User:Moremajorthanmajor/24wtn: Difference between revisions

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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 alternates [[EDF|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.
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 alternate [[EDF|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.


==Optimal Intervals==
==Optimal Intervals==

Revision as of 18:24, 31 May 2021

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 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.

Optimal Intervals

Minimum a Maximum a Minimum b Maximum b
1 58.49625
2 116.9925
3 175.48875
4 233.985
5 292.48125
6 350.9775
7 409.47375
8 467.97
9 526.46625
10 584.9625
11 643.45875
12 701.955
13 761.955 766.2407 755.2883 759.0979
14 821.955 830.5264 808.6117 816.2407
15 881.955 894.8121 861.955 873.3836
16 941.955 959.0979 915.2883 930.5264
17 1001.955 1023.3836 968.6117 987.6693
18 1061.955 1087.6693 1021.955 1044.8121
19 1121.955 1151.955 1075.2883 1101.955
20 1181.955 1216.2407 1128.6117 1159.0979
21 1241.955 1280.5264 1181.955 1216.2407
22 1301.955 1344.8121 1235.2883 1273.3836
23 1361.955 1409.0907 1288.6117 1330.5264
24 1441.955 1473.3836 1341.955 1387.6693