User:Moremajorthanmajor/15edX

15edX is the scale which occurs as the dominant minor edX.

Intervals

Degrees	Enneatonic		Minor mode Middletown temperament								Neutral mode Middletown temperament		Major mode Middletown temperament
			Aeolian-Dorian		Dorian						Dorian-Mixolydian		Mixolydian								Mixolydian-Ionian
					Subpental		Pental		Superpental				Subpental		Pental		Superpental
																	Soft		Intense
			Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum	Minimum	Maximum
1	F#/Gb		96	97.778		100		101.818		102.857		104		105		106.667		107.586		110.345		112
2	G		192	195.556		200		203.636		205.714		208		210		213.333		215.172		220.69		224
3	G#/Jb	G#/Ab	288	293.333		300		305.4545		308.571		312		315		320		322.759		331.034		336
4	J	A	384	391.111		400		407.273		411.429		416		420		426.667		430.345		441.379		448
5	A	B	480	488.889		500		509.091		514.286		520		525		533.333		537.931		551.724		560
6	A#/Bb	B#/Hb	576	586.667		600		610.909		617.143		624		630		640		645.517		662.069		672
7	B	H	672	684.444		700		712.727		720		728		735		746.667		753.103		772.414		784
8	B#/Hb	H#/Cb	768	782.822		800		814.5455		822.857		832		845		853.333		860.69		882.759		896
9	H	C	864	880		900		916.364		925.714		936		940		960		968.276		993.103		1008
10	C	D	960	977.778		1000		1018.182		1028.571		1040		1050		1066.667		1075.862		1103.448		1120
11	C#/Db	D#/Sb	1056	1075.556		1100		1120		1131.429		1144		1155		1173.333		1183.448		1213.379		1232
12	D	S	1152	1173.333		1200		1221.818		1234.286		1248		1260		1280		1291.034		1324.138		1344
13	D#/Eb	S#/Eb	1248	1271.111		1300		1323.636		1337.143		1352		1365		1386.667		1398.621		1424.483		1456
14	E		1344	1368.889		1400		1425.4545		1440		1456		1470		1493.333		1506.207		1544.827		1568
15	F		1440	1466.667		1500		1527.273		1542.857		1560		1575		1600		1613.793		1655.172		1680

Golden tunings

Degrees	Enneatonic		Minor mode Middletown temperament				Neutral mode Middletown temperament	Major mode Middletown temperament
			Aeolian-Dorian	Dorian			Dorian-Mixolydian	Mixolydian				Mixolydian-Ionian
				Subpental	Pental	Superpental		Subpental	Pental	Superpental
										Soft	Intense
1	F#/Gb		97.323	98.257	101.4845	102.1115	103.655	104.721	105.173	107.531	109.291	110.504
2	G		194.647	196.513	202.969	204.223	207.31	209.443	210.346	215.032	218.582	221.008
3	G#/Jb	G#/Ab	291.97	294.77	304.454	306.334	310.965	314.164	315.519	322.593	327.873	331.613
4	J	A	389.294	394.027	405.938	408.446	414.6195	418.885	420.639	430.124	437.1345	442.017
5	A	B	486.617	491.283	507.423	510.557	518.274	523.607	525.865	537.655	546.456	552.521
6	A#/Bb	B#/Hb	583.94	589.54	608.907	612.669	621.929	628.328	631.0385	645.186	655.747	663.025
7	B	H	681.364	687.7965	710.392	714.78	725.584	733.0495	736.212	752.717	765.038	773.5235
8	B#/Hb	H#/Cb	778.587	786.053	811.877	816.892	829.239	837.771	841.385	860.248	874.329	884.033
9	H	C	875.9105	884.31	913.361	919.003	932.893	942.492	946.558	967.7785	983.62	994.538
10	C	D	973.234	982.5665	1014.8455	1021.115	1036.549	1047.214	1051.731	1075.3095	1092.911	1105.042
11	C#/Db	D#/Sb	1070.557	1080.823	1116.33	1123.226	1140.204	1151.935	1156.904	1182.84	1202.202	1215.546
12	D	S	1167.881	1179.08	1217.8145	1225.3375	1243.859	1256.656	1262.077	1290.371	1311.4935	1326.051
13	D#/Eb	S#/Eb	1265.204	1277.336	1319.299	1327.449	1347.513	1361.378	1367.25	1397.902	1420.785	1436.555
14	E		1362.527	1375.593	1420.783	1429.56	1451.168	1466.099	1472.423	1505.433	1530.076	1547.059
15	F		1459.851	1473.85	1522.268	1531.672	1554.823	1570.82	1577.596	1612.964	1639.366	1657.563

By a surprising coincidence, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Aeolian-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.