Let us now consider the relation between this fixed or standard scale and the varieties denoted by the terms harmonia and tonos.

With regard to the tonoi or Keys of Aristoxenus we are not left in doubt. A system, as we have seen, is a series of notes whose relative pitch is fixed. The key in which the System is taken fixes the absolute pitch of the series. As Aristoxenus expresses it, the Systems are melodies set at the pitch of the different keys (tous tonous, eph' hÔn tithemena ta systÊmata melÔdeitai). If then we speak of HypatÊ or MesÊ (just as when we speak of a moveable Do), we mean as many different notes as there are keys: but the Dorian HypatÊ or the Lydian MesÊ has an ascertained pitch. The Keys of Aristoxenus, in short, are so many transpositions of the scale called the Perfect System.

Such being the relation of the standard System to the key, can we suppose any different relation to have subsisted between the standard System and the ancient 'modes' known to Plato and Aristotle under the name of harmoniai?

It appears from the language used by Plato in the Republic that Greek musical instruments differed very much in the variety of modes or harmoniai of which they were susceptible. After Socrates has determined, in the passage quoted above (p. 7), that he will admit only two modes, the Dorian and Phrygian, he goes on to observe that the music of his state will not need a multitude of strings, or an instrument of all the modes (panarmonion) [15]. 'There will be no custom therefore for craftsmen who make triangles and harps and other instruments of many notes and many modes. How then about makers of the flute (aulos) and players on the flute? Has not the flute the greatest number of notes, and are not the scales which admit all the modes simply imitations of the flute? There remain then the lyre and the cithara for use in our city; and for shepherds in the country a syrinx (pan's pipes).' The lyre, it is plain, did not admit of changes of mode. The seven or eight strings were tuned to furnish the scale of one mode, not of more. What then is the relation between the mode or harmonia of a lyre and the standard scale or systÊma which (as we have seen) was based upon the lyre and its primitive gamut?

If harmonia means 'key,' there is no difficulty. The scale of a lyre was usually the standard octave from HypatÊ to NÊtÊ: and that octave might be in any one key. But if a mode is somehow characterised by a particular succession of intervals, what becomes of the standard octave? No one succession of intervals can then be singled out. It may be said that the standard octave is in fact the scale of a particular mode, which had come to be regarded as the type, viz. the Dorian. But there is no trace of any such prominence of the Dorian mode as this would necessitate. The philosophers who recognise its elevation and Hellenic purity are very far from implying that it had the chief place in popular regard. Indeed the contrary was evidently the case [16].