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
