User:Moremajorthanmajor/15edX

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15edX is the scale which occurs as the dominant minor edX (equal division of a tenth interval).

Intervals

Degrees	Enneatonic		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	G#/Jb	G#/Ab	93.333-96	97.143	95.111-100.444		98.4615	97.333-102.667		101.333	99.1515-104.485		102.222	102.857-105.524
2	J	A	186.667-192	194.286	190.222-200.889		196.923	194.667-205.333		202.667	198.303-208.97		204.444	205.714-211.048
3	J#/Ab	A#/Bb	280-288	291.429	285.333-301.333		295.385	292-308		304	297.4545-313.4545		306.667	308.571-316.571
4	A	B	373.333-384	388.571	380.444-401.778		393.846	389.333-410.667		405.333	396.606-417.939		408.889	411.429-422.095
5	B	C	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
6	B#/Cb	C#/Qb	560-576	582.857	570.667-602.667		590.769	584-616		608	594.909-626.909		613.333	617.143-633.143
7	C	Q	653.333-672	680	665.778-703.111		689.231	681.333-718.667		709.333	694.061-731.394		715.556	720-738.667
8	C#/Qb	Q#/Db	746.667-768	757.143	760.889-803.556		787.692	778.667-821.333		810.667	793.212-835.879		817.778	822.857-844.1905
9	Q	D	840-864	874.286	856-904		886.154	876-924		912	892.364-940.364		920	925.714-949.714
10	D	S	933.333-960	971.429	951.111-1004.444		984.615	973.333-1026.667		1013.333	991.515-1044.8485		1022.222	1028.571-1055.238
11	D#/Eb	S#/Eb	1026.667-1056	1068.571	1046.222-1104.889		1083.077	1070.667-1129.333		1114.667	1090.667-1149.333		1124.444	1131.429-1160.761
12	E		1120-1152	1165.714	1141.333-1205.333		1181.5385	1168-1232		1216	1189.818-1253.818		1226.667	1234.286-1266.286
13	E#/Fb		1213.333-1248	1262.857	1236.444-1305.778		1280	1265.333-1334.667		1317.333	1288.97-1358.303		1328.889	1337.143-1371.8095
14	F		1306.667-1344	1360	1331.556-1406.222		1378.4615	1363.667-1437.333		1418.667	1388.121-1462.788		1431.111	1440-1477.333
15	G		1400-1440	1457.143	1426.667-1506.667		1476.923	1460-1540		1520	1487.273-1567.273		1533.333	1542.857-1582.857

Degrees	Enneatonic				Mohajira				Beatles
					Min-comma	r¢	Med	Max+comma~Min-comma		Med	Max+comma
1	F#/Gb		G#/Jb	G#/Ab	100.1905-102.857	103.333		100.863-106.196		103.704	104-106.667
2	G		J	A	200.381-205.714	206.667		201.7255-212.392		207.407	208-213.333
3	G#/Jb	G#/Ab	J#/Ab	A#/Bb	300.571-308.571	310		302.588-318.588		311.111	312-320
4	J	A	A	B	400.702-411.429	413.333		403.451-424.784		414.815	416-426.667
5	A	B	B	C	500.952-514.286	516.667		504.314-530.98		518.5185	520-533.33
6	A#/Bb	B#/Hb	B#/Cb	C#/Qb	601.143-617.143	620		605.1765-637.1765		622.222	624-640
7	B	H	C	Q	701.333-720	723.333		706.04-743.3725		725.926	728-746.667
8	B#/Hb	H#/Cb	C#/Qb	Q#/Db	801.524-822.857	826.667		806.902-849.569		829.63	832-853.333
9	H	C	Q	D	901.714-925.714	930		907.765-955.765		933.333	936-960
10	C	D	D	S	1001.905-1048.571	1033.333		1008.6275-1061.961		1037.037	1040-1066.667
11	C#/Db	D#/Sb	D#/Eb	S#/Eb	1102.095-1131.429	1136.667		1109.49-1168.157		1140.741	1144-1173.333
12	D	S	E		1202.286-1234.286	1240		1210.353-1274.353		1244.444	1248-1280
13	D#/Eb	S#/Eb	E#/Fb		1302.476-1337.143	1343.333		1311.216-1380.549		1348.148	1352-1386.667
14	E		F		1402.667-1440	1446.667		1412.078-1486.745		1451.852	1456-1493.333
15	F		G		1502.857-1542.857	1550		1512.941-1592.941		1555.556	1560-1600

