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Thus, parhypate, which in the enharmonic is at the interval of half a semitone from hypate, has a semitone interval when transferred to the chromatic. What is called lichanos in the enharmonic is at the interval of a semitone from hypate; but when shifted to the chromatic, it goes two semitones away; and in the diatonic it is at an interval of three semitones from hypate.
But it holds the chief and highest power, as mese to hypate, in respect of the concupiscent; as mese to nete, in respect of the irascible; insomuch as it depresses and heightens, and in fine makes a harmony, by abating what is too much and by not suffering them to flatten and grow dull. For what is moderate and symmetrous is defined by mediocrity.
Their names are proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon. The moveable notes are those which, being arranged in the tetrachord between the immoveable, change from place to place according to the different classes.
If the theatre be of no great size, mark out a horizontal range halfway up, and in it construct thirteen arched niches with twelve equal spaces between them, so that of the above mentioned "echea" those which give the note nete hyperbolaeon may be placed first on each side, in the niches which are at the extreme ends; next to the ends and a fourth below in pitch, the note nete diezeugmenon; third, paramese, a fourth below; fourth, nete synhemmenon; fifth, mese, a fourth below; sixth, hypate meson, a fourth below; and in the middle and another fourth below, one vessel giving the note hypate hypaton.
Indeed, according to the natural system of the parts, the place of the irascible faculty must be in the middle, and of the rational in the highest, which the Greeks call hypate.
But it may be ridiculous to describe the first, middle, and last by their place; since we see hypate highest in the harp, lowest in the pipe; and wheresoever you place the mese in the harp, provided it is tunable, it sounds more acute than hypate, and more grave than nete. Nor does the eye possess the same place in all animals; but whereever it is placed, it is natural for it to see.
But I wonder Lamprias did not mind what the Delphians say in this matter; for they affirm that the Muses amongst them were not named so either from the strings or sounds in music; but the universe being divided into three parts, the first portion was of the fixed stars, the second of the planets, the third of those things that are under the concave of the moon; and all these are ordered according to harmonical proportions, and of each portion a Muse takes care; Hypate of the first, Nete of the last, and Mese in the middle, combining as much as possible, and turning about mortal things with the gods and earthly with heavenly.
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