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
|
|
|
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
|