Degrees	Enneatonic		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	F#/Gb		101.333-104	104.615	102.333-107.667		105.263	104-109.333		107.5	104.9195-110.253		108.9655	107.678-113.0115		110.588	112-114.667
2	G		202.667-208	209.231	204.667-215.333		210.526	208-218.667		215	209.809-220.506		217.931	215.356-226.023		221.1765	224-229.333
3	G#/Jb	G#/Ab	304-312	313.846	307-323		315.7895	312-328		322.5	314.759-330.759		326.897	323.0345-339.0345		331.765	336-344
4	J	A	405.333-416	418.4615	409.333-435.667		421.053	416-437.333		430	419.678-441.0115		435.862	430.713-452.046		442.353	448-458.667
5	A	B	516.667-520	523.077	511.667-538.333		526.316	520-546.667		537.5	524.598-541.264		544.828	538.391-565.0575		552.941	560-573.333
6	A#/Bb	B#/Hb	608-624	627.692	614-646		631.579	624-656		645	629.517-661.517		653.793	646.069-678.069		663.529	672-688
7	B	H	709.333-728	732.308	716.333-753.667		736.842	728-765.333		752.5	734.437-771.77		762.759	753.747-791.0805		774.118	784-802.667
8	B#/Hb	H#/Cb	810.666-832	836.923	818.667-861.333		842.103	832-874.667		860	839.356-882.023		871.724	861.425-904.092		884.706	896-917.333
9	H	C	912-936	941.5385	921-969		947.368	936-984		967.5	944.276-992.276		980.69	969.103-1007.103		995.294	1008-1032
10	C	D	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
11	C#/Db	D#/Sb	1114.667-1144	1150.769	1125.667-1184.333		1157.895	1144-1202.667		1182.5	1154.115-1212.782		1198.621	1184.46-1243.126		1216.471	1232-1261.333
12	D	S	1216-1248	1255.385	1228-1292		1263.158	1248-1312		1290	1259.0345-1323.0345		1307.586	1292.138-1356.138		1327.059	1344-1376
13	D#/Eb	S#/Eb	1317.333-1352	1360	1330.333-1399.667		1368.421	1352-1421.333		1397.5	1363.954-1433.287		1416.552	1399.816-1469.149		1437.647	1456-1490.667
14	E		1418.667-1456	1464.615	1432.667-1506.333		1473.684	1456-1530.337		1505	1468.874-1534.54		1525.517	1507.494-1582.161		1548.235	1568-1605.333
15	F		1520-1560	1569.231	1535-1615		1578.947	1560-1640		1612.5	1573.793-1653.793.		1634.483	1615.172-1695.172		1658.8235	1680-1720

Relative cents

Degrees	Enneatonic		Intense Aeolian-Subpental Dorian	Dorian	Subpental-Soft Superpental Mixolydian	Intense Superpental Mixolydian ~ Mixolydian-Ionian
1	G#/Jb	G#/Ab	96.667	100	106.667	110
2	J	A	193.333	200	213.333	220
3	J#/Ab	A#/Bb	290	300	320	330
4	A	B	386.667	400	426.667	440
5	B	C	483.333	500	533.333	550
6	B#/Cb	C#/Qb	580	600	640	660
7	C	Q	676.667	700	746.667	770
8	C#/Qb	Q#/Db	773.333	800	853.333	880
9	Q	D	870	900	960	990
10	D	S	966.667	1000	1066.667	1100
11	D#/Eb	S#/Eb	1063.333	1100	1173.333	1210
12	E		1160	1200	1280	1320
13	E#/Fb		1256.667	1300	1386.667	1430
14	F		1353.333	1400	1493.333	1540
15	G		1450	1500	1600	1650

Golden/Pyrite Tunings±13¢

Degrees	Enneatonic		Intense Aeolian-Subpental Dorian	Dorian
				Subpental	Pental	Superpental
1	G#/Jb	G#/Ab	96.457-98.19	97.39-99.123	100.618-102.351	101.245-102.978
2	J	A	192.913-196.38	194.78-198.247	201.236-204.702	202.49-205.956
3	J#/Ab	A#/Bb	289.37-294.57	292.17-297.37	301.854-204.702	303.734-308.934
4	A	B	385.829-392.76	389.56-396.493	402.4715-307.054	404.979-411.9215
5	B	C	482.284-490.95	486.95-495.617	503.089-511.756	509.502-514.891
6	B#/Cb	C#/Qb	578.74-589.14	584.334-594.74	603.707-614.107	607.469-617.869
7	C	Q	675.197-687.33	681.73-693.863	704.325-716.4585	708.7135-720.847
8	C#/Qb	Q#/Db	771.654-785.52	779.12-792.9865	804.943-818.81	809.958-823.825
9	Q	D	868.1105-883.7105	876.51-892.11	905.561-921.161	911.203-926.823
10	D	S	964.567-981.901	973.9-991.233	1006.179-1023.512	1012.448-1029.781
11	D#/Eb	S#/Eb	1061.024-1080.091	1071.39-1090.356	1106.797-1125.863	1113.693-1132.759
12	E		1157.481-1178.281	1168.68-1189.48	1207.4145-1228.2145	1214.9375-1235.7375
13	E#/Fb		1253.937-1276.471	1266.07-1288.603	1308.032-1330.566	1316.182-1338.716
14	F		1350.394-1374.661	1363.46-1387.726	1408.65-1432.917	1417.427-1441.694
15	G		1446.851-1472.851	1460.85-1486.85	1509.268-1535.268	1518.672-1544.672

