User:Moremajorthanmajor/42wtn
A 42 tone well tempered nonet (42WTN) is related to well temperaments of 36edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 21 equal parts (21EDF) with sequences of twenty-one equal steps of 28.5714 to 38.0952 cents each. This will create twenty-one equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
Patent Intervals
| Target | Alternating edo and *ed(9/8) | |
|---|---|---|
| 1 | 33.4264 | 33.3333 |
| 2 | 66.8529 | 66.6667 |
| 3 | 100.2793 | 100 |
| 4 | 133.7057 | 133.3333 |
| 5 | 167.1321 | 166.6667 |
| 6 | 200.5586 | 200 |
| 7 | 233.985 | 233.3333 |
| 8 | 267.4114 | 266.6667 |
| 9 | 300.8379 | 300 |
| 10 | 334.2643 | 333.3333 |
| 11 | 367.6907 | 366.6667 |
| 12 | 401.1171 | 400 |
| 13 | 434.5436 | 433.3333 |
| 14 | 467.97 | 466.6667 |
| 15 | 501.3964 | 500.00 |
| 16 | 534.8229 | 533.3333 |
| 17 | 568.2493 | 566.6667 |
| 18 | 601.6757 | 600 |
| 19 | 635.1021 | 633.3333 |
| 20 | 668.5286 | 666.6667 |
| 21 | 701.955 | 700 |
| 22 | 735.158 | 733.3333 |
| 23 | 768.361 | 766.6667 |
| 24 | 801.564 | 800 |
| 25 | 834.767 | 833.3333 |
| 26 | 867.97 | 866.6667 |
| 27 | 901.173 | 900 |
| 28 | 934.376 | 933.3333 |
| 29 | 967.579 | 966.6667 |
| 30 | 1000.782 | 1000 |
| 31 | 1033.985 | 1033.3333 |
| 32 | 1067.188 | 1066.6667 |
| 33 | 1100.391 | 1100 |
| 34 | 1133.594 | 1133.3333 |
| 35 | 1166.797 | 1166.6667 |
| 36 | 1200 | 1200 |
| 37 | 1233.203 | 1233.985 |
| 38 | 1266.406 | 1267.97 |
| 39 | 1299.609 | 1301.995 |
| 40 | 1332.812 | 1335.94 |
| 41 | 1366.015 | 1369.925 |
| 42 | 1399.218 | 1403.91 |