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.

Tuning spectrum

Degrees	Octatonic	Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
		Absolute Minimum	5ed(21/16)	8ed(14/9)	Minimum	3ed(13/11)	4ed(5/4)	10ed(7/4)	Golden	<… -3 0 8|/48	7ed(40/27)	<-18 -4 13|\72	Median	8ed(11/7)	9ed(5/3)	14ed(20/9)	Mean	5ed(4/3)	7edf	ed(15/7)	Maximum
1	F#/Gb	92.308	94.156	95.6145	96	96.403	96.578	96.883	97.098	97.107	97.207	97.42	97.582	97.8115	98.262	98.743	98.769	99.609	100.279	101.496	101.5385
2	G	184.615	188.312	191.229	192	192.8065	193.157	193.765	194.196	194.213	194.414	194.8405	195.164	195.623	196.524	197.486	197.5385	199.218	200.559	202.991	203.077
3	G#/Ab	276.923	282.469	286.843	288	289.21	289.735	290.648	291.293	291.322	291.621	292.261	292.747	293.4345	294.786	286.229	296.308	298.827	300.837	304.487	304.615
4	A	369.231	376.625	382.458	384	385.613	386.314	387.53	388.391	388.429	338.828	389.681	390.329	391.246	393.048	394.9725	395.076	398.436	401.117	405.982	406.154
5	B	461.5385	470.781	478.072	480	482.016	482.892	484.413	485.489	485.537	486.035	487.101	487.912	489.0575	491.31	493.716	493.846	498.045	501.396	507.478	507.692
6	B#/Hb	553.846	564.937	573.687	576	875.419	579.471	581.2955	582.587	582.644	583.242	584.5215	585.4945	586.869	589.5725	592.459	592.615	597.654	601.676	608.974	609.231
7	H	646.154	659.093	669.301	672	674.823	676.049	678.178	679.685	679.752	680.448	681.942	683.077	684.6805	687.835	691.202	691.385	697.263	701.955	710.469	710.769
8	C	738.4615	753.2495	764.916	768	771.226	772.627	775.06	776.782	776.859	777.656	779.362	780.659	782.492	786.097	789.945	790.154	796.872	802.234	811.965	812.308
9	C#/Db	830.769	847.406	860.53	864	867.629	869.206	871.943	873.880	873.966	874.862	876.782	878.242	880.3035	884.359	888.688	888.923	896.481	902.514	913.46	913.846
10	D	923.077	941.562	956.145	960	964.032	965.784	968.826	970.978	971.073	972.07	974.2025	975.824	978.115	982.621	987.431	987.692	996.09	1002.793	1014.956	1015.385
11	D#/Eb	1015.385	1035.718	1051.759	1056	1060.436	1062.363	1065.7085	1068.076	1068.181	1069.277	1071.623	1073.407	1075.9265	1080.882	1086.174	1086.4615	1095.699	1103.072	1116.451	1116.923
12	E	1107.692	1129.874	1147.374	1152	1156.839	1158.941	1162.591	1165.1735	1165.2885	1166.4835	1169.043	1170.989	1173.738	1179.145	1184.9175	1185.231	1195.308	1203.3514	1217.947	1218.4615
13	F	1200	1224.03	1242.988	1248	1253.242	1255.52	1259.474	1262.271	1262.396	1263.6905	1266.463	1268.571	1271.55	1277.407	1283.661	1284	1294.916	1303.631	1319.443	1320

