- tigators that lasted long after the Christian Era. His followers tended to
regulate all musical procedure by mathematics, and the opposition long continued between them and the disciples of Aristoxenos, born about 354 B.C., who advocated taste and instinct as normative principles.
Through these studies, with experiments in singing and
instrument-making, an extensive theoretical tone-system was
gradually developed. The shaping and nomenclature of this
were largely determined by the constant use of the lyre. From
the first the comprehensive units recognized were the octave
and the tetrachord (a series of four tones within the interval of
a fourth). All tone-series were reckoned downward instead of
upward (as in modern music).
Three 'genera,' or ways of dividing the tetrachord, were used: (a) the
diatonic, consisting of two whole steps or 'tones' and a half-step or
hemitone, (b) the chromatic, consisting of an extra long step with two
half-steps, and (c) the enharmonic, consisting of a double-step with two
quarter-steps. These arrangements may be illustrated through modern
letter-names thus:—
Diatonic, E D C B
Chromatic, E C# C B
Enharmonic, E C[Cb]B
The diatonic genus was felt to be the most important of the three, and as it is the form that has had historic influence since, it will be the only one taken for further illustration here.
Within a diatonic tetrachord all the three possible arrangements of half-steps were utilized—the Dorian, with the half-step below, the Phrygian, with it in the middle, and the Lydian, with it above. These may be illustrated thus:—
Dorian, E D C B
Phrygian, E D C# B or D C B A
Lydian, E D# C# B or C B A G
Various 'species' or octave-scales were constructed by joining two similar tetrachords together and adding one step to complete the octave. Seven such species or modes were recognized, formed in three ways, according to the position of the added step:—
_________ _________
| | | |
Dorian species or mode, E D C B A G F E
Phrygian species or mode, D C B A G F E D
Lydian species or mode, C B A G F E D C
_________ _______
| || |
Hypodorian species or mode, A G F E D C B A
Hypophrygian species or mode, G F E D C B A G
Hypolydian species or mode, F E D C B A G F
______ __________
| | | |
Mixolydian species or mode, B A G F E D C B
