeatedly from 1960 onward. The timbila of the Chopi in Mozambique, documented by Hugh Tracey in 1948, are graded xylophone ensembles tuned to an approximately equal seven-fold division — about 171 cents a step. The Senufo balafon of Côte d'Ivoire, recorded by Hugo Zemp, has twelve keys and five equidistant degrees to the octave.

Two honest qualifications. These are approximations, not equalities — Kubik's own term is pen-equidistant, and the spread between communities runs to fifty cents. And no documented African practice divides the octave into nine. Five and seven, approximately. Not nine.

And yet

The temperament family that nine equal tones belong to is named after a village in Mozambique.

Erv Wilson — the theorist behind essentially every generalised microtonal keyboard now sold — developed it around 1989 after studying Chopi timbila tuning from Hugh Tracey's recordings, and named it mavila, after Mavila in Zavala District, Inhambane Province, in the Chopi heartland. Tracey's archive carries recordings credited to the Ngodo of Mavila.

So Francisco arrived at nine equal tones by an Afro-diasporic route out of Detroit and the Arkestra, working from a numerical intuition. Western tuning theory arrived in the same neighbourhood from Mozambican xylophones, and named it after the village. The two routes reached the same place from opposite directions, and neither knew about the other.

Stated precisely, because the looser version is wrong: nine equal tones support the mavila temperament; mavila is named for a Chopi locality documented by Hugh Tracey; Wilson developed it after engaging with Chopi tuning. Chopi practice itself sits near a seven-fold division. Mavila is inspired by that tradition, not a model of it — and nine equal tones are not, and should not be called, an African tuning.

What follows from it

That every documented equal-division tradition above is a tuned-bar tradition. The struck version of this instrument is not a romantic afterthought. It is the form this family of tuning has actually taken for centuries, and a percussionist was always going to end up there.

Blue Monkey's Electric World, 1997. Four pieces — as far as we can establish, the only jazz ever recorded in nine equal tones.

The session masters are being located and transferred. Audio will appear here once that is done.

© Blue Monkey's Electric World, 1997. All rights reserved.

Nine-Tone Studio is a synthesiser built to Francisco's 1997 specification — three oscillators, filter, envelope, effects — with nine keys to the octave and both reference pitches.

It runs in a browser, including on an iPad, and needs no connection. The five white keys form a usable scale on their own, so it plays itself within a minute.

A native iPad version is in preparation. Anyone who would like to try it early is welcome to write.

Nine equal tones do not make a poor twelve-tone system. They make a good septimal one.

Two facts decide everything about how this music is written. The subminor third (7/6) and the supermajor sixth (12/7) land within a fifth of a cent of pure — cleaner than twelve-tone equal temperament manages for anything except the octave itself. The home chord of the system is that stack, and it simply rings.

And the perfect fifth is thirty-five cents flat, past the point where the ear forgives. Functional harmony cannot be written here. That is not a defect waiting to be repaired; it is the reason the system has a character at all.

Between them, the major third survives intact — it is exactly the major third on a piano — and three of them stack to an octave.

Where to start

• 0 · 2 · 7 — the septimal chord. The consonance of the system.
• 0 · 3 · 6 — the augmented triad. The bridge to conventional instruments.
• The five white keys alone — an evenly spread pentatonic that is playable on sight.
• The antidiatonic mode — seven of the nine tones, in which major and minor are inverted from what the ear expects.

No keyboard with nine keys to the octave is sold anywhere in the world. No luthier frets a guitar in nine equal tones. For fifty years this music has existed on instruments built for a different scale.

Everything written in the system so far has been played on a twelve-key keyboard with three keys switched off — an honest workaround, and a permanent mismatch between what the hand does and what the ear hears. Generalised hexagonal controllers exist and can be mapped to any tuning, but they are grids of identical buttons; nothing about them tells a player where they are.

Francisco drew the alternative in 2021: five white keys and four black to the octave, with a landmark at the octave boundary doing the job that B–C and E–F do on a piano. It has never been built.

We are building it. The instrument is narrower to the octave than a piano, which means a ninth falls under the hand where an octave does today, and voicings that are physically impossible on a keyboard become ordinary. Detailed drawings are held back for now. A struck version is also under consideration — and on the evidence above, that may be the truer form.

Francisco Mora Catlett — drummer and composer; Sun Ra Arkestra, AACE Records, Innerzone Orchestra; Michigan State. Originator of the system, roughly fifty years ago.

Dale Joachim — engineer; the frequency tables, the software, and the instrument. Piano on 9tone Blues.

We are looking for a third voice — a percussionist or composer willing to work in a tuning with no repertoire — and for a fabricator interested in an instrument nobody has made before. If that is you, please write.