The Ten Books on Architecture, 5.4.6

Vitruvius  Parallel editions

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Gwilt translation

6Those sounds which shift their places, change also their nature, and are at different intervals, as, for instance, the interval between hypatè and parhypatè, which in the enharmonic genus is only a diesis or quarter tone, is in the chromatic genus a semitone. So the lichanos is only a semitone distant from the hypatè in the enharmonic genus; whereas in the chromatic it is two semitones distant, and in the diatonic three semitones. Thus, the ten sounds, by their situation in the different genera, make three different sorts of melody.

Morgan translation

6These 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.