User:Moremajorthanmajor/13edIX

This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.

Intervals

Degrees	Octatonic	Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)				Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)			Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Degrees	Octatonic	Absolute Minimum	Minimum	Median	Maximum	Minimum	Median	Maximum	Minimum	Median	Maximum
1	F#/Gb	92.308	97.582	98.4615	101.5385		103.167	105.4945		107.692	110.769
2	G	184.615	195.165	196.923	203.077		206.335	210.989		215.385	221.5385
3	G#/Ab	276.923	292.747	295.385	304.615		309.502	316.4835		323.077	332.308
4	A	369.231	390.33	393.846	406.154		412.67	421.978		430.769	443.076
5	B	461.5385	487.912	491.308	507.692		515.837	527.4725		538.4615	553.846
6	B#/Hb	553.846	585.4945	589.769	609.231		619.0045	632.967		646.154	664.615
7	H	646.154	683.077	690.231	710.769		722.172	738.4615		754.846	775.385
8	C	738.4615	780.66	788.692	812.308		825.339	843.856		861.5385	886.154
9	C#/Db	830.769	878.242	896.154	913.846		929.507	949.4505		969.231	996.923
10	D	923.077	975.824	984.615	1015.385		1031.674	1054.945		1076.923	1107.692
11	D#/Eb	1015.385	1073.407	1083.077	1116.923		1134.842	1160.44		1184.615	1218.4615
12	E	1107.692	1170.99	1181.5385	1218.4615		1238.009	1265.9348		1292.308	1329.231
13	F	1200	1268.571	1280	1320		1341.1765	1371.429		1400	1440

Most harmonic tunings

Degrees	Octatonic	Phrygian Mode (natural minor)	Phrygian-Aeolian Mode (intermediate minor)	Aeolian Mode (melodic/harmonic minor)
Degrees	Octatonic	15/7±13¢	11/5±13¢	9/4±13¢
1	F#/Gb	100.496-102.496	104-106	106.993-108.993
2	G	200.991-204.912	208.001-212.001	213.986-217.986
3	G#/Ab	301.487-307.487	312.001-318.001	320.979-326.979
4	A	401.982-409.982	416.001-424.001	427.972-435.972
5	B	502.478-512.478	520.002-530.002	534.965-544.965
6	B#/Hb	602.974-614.974	624.002-636.002	641.9585-653.9585
7	H	703.469-717.469	728.002-742.0022	748.9515-762.9515
8	C	803.965-819.965	832.003-848.002	855.945-871.945
9	C#/Db	904.46-922.46	936.003-924.003	962.938-980.938
10	D	1004.956-1024.956	1040.003-1060.003	1069.931-1089.931
11	D#/Eb	1105.452-1127.452	1144.004-1166.004	1177-924-1199.924
12	E	1205.947-1299.947	1248.004-1272.004	1283.917-1307.917
13	F	1306.443-1332.443	1352.004-1378.004	1390.91-1416.91

Golden Tunings

Phrygian Mode (natural minor)

Degrees	Octatonic	Min-Med-13c	Min-Max-13c	Min-Med	Min-Max	Med-Max-13c	Min-Med+13c	Min-Max+13c	Med-Max	Med-Max+13c
1	F#/Gb	96.7665	97.176	97.7665	98.176	98.359	98.7665	99.176	99.359	100.359
2	G	193.533	194.352	195.533	196.352	196.719	197.533	198.352	198.719	200.719
3	G#/Ab	291.2995	291.528	293.2995	294.528	295.078	296.2995	297.528	298.078	301.078
4	A	388.063	389.705	391.063	392.705	393.4375	394.063	396.705	397.4375	401.4375
5	B	484.833	486.881	488.833	490.881	492.797	492.833	495.881	496.797	501.797
6	B#/Hb	581.299	583.057	586.299	589.057	591.156	591.299	595.057	596.156	602.156
7	H	678.366	681.233	684.366	687.233	689.516	690.366	694.233	695.516	702.516
8	C	775.132	778.409	782.132	785.409	787.875	789.132	793.409	794.875	802.875
9	C#/Db	871.899	874.585	879.899	883.585	886.234	888.899	891.585	894.234	903.234
10	D	967.665	971.761	977.665	981.761	984.594	987.665	991.761	993.594	1003.594
11	D#/Eb	1067.432	1068.9375	1075.432	1079.9375	1082.953	1086.432	1091.9375	1092.953	1103.953
12	E	1162.198	1166.114	1173.198	1178.114	1181.312	1185.198	1190.114	1192.312	1204.312
13	F	1257.965	1263.29	1270.965	1276.29	1278.672	1283.965	1289.29	1291.672	1304.672

