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Perfect Immutable System† in 72 Note Equal Temperament (Ionian) |
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| 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] |
g
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Lichanos |
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¢)
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| 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) |
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| 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]
return to Aristoxenus
