Page:Vitruvius the Ten Books on Architecture.djvu/176

142 parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, paranete synhemmenon, trite die­zeugmenon, paranete diezeugmenon, trite hyperbolaeon, para­nete hyperbolaeon.

6. These notes, from being moveable, take on different quali­ties; for they may stand at different intervals and increasing dis­tances. 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. Hence the ten notes produce three different kinds of modes on account of their changes of position in the classes.

7. There are five tetrachords: first, the lowest, termed in Greek ; second, the middle, called ; third, the conjunct, termed, fourth, the disjunct, named ; the fifth, which is the highest, is termed in Greek. The concords, termed in Greek, of which human modulation will natur­ally admit, are six in number: the fourth, the fifth, the octave, the octave and fourth, the octave and fifth, and the double octave.

8. Their names are therefore due to numerical value; for when the voice becomes stationary on some one note, and then, shift­ing its pitch, changes its position and passes to the limit of the fourth note from that one, we use the term "fourth"; when it passes to the fifth, the term is "fifth."

9. For there can be no consonancies either in the case of the notes of stringed instruments or of the singing voice, between two intervals or between three or six or seven; but, as written above, it is only the harmonies of the fourth, the fifth, and so on up to the double octave, that have boundaries naturally corres­ponding to those of the voice: and these concords are produced by the union of the notes.