'The Mixo-lydian, too, is pathetic and suitable to tragedy. And Aristoxenus says that Sappho was the inventor of the Mixo-lydian, and that from her the tragic poets learned it. They combined it with the Dorian, since that mode gives grandeur and dignity, and the other pathos, and these are the two elements of tragedy. But in his Historical Treatise on Music ([Greek: historika tês harmonias hypomnêmata]) he says that Pythoclides the flute-player was the discoverer of it. And Lysis says that Lamprocles the Athenian, perceiving that in it the disjunctive tone ([Greek: diazeuxis]) is not where it was generally supposed to be, but is at the upper end of the scale, made the form of it to be that of the octave from Paramesê to Hypatê Hypatôn ([Greek: toiouton autês apergasasthai to schêma hoion to apo paramesês epi hypatên hypatôn]). Moreover, it is said that the relaxed Lydian ([Greek: epaneimenên Lydisti]), which is the opposite of the Mixo-lydian, being similar to the Ionian ([Greek: paraplêsian ousan tê Iadi]), was invented by Damon the Athenian.' 'These modes then, the one plaintive, the other relaxed ([Greek: eklelymenê]), Plato properly rejected, and chose the Dorian, as befitting warlike and temperate men.' In this passage the 'high-pitched Lydian' ([Greek: Syntonolydisti]) of Plato is called simply Lydian. There is every reason to suppose that it is the mode called Lydian by Aristotle and Heraclides Ponticus[1]. If this is so, it follows almost of necessity that the Lydian of Plato, called slack ([Greek: chalara]) by him--Plutarch's [Greek: epaneimenê Lydisti]--is to be identified with the later Hypo-lydian. [Footnote 1: An objection to this identification has been based on the words of Pollux, _Onom._ iv. 78 [Greek: kai harmonia men aulêtikê Dôristi, Phrygisti, Lydios kai Iônikê, kai syntonos Lydisti ên Anthippos exeure]. The source of this statement, or at least of the latter part of it, is evidently the same as that of the notice in Plutarch. The agreement with Plato's list makes it probable that this source was some comment on the passage in the _Republic_. If so, it can hardly be doubted that Pollux gives the original terms, the Platonic [Greek: Lydisti] and [Greek: Syntonolydisti], and consequently that the later Lydian is not to be found in his [Greek: Lydios] (which is a 'relaxed' mode), but in his [Greek: syntonos Lydisti]. There is no difficulty in supposing that the mode was called [Greek: syntonos] merely in contrast to the other.] The point, however, is not free from difficulty: for (as we have seen, p. 18), the name Hypo-lydian is not in the list of keys given by Aristoxenus--the key which was ultimately called Hypo-lydian being known to him as the Hypo-dorian. If, however, the confusion in the nomenclature of the keys was as great as Aristoxenus himself describes, such a contradiction as this cannot be taken to prove much[1].