Degrees	Octatonic	Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
		Minimum	8ed(8/5)	10ed(9/5)	2ed(9/8)	9ed(17/10)	ed(28/13)	14ed(16/7)	Golden	ed(13/6)	<17 8 -11|/48	Mean	9ed(12/7)	ed(24/11)	5ed(27/20)	7ed(32/21)	4ed(14/11)	Median	ed(11/5)	3ed(6/5)	Maximum
1	F#/Gb	101.5385	101.711	101.76	101.955	102.071	102.177	102.227	102.733	102.967	103.462	103.5165	103.681	103.895	103.91	104.174	104.377	104.615	105	105.213	105.4945
2	G	203.077	203.422	203.519	203.91	204.143	204.354	204.453	205.466	205.934	206.9245	207.033	207.362	207.79	207.8205	208.348	208.754	209.231	210.001	210.4275	210.989
3	G#/Ab	304.615	305.132	305.279	305.865	306.214	306.53	306.68	308.199	308.901	310.387	310.5465	311.043	311.6855	311.731	312.5225	313.131	313.846	315.001	315.641	316.4835
4	A	406.154	406.843	407.0385	407.82	408.285	408.707	408.907	410.932	411.8685	413.849	414.066	414.724	415.581	415.641	416.697	417.508	418.4615	420.001	420.855	421.978
5	B	507.692	508.554	508.798	509.775	510.3565	510.884	511.134	513.6655	514.836	517.311	517.582	518.405	519.476	519.551	520.871	521.885	523.077	525.002	526.069	527.4725
6	B#/Hb	609.231	610.265	610.558	611.73	612.428	613.061	613.36	616.399	617.803	620.774	621.099	622.086	623.371	623.4615	625.045	626.262	627.692	630.002	631.283	632.967
7	H	710.769	711.976	712.317	713.685	714.499	715.2375	715.587	719.132	720.769	724.236	724.615	725.767	727.266	727.372	729.219	730.639	732.318	735.002	736.496	738.4615
8	C	812.308	813.686	814.077	815.64	816.57	817.414	817.814	821.865	823.737	827.698	828.132	829.448	831.161	831.282	833.393	835.016	836.923	840.003	841.71	843.856
9	C#/Db	913.846	915.397	915.837	917.595	918.462	919.591	920.041	924.598	926.704	931.1605	931.648	933.129	935.056	935.192	937.567	939.393	941.5385	945.003	946.924	949.4505
10	D	1015.385	1017.108	1017.596	1019.55	1020.712	1021.768	1022.267	1027.331	1029.671	1034.623	1035.165	1036.81	1038.952	1039.103	1041.742	1043.77	1046.154	1050.003	1052.138	1054.945
11	D#/Eb	1116.923	1118.819	1119.356	1121.505	1122.784	1123.945	1124.494	1130.064	1132.638	1138.085	1138.681	1140.491	1142.847	1143.013	1145.916	1148.147	1150.769	1155.004	1157.351	1160.44
12	E	1218.4615	1220.529	1221.1155	1223.46	1224.856	1226.1215	1226.721	1232.797	1235.6055	1241.547	1242.198	1244.172	1246.742	1246.923	1250.09	1252.524	1255.385	1260.004	1262.565	1265.9348
13	F	1320	1322.24	1322.875	1325.415	1326.927	1328.298	1238.947	1335.53	1338.573	1345.0095	1345.714	1347.853	1350.637	1350.833	1354.264	1356.901	1360	1365.004	1367.779	1371.429

Degrees	Octatonic	Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
		Minimum	ed(20/9)	Golden	26ed5	Median	9ed(5/3)	ed(9/4)	52ed(180/7)	Mean	4ed(9/7)	26ed(36/7)	ed(16/7)	Maximum
1	F#/Gb	105.4945	106.339	107.11	107.166	107.692	98.262	107.993	108.104	108.132	108.771	109.042	110.09	110.769
2	G	210.989	212.6775	214.22	214.332	214.385	196.524	215.986	216.208	216.264	217.542	218.083	220.181	221.5385
3	G#/Ab	304.615	319.016	321.33	321.498	322.077	294.786	323.979	324.311	324.396	326.313	327.125	330.271	332.308
4	A	421.978	425.355	428.44	428.664	429.769	393.048	431.972	432.415	432.5275	435.084	436.167	440.361	443.076
5	B	527.4725	531.694	535.55	535.83	583.4615	491.31	539.965	540.519	540.659	543.855	545.2085	550.452	553.846
6	B#/Hb	609.231	638.0325	642.6595	642.9945	646.154	589.5725	647.9585	948.943	648.791	652.626	654.25	660.542	664.615
7	H	710.769	744.371	749.769	750.161	753.846	687.835	755.9515	756.727	756.923	761.397	863.292	770.632	775.385
8	C	812.308	850.71	856.879	857.327	861.5385	786.097	863.945	864.83	865.055	870.168	872.334	880.7225	886.154
9	C#/Db	913.846	957.049	963.989	964.493	969.231	884.359	971.938	972.934	973.187	978.939	981.375	990.813	996.923
10	D	1015.385	1063.3875	1071.099	1071.659	1076.923	982.621	1079.931	1081.038	1081.319	1087.71	1090.416	1100.903	1107.692
11	D#/Eb	1116.923	1169.726	1178.209	1178.825	1184.615	1080.882	1187.924	1189.142	1189.4505	1196.481	1199.459	1210.9935	1218.4615
12	E	1218.4615	1276.065	1285.319	1285.991	1292.308	1179.145	1295.917	1297.246	1297.582	1305.252	1308.5	1321.084	1329.231
13	F	1371.429	1382.403	1392.429	1393.157	1400	1277.407	1403.91	1405.3495	1405.714	1414.023	1417.524	1431.174	1440