User:Moremajorthanmajor/18wtn

18WTN is the non-octave well temperament 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.

Theory

The best tunings of 18WTN are very closely related to Carlos Alpha and valentine temperament. For a list of 11-limit dyadic chords of Carlos Alpha, see Chords of valentine.

They have a very good representation of the 7:8:10:11:12 chord from the harmonic series.

Intervals

	“fifth” 2 = 600¢	“nonet” = 1351.429¢	“nonet” = 1460¢	“fifth” 2 = 800¢
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	768.622	774.119	786.182	790.844
11	835.288	846.2825	870.409	879.733
12	901.955	918.446	954.637	968.622
13	968.622	990.61	1038.864	1057.511
14	1035.288	1062.774	1123.091	1146.399
15	1101.955	1134.937	1207.318	1235.288
16	1168.622	1207.101	1291.546	1324.177
17	1235.288	1279.265	1375.773	1413.066
18	1301.955	1351.429	1460	1501.955

Common 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	1225.955	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