Degrees	Enneatonic				Mohajira	Beatles
1	F#/Gb		G#/Jb	G#/Ab	102.526-104.26	102.788-104.5215
2	G		J	A	205.053-208.519	205.576-209.431
3	G#/Jb	G#/Ab	J#/Ab	A#/Bb	307.579-312.779.	308.365-313.565
4	J	A	A	B	410.1055-417.099	411.153-418.086
5	A	B	B	C	512.632-521.2985	513.941-522.607
6	A#/Bb	B#/Hb	B#/Cb	C#/Qb	615.158-625.558	616.729-627.129
7	B	H	C	Q	717.685-729.818	719.5175-731.651
8	B#/Hb	H#/Cb	C#/Qb	Q#/Db	820.211-834.078	822.306-836.172
9	H	C	Q	D	922.737-938.337	925.094-940.694
10	C	D	D	S	1025.264-1042.597	1027.882-1045.215
11	C#/Db	D#/Sb	D#/Eb	S#/Eb	1127.79-1146.857	1130.67-1149.737
12	D	S	E		1230.316-1251.116	1233.459-1254.259
13	D#/Eb	S#/Eb	E#/Fb		1332.843-1355.376	1336.247-1358.78
14	E		F		1435.369-1459.666	1439.035-1463.302
15	F		G		1537.8955-1563.8955	1541.823-1577.823

Degrees	Enneatonic		Mixolydian				Mixolydian-Ionian
			Subpental	Pental	Superpental
					Soft	Intense
1	F#/Gb		103.855-105.788	104.306-106.04	106.664-108.398	108.4245-110.158	109.6375-111.371
2	G		207.709-211.576	208.613-212.08	213.329-216.795	216.849-220.316	219.275-222.742
3	G#/Jb	G#/Ab	311.564-317.364	312.919-318.119	319.993-325.193	325.273-330.473	328.913-334.113
4	J	A	415.419-423.152	417.226-424.159	426.657-433.5905	433.698-440.631	438.55-445.4835
5	A	B	519.2735-528.94	521.532-530.199	533.321-541.988	542.122-550.789	548.188-556.854
6	A#/Bb	B#/Hb	623.128-634.728	625.8385-636.238	639.987-650.386	650.547-660.947	657.825-668.225
7	B	H	726.983-740.516	730.145-742.278	746.65-758.783	758.971-771.105	767.463-779.596
8	B#/Hb	H#/Cb	830.8375-844.704	834.451-848.318	853.314-867.181	867.396-881.262	877.1-890.967
9	H	C	934.693-952.092	938.758-954.358	959.9785-975.5785	975.82-991.42	986.738-1002.338
10	C	D	1038.547-1057.88	1043.064-1060.3975	1066.643-1083.976	1084.245-1101.578	1096.3755-1113.709
11	C#/Db	D#/Sb	1142.402-1163.668	1147.3705-1166.437	1173.307-1192.374	1192.669-1211.736	1206.013-1225.08
12	D	S	1246.256-1269.456	1251.677-1272.477	1279.971-1300.771	1301.0395-1321.8935	1315.651-1336.451
13	D#/Eb	S#/Eb	1353.111-1275.244	1355.983-1378.517	1386.636-1409.169	1409.518-1425.288	1438.993-1447.8215
14	E		1453.966-1481.032	1460.29-1484.556	1493.3-1517.567	1517.9425-1534.926	1541.778-1559.192
15	F		1557.82-1583.82	1564.596-1590.596	1599.964-1625.964	1626.366-1652.366	1644.563-1670.563

By a surprising coincidence, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden and Pyrite tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Intense Aeolian-Subpental Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.

See also

• 15ed5/2 - equal division of the classic major tenth
• 15ed7/3 - equal division of the septimal minor tenth