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 | 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 |