It will be seen that (with one marked exception) there was agreement about the order of the keys in respect of pitch, and that some at least had reduced the intervals to the succession of tones and semitones which characterises the diatonic scale. The exception is the Mixo-lydian, which some ranked immediately below the Dorian, others above the Lydian. Westphal attributes this strange discrepancy to the accidental displacing of some words in the MSS. of Aristoxenus[1]. However this may be, it is plain that in the time of Aristoxenus considerable progress had been made towards the scheme of keys which was afterwards connected with his name. This may be represented by the following table, in which for the sake of comparison the later Hypo-lydian and Hypo-dorian are added in brackets: Mixo-lydian semitone - { Lydian tone - { Phrygian tone - { Dorian semitone - { Hypo-dorian [Hypo-lydian] tone - { Hypo-phrygian tone - { [Hypo-dorian] [Footnote 1: _Harm._ p. 37, 19 Meib. [Greek: houtô gar hoi men tôn harmonikôn legousi barytaton men ton Hypodôrion tôn tonôn, hêmitoniô de oxyteron toutou ton Mixolydion, toutou de hêmitoniô ton Dôrion, tou de Dôriou tonô ton Phrygion: hôsautôs de kai tou Phrygiou ton Lydion heterô tonô.] Westphal (_Harmonik und Melopöie_ p. 165) would transfer the words [Greek: hêmitoniô ... Mixolydion] to the end of the sentence, and insert [Greek: oxyteron] before [Greek: ton Dôrion]. The necessity for this insertion shows that Westphal's transposition is not in itself an easy one. The only reason for it is the difficulty of supposing that there could have been so great a difference in the pitch of the Mixo-lydian scale. As to this, however, see p. 23 (note). The words [Greek: Hypophrygion aulon] have also been condemned by Westphal (_Aristoxenus_, p. 453). He points out the curious contradiction between [Greek: pros tên tôn aulôn trypêsin blepontes] and the complaint [Greek: ti d' esti pros ho blepontes ... ouden eirêkasin]. But if [Greek: pros tên ... blepontes] was a marginal gloss, as Westphal suggests, it was doubtless a gloss on [Greek: aulon], and if so, [Greek: aulon] is presumably sound. Since the [Greek: aulos] was especially a Phrygian instrument, and regularly associated with the Phrygian mode (as we know from Aristotle, see p. 13), nothing is more probable than that there was a variety of flute called Hypo-phrygian, because tuned so as to yield the Hypo-phrygian key, either by itself or as a modulation from the Phrygian.]