User:Moremajorthanmajor/9edX

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This is the neutral scale of the Middletown temperament family.

Intervals

Degrees	Intense Aeolian-Subpental Dorian			Dorian
				Subpental			Pental			Superpental
	Min-comma	Med	Max+comma~Min-comma		Med	Max+comma~Min-comma		Med	Max+comma~Min-comma		Med	Max+comma
1	155.556-160	161.905	158.5185-167.407		164.103	162.222-171.111		168.889	165.2525-174.141		170.37	171.429-175.873
2	311.111-320	323.8095	317.037-334.814		328.205	324.444-342.222		337.778	330.505-348.283		340.741	342.857-351.746
3	466.667-480	485.714	475.556-502.222		492.308	486.667-513.333		506.667	495.758-522.424		511.111	514.286-527.619
4	622.222-640	647.619	634.074-669.63		656.41	648.889-684.444		675.556	661.01-696.566		681.4815	685.714-703.492
5	777.778-800	809.524	792.593-837.037		820.512	811.111-855.556		844.444	826.263-870.707		851.852	857.143-878.365
6	943.333-960	971.429	951.111-1004.444		984.615	973.333-1026.667		1013.333	988.515-1044.848		1022.222	1028.571-1055.238
7	1088.889-1120	1133.333	1109.63-1171.852		1148.718	1135.556-1197.778		1182.222	1156.768-1218.99		1192.593	1200-1231.111
8	1244.444-1280	1295.238	1238.148-1339.259		1312.8205	1297.778-1368.889		1351.111	1321.02-1392.131		1362.963	1371.429-1406.984

Degrees	Mohajira				Beatles
	Min-comma	r¢	Med	Max+comma~Min-comma		Med	Max+comma
1	166.984-171.429	172.222		168.105-176.9935		172.8395	173.333-177.778
2	333.968-342.857	344.444		336.209-353.987		345.679	346.667-355.556
3	500.952-514.286	516.667		504.314-530.98		518.5185	520-533.333
4	667.9365-685.714	688.889		672.418-707.974		691.358	693.333-711.111
5	834.921-857.143	861.111		840.523-885.967		864.1975	866.667-888.889
6	1001.904-1028.571	1033.333		1008.6275-1062.961		1037.037	1040-1066.667
7	1168.889-1200	1205.556		1176.732-1239.954		1209.8765	1213.333-1244.444
8	1335.873-1371.429	1377.778		1344.837-1416.948		1382.716	1386.667-1422.222

Degrees	Mixolydian												Mixolydian-Ionian
	Subpental			Pental			Superpental
							Soft			Intense
	Min-comma	Med	Max+comma~Min-comma		Med	Max+comma~Min-comma		Med	Max+comma~Min-comma		Med	Max+comma~Min-comma		Med	Max+comma
1	168.889-173.333	174.359	170.556-179.444		175.439	173.333-182.222		179.167	174.866-183.755		181.609	179.464-188.3525		184.314	186.667-191.111
2	337.778-346.667	348.718	341.111-358.889		350.877	346.667-364.444		358.333	349.732-367.51		363.218	368.927-376.705		368.6275	373.333-382.222
3	506.667-520	523.077	511.667-538.333		526.316	520-546.667		537.5	524.598-551.264		544.828	538.391-565.0575		552.941	560-573.333
4	675.556-693.333	697.436	682.222-717.778		701.754	693.333-728.889		716.667	699.464-735.019		726.437	717.854-753.41		737.255	746.667-764.444
5	844.444-866.667	871.795	852.778-897.222		877.193	866.667-911.111		895.833	874.3295-918.774		908.046	897.318-942.7625		921.569	933.333-955.556
6	1013.333-1040	1046.154	1023.333-1076.667		1052.632	1040-1093.333		1075	1049.195-1102.529		1089.655	1076.782-1130.115		1105.882	1120-1146.667
7	1182.222-1213.333	1220.513	1193.889-1256.111		1228.07	1213.333-1275.556		1254.167	1224.061-1286.2835		1271.264	1256.245-1318.457		1290.196	1306.667-1337.778
8	1351.111-1386.667	1394.872	1364.444-1435.556		1403.509	1386.667-1457.778		1433.333	1398.927-1470.038		1452.874	1438.709-1506.82		1474.51	1493.333-1528.889

Relative cents

Degrees	Intense Aeolian-Subpental Dorian	Dorian	Subpental-Soft Superpental Mixolydian	Intense Superpental Mixolydian ~ Mixolydian-Ionian
1	161.111	166.667	177.778	183.333
2	322.222	333.333	355.556	366.667
3	483.333	500	533.333	550
4	644.444	666.667	711.111	733.333
5	805.556	833.333	888.889	916.667
6	966.667	1000	1066.667	1100
7	1127.778	1166.666	1244.444	1283.333
8	1288.889	1333.333	1422.222	1466.667

Golden/Pyrite Tunings±13¢

Degrees	Intense Aeolian-Subpental Dorian	Dorian
		Subpental	Pental	Superpental
1	160.761-163.65	162.317-165.2055	167.6965-170.585	168.741-171.63
2	321.522-327.3	364.633-330.411	335.393-341.171	337.483-343.36
3	482.284-490.95	486.95-495.617	503.089-511.756	506.224-514.891
4	643.045-654.6	649.2665-660.822	670.786-682.341	674.965-686.521
5	803.806-818.25	811.583-826.028	838.482-852.927	843.707-858.151
6	964.567-981.9	973.9-991.233	1006.179-1023.512	1012.448-1029.781
7	1125.328-1145.55	1136.216-1156.439	1173.875-1194.0975	1181.189-1201.411
8	1286.09-1309.2	1278.2435-1321.644	1341.572-1343.36	1349.9305-1373.042

Degrees	Mohajira	Beatles
1	170.877-173.776	171.314-174.203
2	341.755-347.513	342.627-348.405
3	512.632-521.2985	513.941-522.607
4	683.509-695.065	685.255-696.81
5	854.386-868.831	856.568-870.112
6	1025.264-1042.597	1027.882-1045.215
7	1196.141-1216.363	1199.196-1219.418
8	1367.018-1389.119	1370.5095-1393.621

Degrees	Mixolydian				Mixolydian-Ionian
	Subpental	Pental	Superpental
			Soft	Intense
1	173.091-175.98	173.844-176.733	177.774-180.663	180.707-183.596	182.729-185.618
2	346.182-351.96	347.688-353.466	355.548-361.325	361.415-367.193	365.4585-371.236
3	519.2735-527.94	521.532-530.199	533.321-541.988	542.122-550.789	548.188-556.854
4	692.365-703.92	695.376-706.932	711.095-722.651	722.83-734.385	730.917-742.4725
5	865.456-879.9	869.22-883.6645	888.896-903.3135	903.537-917.982	913.646-928.091
6	1038.547-1055.88	1043.064-1060.3975	1033.634-1083.976	1084.245-1101.578	1096.3755-1113.709
7	1211.638-1231.86	1216.908-1237.13	1244.417-1264.639	1264.952-1285.174	1279.105-1299.327
8	1384.729-1407.84	1390.752-1413.863	1422.19-1445.3015	1445.6595-1445.821	1461.834-1484.945

By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of 34edo. Additionally, those of the Golden Subpental Dorian and Pental and Intense Superpental Mixolydian tenths are almost exactly every third step of 22edo, 4edf and equal multiples of 10/9 respectively.

See also

• 9ed5/2 - equal division of the classic major tenth
• 9ed7/3 - equal division of the septimal minor tenth