18WTN is optimally 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. It also has the peculiar property of being a patent wtn related to equal divisions of nonets of two different integer cent sizes.
Patent Intervals
|
|
Target a
|
Target b
|
Alternating edo and *ed(9/8) a
|
Alternating edo and *ed(9/8) b
|
| 1
|
77.995
|
80
|
75
|
| 2
|
155.99
|
160
|
150
|
| 3
|
233.985
|
240
|
225
|
| 4
|
311.98
|
320
|
300
|
| 5
|
389.975
|
400
|
375
|
| 6
|
467.97
|
480
|
450
|
| 7
|
545.965
|
560
|
525
|
| 8
|
623.96
|
640
|
600
|
| 9
|
701.955
|
720
|
675
|
| 10
|
784.9625
|
773.104
|
800
|
750
|
| 11
|
867.97
|
844.253
|
880
|
825
|
| 12
|
950.9775
|
915.403
|
960
|
900
|
| 13
|
1033.985
|
986.552
|
1040
|
975
|
| 14
|
1116.9925
|
1057.701
|
1120
|
1050
|
| 15
|
1200
|
1128.896
|
1200
|
1125
|
| 16
|
1283.0075
|
1200
|
1267.97
|
1200
|
| 17
|
1366.015
|
1262.2556
|
1333.94
|
1301.955
|
| 18
|
1449.0225
|
1324.511
|
1403.91
|
|
|
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
|
Todo: clarify, unify precision