User:Moremajorthanmajor/14edIX

This scale, a Long Common Practice minor mode,occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis 6L 2s 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	85.714	89.143	91.429	94.286		95.798	97.959		100	102.857
2	G	171.429	178.286	182.857	188.571		191.597	195.918		200	205.714
3	G#/Ab	257.143	267.429	274.286	282.857		287.395	293.878		300	308.571
4	A	342.857	356.571	365.714	377.143		383.193	391.836		400	411.429
5	A#/Bb	428.571	445.714	467.143	471.429		478.992	489.796		500	514.286
6	B	514.286	534.857	548.571	565.714		574.79	587.755		600	617.143
7	H	600	624	640	660		670.588	685.714		700	720
8	H#/Cb	685.714	713.143	731.429	754.286		766.387	783.6735		800	822.857
9	C	771.429	802.286	822.857	848.571		862.185	881.633		900	925.714
10	C#/Db	857.143	891.429	914.286	942.857		957.983	979.592		1000	1028.571
11	D	942.857	980.571	1005.714	1037.143		1053.7815	1077.551		1100	1131.429
12	D#/Eb	1028.571	1069.714	1097.143	1131.429		1149.58	1175.51		1200	1234.286
13	E	1114.286	1158.857	1188.571	1225.714		1245.378	1273.469		1300	1337.143
14	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	93.317-95.1745	96.572-98.429	99.351-101.208
2	G	186.635-190.349	193.1435-196.858	198.701-202.416
3	G#/Ab	279.952-285.5235	289.715-295.287	298.052-303.624
4	A	373.269-380.698	386.287-393.7155	397.403-404.831
5	A#/Bb	466.587-475.872	482.859-492.144	496.754-506.039
6	B	559.904-571.047	579.43-590.573	596.104-607.247
7	H	653.224-666.221	676.002-689.002	695.455-708.455
8	H#/Cb	746.539-761.396	772.574-787.431	794.805-809.663
9	C	839.856-856.57	869.146-885.86	894.156-910.871
10	C#/Db	933.173-951.745	965.717-984.289	993.507-1012.079
11	D	1026.491-1046.919	1062.289-1082.718	1092.858-1113.286
12	D#/Eb	1119.808-1142.094	1158.861-1181.1465	1192.209-1214.494
13	E	1213.1255-1237.268	1255.4325-1279.575	1291.559-1315.702
14	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	Min-Max-13c
1	F#/Gb	89.855	90.235	90.783	91.164	91.334	91.712	92.092	98.531
2	G	179.709	180.47	181.566	182.327	182.667	183.4235	184.184	197.061
3	G#/Ab	269.564	270.705	272.35	273.491	274.001	275.135	276.276	295.592
4	A	359.4185	360.94	363.133	364.654	365.335	366.847	368.3685	394.123
5	A#/Bb	449.273	451.175	453.916	455.818	456.6685	458.559	460.461	492.653
6	B	539.128	541.41	544.699	546.981	548.002	550.271	552.553	591.184
7	H	628.982	631.645	635.482	638.145	639.336	641.982	644.645	689.7145
8	H#/Cb	718.837	721.88	726.2655	729.3085	730.67	733.694	736.737	788.245
9	C	808.692	812.115	817.049	820.472	822.003	825.406	828.829	886.776
10	C#/Db	898.546	902.35	907.832	911.636	913.337	917.118	920.921	985.306
11	D	988.401	992.585	998.615	1002.799	1007.671	1008.829	1013.013	1083.837
12	D#/Eb	1078.255	1082.82	1089.398	1093.963	1096.004	1100.541	1105.106	1182.368
13	E	1168.11	1173.055	1180.1815	1185.126	1187.338	1192.253	1197.198	1280.898
14	F	1257.965	1263.29	1270.965	1276.29	1278.672	1283.965	1289.29	1379.429

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	94.4665	95.308	95.395	96.237	96.324	97.165	97.737
2	G	188.933	190.616	190.79	192.473	192.647	194.3305	195.475
3	G#/Ab	283.399	285.924	286.185	288.71	288.971	291.496	293.212
4	A	377.866	381.228	381.58	384.947	385.294	388.661	390.949
5	A#/Bb	472.332	476.5405	476.975	481.183	481.618	485.826	488.687
6	B	566.799	571.849	572.37	577.42	577.942	582.9915	586.424
7	H	661.265	667.157	667.765	673.658	674.265	680.157	684.161
8	H#/Cb	755.732	762.465	763.16	769.893	770.589	777.322	781.899
9	C	850.198	857.773	858.555	866.13	866.912	874.487	879.636
10	C#/Db	944.665	953.081	953.95	962.367	963.236	971.652	977.373
11	D	1039.131	1048.298	1049.345	1058.603	1059.56	1068.818	1075.111
12	D#/Eb	1113.5975	1143.697	1144.74	1154.84	1155.883	1165.983	1172.848
13	E	1228.064	1239.005	1240.435	1251.077	1252.207	1263.148	1270.585
14	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	98.531	98.666	99.459	99.5945	100.043	100.388	100.971	101.9
2	G	197.061	197.332	198.918	199.189	200.085	200.776	201.943	203.8
3	G#/Ab	295.592	295.998	298.377	298.783	300.128	301.163	302.913	305.6995
4	A	394.123	394.664	397.839	398.378	400.171	401.551	403.885	407.599
5	A#/Bb	492.653	493.3295	497.296	497.972	500.2135	501.939	504.856	509.499
6	B	591.184	591.9955	597.755	597.567	600.256	602.327	605.828	611.399
7	H	689.7145	690.661	696.2145	697.161	700.299	702.7145	706.799	713.299
8	H#/Cb	788.245	789.327	795.674	796.756	800.342	803.102	807.77	815.199
9	C	886.776	887.993	895.133	896.35	900.384	903.49	908.7415	917.099
10	C#/Db	985.306	986.659	994.592	995.945	1000.427	1003.878	1009.713	1018.9985
11	D	1083.837	1085.325	1094.051	1095.539	1100.47	1104.266	1110.684	1120.898
12	D#/Eb	1182.368	1183.991	1193.5105	1195.134	1200.512	1204.653	1211.655	1222.798
13	E	1280.898	1282.657	1292.97	1294.728	1300.555	1305.041	1312.627	1324.698
14	F	1379.429	1381.322	1392.429	1394.322	1400.598	1405.429	1413.598	1426.598