back to list

Equal temperaments

🔗PAULE <ACADIAN/ACADIAN/PAULE%Acadian@...>

Invalid Date Invalid Date
Manuel has just put some wonderful tables on equal temperaments on the
tuning site. To summarize the results for tunings with an integer number of
notes per octave:

(1) (2) (3) (4) (5) (6) (7)
harm- first first first first first second second
onic tuning tuning tuning tuning tuning tuning tuning
limit with with with meeting meeting meeting meeting
consis- unique unique (1)&(2) (1)&(3) (1)&(2) (1)&(3)
tent repre- repre-
repre- senta- senta-
senta- tions tions
tions inclu-
ding
octave
inver-
sions

4 2 3 3 3 3 5 5
5 3 7 9 7 9 9 12
6 3 9 9 9 9 12 12
7 4 14 21 15 27 18 31
8 4 18 21 18 27 22 31
9 5 25 35 26 41 31 46
10 5 34 35 41 41 46 46
11 22 39 57 46 58 58 72
12 22 56 57 58 58 72 72