2. The list of harmoniai as gathered from the writers who treat of them, viz. Plato, Aristotle, and Heraclides Ponticus, is substantially the same as the list of tonoi described by Aristoxenus ([p. 18]): and moreover, there is an agreement in detail between the two lists which cannot be purely accidental. Thus Heraclides says that certain people had found out a new harmonia, the Hypo-phrygian; and Aristoxenus speaks of the Hypo-phrygian tonos as a comparatively new one. Again, the account which Aristoxenus gives of the Hypo-dorian tonos as a key immediately below the Dorian agrees with what Heraclides says of the Hypo-dorian harmonia, and also with the mention of Hypo-dorian and Hypo-phrygian (but not Hypo-lydian) in the Aristotelian Problems. Once more, the absence of Ionian from the list of tonoi in Aristoxenus is an exception which proves the rule: since the name of the Ionian harmonia is similarly absent from Aristotle.
3. The usage of the words harmonia and tonos is never such as to suggest that they refer to different things. In the earlier writers, down to and including Aristotle, harmonia is used, never tonos. In Aristoxenus and his school we find tonos, and in later writers tropos, but not harmonia. The few writers (such as Plutarch) who use both tonos and harmonia do not observe any consistent distinction between them. Those who (like Westphal) believe that there was a distinction, are obliged to admit that harmonia is occasionally used for tonos and conversely.
4. If a series of names such as Dorian, Phrygian, Lydian and the rest were applied to two sets of things so distinct from each other, and at the same time so important in the practice of music, as what we now call modes and keys, it is incredible that there should be no trace of the double usage. Yet our authors show no sense even of possible ambiguity. Indeed, they seem to prefer, in referring to modes or keys, to use the adverbial forms dôristi, phrygisti, &c., or the neuter ta dôria, ta phrygia, &c., where there is nothing to show whether 'mode' or 'key,' harmonia or tonos, is intended.
§ 15. The Systems of Greek Music.
The arguments in favour of identifying the primitive national Modes (harmoniai) with the tonoi or keys may be reinforced by some considerations drawn from the history and use of another ancient term, namely systêma.
A System (systêma) is defined by the Greek technical writers as a group or complex of intervals (to ek pleionôn ê henos diastêmatôn synkeimenon Ps. Eucl.). That is to say, any three or more notes whose relative pitch is fixed may be regarded as forming a particular System. If the notes are such as might be used in the same melody, they are said to form a musical System (systêma emmeles). As a matter of abstract theory it is evident that there are very many combinations of intervals which in this sense form a musical System. In fact, however, the variety of systems recognised in the theory of Greek music was strictly limited. The notion of a small number of scales, of a particular compass, available for the use of the musician, was naturally suggested by the ancient lyre, with its fixed and conventional number of strings. The word for string (chordê) came to be used with the general sense of a note of music; and in this way the several strings of the lyre gave their names to the notes of the Greek gamut[8].
§ 16. The Standard Octachord System.
In the age of the great melic poets the lyre had no more than seven strings: but the octave was completed in the earliest times of which we have accurate information. The scale which is assumed as matter of common knowledge in the Aristotelian Problems and the Harmonics of Aristoxenus consists of eight notes, named as follows from their place on the lyre: