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Page 232
TABLE 8.2.
The 13-key system of Aristoxenus and the reformed 15-key system
Aristoxenus
Reformed system
a'
Hyperlydian
0232-001.gif
Hyperaeolian
g'
Hypermixolydian
Hyperphrygian
0232-002.gif
0232-003.gif
Hyperionian
f'
Hyperdorian
e'
0232-004.gif
Lydian
0232-005.gif
Aeolian
d'
0232-006.gif
Phrygian
0232-007.gif
Ionian
c'
Dorian
Dorian
b
0232-008.gif
Hypolydian
0232-009.gif
Hypoaeolian
a
0232-010.gif
Hypophrygian
0232-011.gif
Hypoionian
g
Hypodorian
Hypodorian

The fifteen-key system left no practical need unprovided for, and on a superficial appraisal it seemed admirably neat and coherent. It won general acceptance, though the prestige of Aristoxenus' name ensured that his system too was remembered. One later theorist, however, produced a powerful critique of both: Ptolemy. He reasserts the principle that the purpose of keys is to bring different segments of the Greater Perfect System,33 i.e. different octave species, each with its own particular ethos, into the most comfortable vocal register. Since there are just seven species, the requisite
(Footnote continued from previous page)
db1017e3fd9b6bbecd5f283ecd392883.gif db1017e3fd9b6bbecd5f283ecd392883.gif
p. 476.33; Censorinus fr. 12 pp. 89. 10-90.4 Jahn; Phrynichus, Praeparatio sophistica p. 24. 16 if. Borries.
db1017e3fd9b6bbecd5f283ecd392883.gif db1017e3fd9b6bbecd5f283ecd392883.gif
33 Ptolemy points out that the System must span the two octaves from Proslambanomenos to Nete hyperbolaion, but that the tetrachord Synemmenon is superfluous, as diversions into it can always be explained as key-changes. Thus he uses what the Aristoxenians call the Greater Perfect System, though he himself calls it the Unmodulating System.

 
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