Perfect Immutable System† in 72 Note Equal Temperament (Ionian)

a' Nete (very lowest string) hyperbolaeon
g' Paranete
f' Trite (third, pl. tritai) [Chalmers, p215]
e' Nete diezeugmenon ("disjunct")
d' Paranete
c' Trite (third, pl. tritai) [Chalmers, p215]
b Paramese (next to the middle)
a Mese (middle) The central note of the Perfect Immutable System .
g Lichanos (index, indicator, pl. lichanoi) [Chalmers, p209]

There is a style of composition which demands a Lichanus at a distance of two tones from the Mese, and that far from being contemptible it is perhaps the noblest of all styles [Aristoxenus, p181]

we shall assume the locus of the Lichanus to be a tone [Aristoxenus, p181]

meson ("middle" or "main")
g (-67¢)
g (-67¢)
f (diatonic being the highest p182) Parhypate (next to the highest, pl. parypatai) [Chalmers, p211] [the locus] of the Parhypate is the smallest diesis (50¢) and is never nearer to the Hypate than a diesis (50¢), and never further from it than a semitone(100¢) [Aristoxenus, p181-182]
f (-33¢) (chromatic coming next, p182)



f (-50¢) [enharmonic Lichani the lowest p182]
e Hypate (meson) [highest string on the kithara, pl. hypatai]
d Lichanos hypaton Lichanos (index, indicator, pl. lichanoi) [Chalmers, p209] Hyperhypate (beyond the highest, the diatonic lichanos hypaton, transliterated as hyperhypate). A note a whole tone below the tonic . . . [Chalmers, p208] hypaton (of the highest)
c Parhypate
B Hypate (hypaton) [highest of the highest string]
A Proslambanomenos

† Ptolemy's "Immutable System" modified by Rick Tagawa from entry "Greece / 3. Theory" by C. André Barbera, Notre Dame University in Randel, Don Michael, The New Harvard Dictionary of Music, The Belnap Press of Harvard University Press, Cambridge, Massachusetts, 1986, p349

half tone = 100¢ = semitone

third tone = 67¢ = smallest chromatic diesis

quarter tone = 50¢ = smallest enharmonic diesis

A tone is the difference in compass between the first two concords, and may be divided by three lowest denominators, as melody admits of half tones, thirds of tones, and quarter-tones, while undeniably rejecting any interval less than these. Let us designate the smallest of these intervals the smallest enharmonic diesis, the next the smallest chromatic diesis, and the greatest a semitone. [Aristoxenus, p180]

Pycnum is the combination of two intervals, the sum of which is less than the complement that makes up the Fourth. [Aristoxenus, p182]

[Aristoxenus, The Harmonics, translated by Henry S. Macran, Oxford, 1902, p182]

[Chalmers, John H. Jr., Divisions of the Tetrachord, Frog Peak Music, Hanover, NH, 1993]


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© 2003 Rick Tagawa