Phrygian-Aeolian Mode (intermediate minor)

Degrees	Octatonic	Min-Med/Min-Max-13c	Med-Max-13c	Min-Med/Min-Max	Med-Max	Min-Med/Min-Max+13c	Med-Max+13c	Min-Med-13c (Aeolian)
1	F#/Gb	101.733	102.639	102.733	103.639	103.733	104.639	105.256
2	G	203.466	205.279	205.466	207.279	207.466	205.279	210.511
3	G#/Ab	305.199	311.9185	308.199	310.9185	311.199	313.9185	315.767
4	A	406.932	410.558	410.932	414.558	414.932	418.558	421.022
5	B	508.6655	513.1975	513.6655	518.1975	518.6655	523.1975	526.278
6	B#/Hb	610.399	615.837	616.399	621.837	622.399	627.837	631.534
7	H	712.132	718.4765	719.132	725.4765	726.132	732.4765	736.789
8	C	813.865	821.116	821.865	829.116	829.865	837.116	842.045
9	C#/Db	915.598	923.755	924.598	932.755	933.598	941.755	947.3
10	D	1017.331	1026.395	1027.331	1036.395	1037.331	1046.395	1052.556
11	D#/Eb	1119.064	1129.034	1130.064	1140.034	1141.064	1151.034	1157.8115
12	E	1220.797	1231.674	1232.797	1243.674	1244.797	1255.674	1264.067
13	F	1322.53	1334.313	1335.53	1347.313	1348.53	1360.313	1368.322

Aeolian Mode (melodic/harmonic minor)

Degrees	Octatonic	Min-Max-13c	Min-Med	Min-Max	Min-Med+13c	Med-Max-13c	Min-Max+13c	Med-Max	Med-Max+13c
1	F#/Gb	106.11	106.256	107.11	107.256	107.738	108.11	108.738	109.738
2	G	212.22	212.511	214.22	214.511	215.477	216.22	217.477	219.477
3	G#/Ab	318.33	318.767	321.33	321.767	323.215	324.33	326.215	329.215
4	A	424.44	425.022	428.44	429.022	430.953	432.44	434.953	438.953
5	B	530.55	531.278	535.55	536.278	538.6915	540.55	543.6915	548.6915
6	B#/Hb	636.6595	637.534	642.6595	643.534	646.43	648.6595	652.43	658.43
7	H	742.769	743.789	749.769	750.789	754.168	756.769	761.168	768.168
8	C	848.879	850.045	856.879	858.045	861.906	864.879	869.906	877.906
9	C#/Db	954.989	956.3	963.989	965.3	969.645	972.989	978.645	986.645
10	D	1061.099	1062.556	1071.099	1072.556	1077.383	1081.099	1087.383	1077.383
11	D#/Eb	1167.209	1168.8115	1178.209	1179.8115	1185.121	1189.209	1196.121	1207.121
12	E	1273.319	1275.067	1285.319	1287.067	1392.86	1297.319	1304.86	1317.86
13	F	1379.429	1381.322	1392.429	1394.322	1400.598	1405.429	1413.598	1426.598