[John Chalmers, Divisions of the Tetrachord]

Harmonically symmetrical musical structures invented by Ervin M. Wilson in the late 1960's. CPS's are generated by taking the products of `n` harmonic factors `m` at a time and reducing the derived tones to a common octave.

The best studied sets are the six tone Hexany (`n`=4, `m`=2) and the 20 element Eikosany (`n`=6, `m`=3).

CPS may be partitioned into sets of inversionally related chords, triads in the case of the Hexany and tetrads in the Eikosany. CPS are also characterized by intervallically symmetrical melodic properties and may be defined in equal temperaments as well as Just Intonation.

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[Paul Erlich, from Yahoo tuning, message 23492 (Mon May 21, 2001 7:16 pm)]

Erv Wilson showed how Partch's scales could be geometrically depicted, with the tonic lying in the center of a fantastically symmetrical shape. Erv's constructions relied on a concept called the lattice: every pitch in a JI tuning system can be mapped to a point in space (sometimes higher-dimensional space), such that its nearest neigbors are the pitches most consonant with it.

Erv Wilson also created new scales which were the perfect theoretical complement to Partch's Tonality Diamonds. Rather than containing one central pitch, the new scales put every note in the scale in an equal position, each sharing an equal number of consonances with its neighbors. Yet there is no "space" in the lattice into which any central (or more central) pitch could be inserted. He called these scales "CPS scales". Very mathematical.

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a&b temperament [a&b are numbers]

55-edo (comma) (Mozart's tuning)

1/1 or 1:1 (ratio)

2/1 or 2:1 (ratio)

a&b temperament [a&b are numbers]

apotome (Greek interval)

aristoxenean (temperament family)

atomic (temperament family)

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blackjack (tuning)

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centitone / iring (unit of interval measurement)

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daseian (musical notation)

dekamu / 10mu (MIDI-unit)

diapason (Greek interval)

diapente (Greek interval)

diatessaron (Greek interval)

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diesic (temperament family)

diezeugmenon (Greek tetrachord)

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doamu / 2mu (MIDI-unit)

dodekamu / 12mu (MIDI-unit)

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enamu / 1mu (MIDI-unit)

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enharmonic semitone (interval)

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enneamu / 9mu (MIDI-unit)

farab (unit of interval measurement)

fifth / 5th (interval)

flu (unit of interval measurement)

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

fourth / 4th (interval)

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

grad (unit of interval measurement)

hexamu / 6mu (MIDI-unit)

Hurrian Hymn (Monzo reconstruction)

hypate (Greek note)

hypaton (Greek tetrachord)

hyperbolaion / hyperboleon (Greek tetrachord)

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JustMusic: A New Harmony [Monzo's book]

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lydian (mode)

magic (temperament family)

Mahler 7th/1 [Monzo score and analysis]

marvel (temperament family)

meantone (temperament family)

mem (unit of interval measurement)

meride (unit of interval measurement)

mese (Greek note)

meson (Greek tetrachord)

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mina (unit of interval measurement)

minerva (temperament family)

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monzo (prime-exponent vector)

Monzo, Joe (music-theorist)

morion / moria (unit of interval measurement)

mutt (temperament family)

mystery (temperament family)

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octave (interval)

oktamu / octamu / 8mu (MIDI-unit)

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pantonality of Schoenberg [Monzo essay]

paramese (Greek note)

paranete (Greek note)

parhypate (Greek note)

pentamu / 5mu (MIDI-unit)

prime-factor notation (JustMusic) [Monzo essay]

proslambanomenos (Greek note)

savart (unit of interval measurement)

schismic / skhismic (temperament family)

Schoenberg's pantonality [Monzo essay]

second / 2nd (interval)

semisixths (temperament family)

semitone (unit of interval measurement)

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sk (unit of interval measurement)

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studloco (tuning)

subminor 3rd (interval)

Sumerian tuning [speculations by Monzo]

synemmenon (Greek tetrachord)

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tenth / 10th (interval)

tetrachord-theory tutorial [by Monzo]

tetradekamu / 14mu (MIDI-unit)

tetramu / 4mu (MIDI-unit)

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thirteenth / 13th (interval)

tina (unit of interval measurement)

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tredek (unit of interval measurement)

triamu / 3mu (MIDI-unit)

tridekamu / 13mu (MIDI-unit)

trihemitone (Greek interval)

trite (Greek note)

tu / temperament-unit (unit of interval measurement)

Türk sent (unit of interval measurement)

twelfth / 12th (interval)

whole-tone (interval)

woolhouse-unit (unit of interval measurement)