User:Moremajorthanmajor/40wtn: Difference between revisions
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Created page with "A '''40 tone well tempered nonet''' (40WTN) is related to well temperaments of 34edo and 35edo, but with a nonet rather than the 2/1 being constant. Its patent tunings..." |
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! colspan="2" |1403.91 | ! colspan="2" |1403.91 | ||
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[[Category:Well tempered nonet]] | |||
[[Category:34edo]] | |||
[[Category:35edo]] | |||
[[Category:20edf]] | |||
Latest revision as of 17:21, 31 March 2025
A 40 tone well tempered nonet (40WTN) is related to well temperaments of 34edo and 35edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 20 equal parts (20EDF) with sequences of twenty equal steps of 30 to 40 cents each. This will create twenty 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 | 35.1 | 35.294 | 34.286 | |
| 2 | 70.2 | 70.588 | 68.571 | |
| 3 | 105.29 | 105.882 | 102.857 | |
| 4 | 140.39 | 141.1765 | 137.143 | |
| 5 | 175.49 | 176.471 | 171.429 | |
| 6 | 210.59 | 211.765 | 205.714 | |
| 7 | 245.68 | 247.059 | 240 | |
| 8 | 280.78 | 282.353 | 274.286 | |
| 9 | 315.88 | 317.647 | 308.571 | |
| 10 | 350.98 | 352.941 | 342.857 | |
| 11 | 386.075 | 388.235 | 377.143 | |
| 12 | 421.17 | 423.529 | 411.429 | |
| 13 | 456.27 | 458.8235 | 445.714 | |
| 14 | 491.37 | 494.118 | 480 | |
| 15 | 526.47 | 529.412 | 514.286 | |
| 16 | 561.56 | 564.706 | 548.571 | |
| 17 | 596.66 | 600.000 | 582.857 | |
| 18 | 631.76 | 635.294 | 617.143 | |
| 19 | 666.86 | 670.588 | 651.429 | |
| 20 | 701.955 | 705.882 | 685.714 | |
| 21 | 737.53 | 735.158 | 741.1765 | 720 |
| 22 | 773.104 | 768.361 | 776.471 | 754.286 |
| 23 | 808.679 | 801.564 | 811.765 | 788.571 |
| 24 | 844.2535 | 834.767 | 847.059 | 822.857 |
| 25 | 879.828 | 867.97 | 882.353 | 857.143 |
| 26 | 915.403. | 901.173 | 917.647 | 891.429 |
| 27 | 950.9775 | 934.376 | 952.941 | 925.714 |
| 28 | 986.552 | 967.579 | 988.235 | 960 |
| 29 | 1022.127 | 1000.782 | 1023.529 | 994.286 |
| 30 | 1057.701 | 1033.985 | 1058.8235 | 1028.571 |
| 31 | 1093.276 | 1067.188 | 1094.118 | 1062.857 |
| 32 | 1128.851 | 1100.391 | 1129.412 | 1097.143 |
| 33 | 1164.425 | 1133.594 | 1164.706 | 1131.429 |
| 34 | 1200 | 1166.797 | 1200 | 1165.714 |
| 35 | 1235.575 | 1200 | 1233.985 | 1200 |
| 36 | 1271.149 | 1233.203 | 1267.97 | 1240.782 |
| 37 | 1306.724 | 1266.406 | 1301.995 | 1281.564 |
| 38 | 1342.2985 | 1299.609 | 1335.94 | 1322.346 |
| 39 | 1377.873 | 1332.812 | 1369.925 | 1363.128 |
| 40 | 1413.448 | 1366.015 | 1403.91 | |