Carlos Gamma

Carlos Gamma is a non-octave equal temperament whose step size is 35.0985422804 cents^[1].

It is very close to the equal division of the just perfect fifth into twenty parts of 35.0978 cents each (20ED3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale. Carlos's original gamma scale has the fifth just slightly sharp (about 0.2 cents) in order to evenly spread out the tuning error amongst a large set of JI intervals.

Carlos Gamma divides the octave in [math]\displaystyle{ \frac{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)} }[/math] ≃ 34.189454 equal steps and the fifth in 19.999549 equal steps of 35.098542 cents each.

Theory

Article by Wendy Carlos

Gamma is a non-octave scale created by Wendy Carlos. It is closely related to the gammic temperament.

Lookalikes: 34edo, 54edt, 96ed7

Intervals

The first steps up to two just perfect fifths should give a feeling of the granularity of this system…

Degrees	ed233\420-5¢	ed31\54	ed121/81 (~ed11\19)	ed696¢ (~69ed4!)	ed32\55	ed700¢=r¢	ed3/2	Pyrite		ed708¢	ed122/81 (~ed13\22)	ed34\57	ed37\60+5¢
Degrees	ed233\420-5¢	ed31\54	ed121/81 (~ed11\19)	ed696¢ (~69ed4!)	ed32\55	ed700¢=r¢	ed3/2	(~ed17\29)	(~ed10\17)	ed708¢	ed122/81 (~ed13\22)	ed34\57	ed37\60+5¢
1	33.04-33.29	34.44	34.74	34.8	34.91	35	35.1	35.18	35.29	35.4	35.45	35.79	37-37.25
2	66.07-66.57	68.89	69.48	69.6	69.82	70	70.2	70.36	70.59	70.8	70.91	71.58	74-74.5
3	99.11-99.86	103.33	104.22	104.4	104.73	105	105.29	105.545	105.88	106.2	106.36	107.37	111-111.75
4	132.14-133.14	137.78	138.96	139.2	139.64	140	140.39	140.72	141.17	141.6	141.81	143.16	148-149
5	165.18-166.43	172.22	173.7	174	174.545	175	175.49	175.91	176.46	177	177.27	178.95	185-186.25
6	198.21-199.71	206.67	208.445	208.8	209.455	210	210.59	211.09	211.76	212.4	212.72	214.74	222-223.5
7	231.25-233	241.11	243.19	243.6	244.36	245	245.68	246.27	247.05	247.8	248.17	250.53	259-260.75
8	264.29-266.29	275.56	277.93	278.4	279.27	280	280.78	281.45	282.34	283.2	283.63	286.32	296-298
9	297.32-299.57	310	312.67	313.2	314.18	315	315.88	316.64	317.635	318.6	319.08	322.105	333-335.25
10	330.35-332.86	344.44	347.41	348	349.09	350	350.98	351.82	352.93	354	354.53	357.895	370-372.5
11	363.39-366.14	378.89	382.15	382.8	384	385	386.075	387	388.22	389.4	389.99	393.68	407-409.75
12	396.43-399.43	413.33	416.89	417.6	418.91	420	421.17	422.18	423.51	424.8	425.44	429.47	444-447
13	429.46-432.71	447.78	451.63	452.4	453.82	455	456.27	457.36	458.81	460.2	460.89	465.26	481-484.25
14	462.5-466	482.22	486.37	487.2	488.73	490	491.37	492.545	494.1	495.6	496.345	501.05	518-521.5
15	495.54-499.29	516.67	521.11	522	523.64	525	526.47	527.73	529.39	531	531.8	536.84	555-558.75
16	528.57-532.57	551.11	555.85	556.8	558.545	560	561.56	562.91	564.68	566.4	567.25	572.63	592-596
17	561.61-565.86	585.56	590.59	591.6	593.455	595	596.66	598.09	599.98	601.8	602.705	608.42	629-633.25
18	594.64-599.14	620	625.33	626.4	628.36	630	631.76	633.27	635.27	637.2	638.16	644.21	666-670.5
19	627.68-632.43	654.44	660.075	661.2	663.27	665	666.86	668.45	670.56	672.6	673.61	680	703-707.75
20	660.71-665.71	688.89	694.82	696	698.18	700	701.955	703.64	705.86	708	709.065	715.79	740-745
21	693.75-699	723.33	729.56	732.8	733.09	735	737.05	738.82	741.15	743.4	744.52	751.58	777-782.25
22	726.79-732.29	757.78	764.3	765.6	768	770	772.15	774	776.44	778.8	779.97	787.37	814-819.5
23	759.82-765.57	792.22	799.04	800.4	802.91	805	807.25	809.18	811.73	813.2	815.425	823.16	851-856.75
24	792.86-798.86	826.67	833.78	835.2	837.82	840	842.35	844.36	847.03	848.6	850.88	858.95	888-894
25	825.89-832.14	861.11	868.52	870	872.73	875	877.44	879.545	882.32	885	886.33	894.74	925-931.25
26	858.93-865.43	895.6	903.26	904.8	907.64	910	912.54	914.73	917.61	920.4	921.78	930.53	962-968.5
27	891.96-898.71	930	938	939.6	942.545	945	947.64	949.91	952.905	955.8	957.24	966.32	999-1005.75
28	925-932	964.4	972.74	974.4	977.455	980	982.74	985.09	988.2	991.2	992.69	1002.105	1036-1043
29	958.04-965.29	998.89	1007.48	1009.2	1012.36	1015	1017.835	1020.27	1023.49	1026.6	1028.14	1039.895	1073-1081.25
30	991.07-998.57	1033.33	1042.22	1044	1047.27	1050	1052.93	1055.45	1058.78	1062	1063.6	1073.68	1110-1117.5
31	1024.11-1031.86	1067.78	1076.965	1078.8	1082.18	1085	1088.03	1090.64	1094.08	1097.4	1099.05	1109.47	1147-1154.75
32	1057.14-1065.14	1102.22	1111.705	1113.6	1117.09	1120	1123.13	1125.82	1129.37	1132.8	1134.5	1145.26	1184-1192
33	1090.18-1098.43	1136.67	1146.45	1148.4	1152	1155	1158.23	1161	1164.66	1168.2	1169.96	1181.05	1221-1229.25
34	1123.21-1131.71	1171.1	1181.19	1183.2	1186.91	1190	1193.32	1196.18	1199.95	1203.6	1205.41	1216.84	1258-1266.5
35	1156.25-1165	1205.56	1215.93	1218	1221.82	1225	1228.42	1231.36	1235.25	1239	1240.86	1252.63	1295-1303.75
36	1189.29-1198.29	1240	1250.67	1252.8	1256.73	1260	1263.52	1266.545	1270.54	1274.4	1276.32	1288.42	1332-1341
37	1222.32-1231.57	1274.44	1285.41	1287.6	1291.64	1295	1298.62	1301.73	1305.83	1309.8	1311.77	1324.42	1369-1377.25
38	1255.36-1263.86	1308.89	1320.15	1322.4	1326.545	1330	1333.715	1336.91	1341.125	1345.2	1347.22	1360	1406-1415.5
39	1288.39-1298.14	1343.33	1354.89	1357.2	1361.455	1365	1368.81	1372.09	1376.42	1380.6	1382.68	1395.79	1443-1452.75
40	1321.43-1331.43	1377.78	1389.6	1392	1396.36	1400	1403.91	1407.27	1411.71	1416	1418.13	1431.6	1480-1490