24wtn

A 24 tone well tempered nonet (24WTN) is related to well temperaments of 20edo and 21edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

Patent Intervals

	Target a	Target b	Alternating edo and *ed(9/8) a	Alternating edo and *ed(9/8) b
1	58.49625		60	57.1429
2	116.9925		120	114.2857
3	175.48875		180	171.4286
4	233.985		240	228.5714
5	292.48125		300	285.7143
6	350.9775		360	342.8571
7	409.47375		420	400.00
8	467.97		480	457.1429
9	526.46625		540	514.2857
10	584.9625		600	571.4286
11	643.45875		660	628.5714
12	701.955		720	685.7143
13	764.2106	757.2933	780	742.8571
14	826.466	812.6317	840	800.00
15	888.7219	867.97	900	857.1429
16	950.9775	923.3083	960	914.285
17	1013.2331	978.6467	1020	971.4286
18	1075.48875	1033.985	1080	1028.5714
19	1137.7444	1089.3233	1140	1085.7143
20	1200	1144.6617	1200.000	1142.8571
21	1262.2556	1200	1250.9775	1200.000
22	1324.511	1255.3383	1301.955	1267.97
23	1386.7669	1310.6767	1352.9325	1333.94
24	1449.0225	1366.015	1403.91

Todo: clarify, unify precision