User:Moremajorthanmajor/18wtn: Difference between revisions
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'''18WTN''' is the non-octave well temperament where [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. | '''18WTN''' is the non-octave well temperament with patent tunings where [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. | ||
== Optimal Intervals == | == Optimal Intervals == | ||
Revision as of 18:00, 31 May 2021
18WTN is the non-octave well temperament with patent tunings where equal division of the just perfect fifth into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine 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 | 77.995 | |||
| 2 | 155.99 | |||
| 3 | 233.985 | |||
| 4 | 311.98 | |||
| 5 | 389.975 | |||
| 6 | 467.97 | |||
| 7 | 545.965 | |||
| 8 | 623.96 | |||
| 9 | 701.955 | |||
| 10 | 781.955 | 787.669 | 770.526 | 775.424 |
| 11 | 861.955 | 873.384 | 839.098 | 848.893 |
| 12 | 941.955 | 959.098 | 907.669 | 921.363 |
| 13 | 1021.955 | 1044.812 | 976.241 | 995.833 |
| 14 | 1101.955 | 1130.526 | 1044.812 | 1069.302 |
| 15 | 1181.955 | 1216.241 | 1113.384 | 1142.771 |
| 16 | 1261.955 | 1301.955 | 1181.955 | 1216.241 |
| 17 | 1341.955 | 1387.669 | 1250.526 | 1289.71 |
| 18 | 1421.955 | 1473.384 | 1319.098 | 1363.2245 |
Valentine Tunings
| fifth 2 = 9\16 | fifth 2 = 18\31 | fifth 2 = Carlos Alpha | fifth 2 = 3\5 | |
|---|---|---|---|---|
| 1 | 77.995 | |||
| 2 | 155.99 | |||
| 3 | 233.985 | |||
| 4 | 311.98 | |||
| 5 | 389.975 | |||
| 6 | 467.97 | |||
| 7 | 545.965 | |||
| 8 | 623.96 | |||
| 9 | 701.955 | |||
| 10 | 776.955 | 779.374 | 779.92 | 781.955 |
| 11 | 851.955 | 856.794 | 857.885 | 861.955 |
| 12 | 925.955 | 934.213 | 935.85 | 941.955 |
| 13 | 1001.955 | 1011.632 | 1013.815 | 1021.955 |
| 14 | 1076.955 | 1089.051 | 1091.78 | 1101.955 |
| 15 | 1151.955 | 1166.471 | 1169.745 | 1181.955 |
| 16 | 1226.955 | 1243.8905 | 1247.71 | 1261.955 |
| 17 | 1301.955 | 1321.31 | 1325.675 | 1341.955 |
| 18 | 1376.955 | 1398.729 | 1403.64 | 1421.955 |
| Fifths | ||||
| 1 | 698.96 | 701.379 | 701.925 | 703.96 |
| 2 | 695.965 | 700.803 | 701.895 | 705.965 |
| 3 | 692.97 | 700.228 | 701.865 | 707.97 |
| 4 | 689.975 | 699.652 | 701.835 | 709.975 |
| 5 | 686.98 | 699.077 | 701.805 | 711.98 |
| 6 | 683.985 | 698.501 | 701.775 | 713.985 |
| 7 | 680.99 | 697.9255 | 701.745 | 715.99 |
| 8 | 677.995 | 697.35 | 701.715 | 717.995 |
| 9 | 675 | 696.774 | 701.685 | 720 |
| 10 | 677.995 | 697.35 | 701.715 | 717.995 |
| 11 | 680.99 | 697.9255 | 701.745 | 715.99 |
| 12 | 683.985 | 698.501 | 701.775 | 713.985 |
| 13 | 686.98 | 699.077 | 701.805 | 711.98 |
| 14 | 689.975 | 699.652 | 701.835 | 709.975 |
| 15 | 692.97 | 700.228 | 701.865 | 707.97 |
| 16 | 695.965 | 700.803 | 701.895 | 705.965 |
| 17 | 698.96 | 701.379 | 701.925 | 703.96 |
| 18 | 701.955 | |||