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contains three semitones. The diatonic tetrachord has 
two consecutive tones, and an interval of a semitone. 
Thus in each genus, the whole tetrachord is equal to two 
whole tones and a semitone. But the intervals in each 
genus, differ when considered separately. For nature 
has made the divisions of tones, semitones, and tetra- 
chords, and has established those proportions of the in- 
tervals, by which workmen are guided in making and 
assigning their just proportions to instruments. Each 
genus consists of eighteen sounds, which the Greeks 
call ø6óyyot (phthongi). Of these, eight sounds in each 
of the genera, vary neither in sound nor situation. The 
remaining ten in each are not common to the other two 
genera. Those which do not vary, contain between 
them the variable sounds, and are the limits of the tetra- 
chords in all the genera. Their names are as follow: 
proslambanomenos, hypatè hypatôn, hypatè mesôn, mese 
neté synèmmenôn, paramesè, netè diezeugmenôn, netè 
hyperbolæön. The variable, which lie between those 
that are not variable, change their places according to 
the genus. Their names are parhypatè hypatôn, lichanos 
hypätön, parhypatè mesôn, lichanos mesôn, tritè synèm- 
menön, paranetè synemmenön, tritè diezeugmenön, 
paranetè diezeugmenôn, tritè hyperbolæôn, paranetè 
hyperbolæôn. Those sounds which shift their places, 
change also their nature, and are at different intervals, 
as, for instance, the interval between hypatè and parhy- 
paté, 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 semi- 
tones. Thus the ten sounds, by their situation in the 
different genera, make three different sorts of melody. 
There are five tetrachords. The Greeks call the lowest 
vrarov (hypaton); the second, which is in the middle, 
pégov (meson). The third, which is joined to the two