Ptolemy's different genera, like all those in ancient times, were bounded by the fixed framework notes which delimited each tetrachord. In the reference tetrachord (meson), these notes are namely mese (ratio 1/1) and hypate (a 4/3 ratio below mese).
Below is a table showing the pitches of the moveable notes ocurring in all shades of Ptolemy's genera. Also shown are some of the xenharmonic-bridges posited by Joe Monzo, which connect notes of the same name across Ptolemy's different genera.
Ptolemy's genera - moveable notes
parhypate / trite
genus shade monzo ratio cents Semitones
3 5 7 11 23
diatonic even [ 2, 0 0 -1 0 > 18 / 11 852.5920594 8.53
diatonic tense [ 0, -1 0 0 0 > 8 / 5 813.6862861 8.14
diatonic ditonic [-4, 0 0 0 0 > 128 / 81 792.1799965 7.92
diatonic tonic [-2, 0 1 0 0 > 14 / 9 764.9159047 7.65
diatonic relaxed [ 2, -1 1 0 0 > 63 / 40 786.4221943 7.86
chromatic tense [ 0, 0 -1 1 0 > 11 / 7 782.4920359 7.82
chromatic relaxed [-2, 0 1 0 0 > 14 / 9 764.9159047 7.65
enharmonic [-1, -1 0 0 1 > 23 / 15 740.0056325 7.40
some xenharmonic-bridges:
[-6, 1 -1 0 0 > 5120 / 5103 5.757802203 0.06
[-4, 0 1 -1 0 > 896 / 891 9.687960643 0.1
[ 2, -1 2 -1 0 > 441 / 440 3.930158439 0.04
[ 4, 0 -1 -1 0 > 81 / 77 87.67615463 0.88
[ 3, 1 0 -1 -1 > 270 / 253 112.5864268 1.13
lichanos / paranete
diatonic even [ 2, -1 0 0 0 > 9 / 5 1017.596288 10.18
diatonic tense [ 2, -1 0 0 0 > 9 / 5 1017.596288 10.18
diatonic ditonic [-2, 0 0 0 0 > 16 / 9 996.0899983 9.96
diatonic tonic [-2, 0 0 0 0 > 16 / 9 996.0899983 9.96
diatonic relaxed [ 0, 0 1 0 0 > 7 / 4 968.8259065 9.69
chromatic tense [ 1, 0 -1 0 0 > 12 / 7 933.1290944 9.33
chromatic relaxed [-1, 1 0 0 0 > 5 / 3 884.358713 8.84
enharmonic [ 0, -1 0 0 0 > 8 / 5 813.6862861 8.14
one xenharmonic-bridge:
[ 2, 0 0 0 0 > 9 / 8 203.9100017 2.04
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