editing disabled

Division of the sixth harmonic into n equal parts


The sixth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see 44ed6 and 49ed6). However, this is not to say of ed6s not supporting this important 13&18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.

4ed6 squares generator (with octaves)
5ed6 tritonic generator (with octaves)
6ed6 compare 7ed8
7ed6 sensi generator (with octaves)
8ed6 würschmidt generator (with octaves)
9ed6 compare 7ed4
10ed6 myna generator (with octaves)
11ed6 compare 17ed16
12ed6 compare 14ed8
13ed6 compare 5edo and 8edt
14ed6
15ed6
16ed6 hemiwuerschimdt generator (with octaves)
17ed6 Minortonic generator (with octaves)
18ed6 compare 7edo and 11edt
19ed6 Porcupine generator (with octaves)
20ed6
21ed6 progression generator (with octaves)
22ed6 compare 17ed4
23ed6 compare 9edo and 14edt
24ed6 twothirdtonic generator (with octaves)
25ed6
26ed6 compare 10edo and 16edt
27ed6
28ed6
29ed6
30ed6
31ed6 compare 12edo and 19edt
32ed6
33ed6
34ed6
35ed6 octacot generator (with octaves)
36ed6 compare 14edo and 22edt
37ed6
38ed6
39ed6 compare 15edo and 24edt
40ed6 valentine generator (with octaves)
41ed6 compare 16edo and 25edt
42ed6
43ed6
44ed6 compare 17edo and 27edt
45ed6
46ed6
47ed6
48ed6 compare 56ed8
49ed6 compare 19edo and 30edt
50ed6
51ed6
52ed6 compare 20edo and 32edt
53ed6
54ed6 compare 21edo and 33edt
55ed6
56ed6
57ed6 compare 22edo and 35edt
58ed6
59ed6
60ed6
61ed6
62ed6 compare 24edo and 38edt
63ed6
64ed6
65ed6 (compare 25edo and 40edt)
66ed6 compare 51ed4
67ed6 compare 26edo and 41edt
68ed6
69ed6
70ed6 compare 27edo and 43edt
71ed6 compare 55ed4
72ed6 compare 28edo and 44edt
73ed6
74ed6
75ed6 compare 29edo and 46edt