ハルモニア(音階)の有するエートスの問題

As is well known, in the Respublica III Plato remarks many kinds of harmoniai, among which he selects the Dorian and the Phrygian as fitting subject matter for education of the young The aim of this paper is firstly to find out the real nature of Dorian and other harmoniai The detailed structures are shown in the additional paragraph of Aristides Quintihanus (Arq)' De Musica I ch 9 as old-fashioned harmoniai, according to which we can guess that Plato's Dorian is akin to the form of disjunction of two tetrachords, the standard style of a scale of an octave On the other hand the rationalized styles of harmoniai as the species of an octave are also described in Arq (I ch 8) These structures correspond to the modes of Western Medieval and Renaissance music Historically speaking the standard schema of an octave has developed through Terpander's improvement Terpander's schema has been guessed to be conjunction of tetrachords added the tonos uppermost But this schema shows the Mixolydian octave instead of the Dorian To be Dorian the schema must be the form of disjunction As an evidence of the disjunct octave we can take up Nicomachus' description of Philolaus' scale in the Enchilidion ch 9 This passage is opposed to the description of Pythagoras' scale (Ench ch 5), which is an improvement of the old-fashioned conjunct scale Compared to Nicomachus' passages we can conclude that Terpander's schema must have been the disjunct schema devoid of the trite Terpander arranged the old-fashioned Dorian which had appeared much earlier into the rationalized schema of the disjunct octave Contrary to the Dorian the other old-fashioned harmoniai are supposed to come into existence respectively These traces could be seen in Plutarch's description (mainly on the Mixolydian) So the rationalized style of harmoniai which form the species of an octave should have come into existence somewhat later They might have been constructed artificially about BC430 when Eratocles (an inventor of the circularity of a scale) and Damon were both in their akme Plato's so called Dorianism is supposed to be a reaction against the overflowing of ethos of his age But Plato was not a theorist of harmonics, so he was unable to make an actual reformation It was Aristoxenus (Arx ) who reformed the musical situation by replacing the species with tonoi (pitch) Each tonos is also the same fragment as the species of an octave, but there is a central note, the mese, around which all of the other notes move As the mese works as a central note, many kinds of ethos in the species of an octave disappear, and the scale is reduced to the Dorian The system of tonos presupposes the Great Perfect System (GPS), two octaves system which has the mese as a central note Usually GPS wasconjectured to be arranged about at the middle of the 4^<th> century BC and succeeded by Arx , but I assert as a conclusion that it was invented by Arx constructing the system of tonos