User:Moremajorthanmajor/18wtn: Difference between revisions

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Line 6: Line 6:
!Minimum a
!Minimum a
!Maximum a
!Maximum a
![3\5 83.0075¢]
!Minimum b
!Minimum b
!Maximum b
!Maximum b
|-
|-
| |1
| |1
! colspan="4" |77.995
! colspan="5" |77.995
|-
|-
| |2
| |2
! colspan="4" |155.99
! colspan="5" |155.99
|-
|-
| |3
| |3
! colspan="4" |233.985
! colspan="5" |233.985
|-
|-
| |4
| |4
! colspan="4" |311.98
! colspan="5" |311.98
|-
|-
| |5
| |5
! colspan="4" |389.975
! colspan="5" |389.975
|-
|-
| |6
| |6
! colspan="4" |467.97
! colspan="5" |467.97
|-
|-
| |7
| |7
! colspan="4" |545.965
! colspan="5" |545.965
|-
|-
| |8
| |8
! colspan="4" |623.96
! colspan="5" |623.96
|-
|-
| |9
| |9
! colspan="4" |701.955
! colspan="5" |701.955
|-
|-
| |10
| |10
|781.955
|781.955
|787.669
|787.669
|784.9625
|770.526
|770.526
|775.424
|775.424
Line 45: Line 47:
|861.955
|861.955
|873.384
|873.384
|867.97
|839.098
|839.098
|848.893
|848.893
Line 51: Line 54:
|941.955
|941.955
|959.098
|959.098
|950.9775
|907.669
|907.669
|921.363
|921.363
Line 57: Line 61:
|1021.955
|1021.955
|1044.812
|1044.812
|1033.985
|976.241
|976.241
|995.833
|995.833
Line 63: Line 68:
|1101.955
|1101.955
|1130.526
|1130.526
|1116.9925
|1044.812
|1044.812
|1069.302
|1069.302
Line 69: Line 75:
|1181.955
|1181.955
|1216.241
|1216.241
|1200
|1113.384
|1113.384
|1142.771
|1142.771
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|1261.955
|1261.955
|1301.955
|1301.955
|1273.985
|1181.955
|1181.955
|1216.241
|1216.241
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|1341.955
|1341.955
|1387.669
|1387.669
|1347.97
|1250.526
|1250.526
|1289.71
|1289.71
Line 87: Line 96:
|1421.955
|1421.955
|1473.384
|1473.384
|1421.955
|1319.098
|1319.098
|1363.2245
|1363.2245

Revision as of 22:25, 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 [3\5 83.0075¢] 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
10 781.955 787.669 784.9625 770.526 775.424
11 861.955 873.384 867.97 839.098 848.893
12 941.955 959.098 950.9775 907.669 921.363
13 1021.955 1044.812 1033.985 976.241 995.833
14 1101.955 1130.526 1116.9925 1044.812 1069.302
15 1181.955 1216.241 1200 1113.384 1142.771
16 1261.955 1301.955 1273.985 1181.955 1216.241
17 1341.955 1387.669 1347.97 1250.526 1289.71
18 1421.955 1473.384 1421.955 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
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