Cotoneum

Cotoneum temperament is temperament for the 7, 11, 13, 17, and 19 prime limits. It is a member of hemimage temperaments, quince clan, and garischismic clan.

See Hemimage temperaments #Cotoneum for more technical data.

Interval chain

Number of Fifth generators	Cents value*	Approximate Ratios
0	0.000	1/1
1	702.308	3/2
2	204.615	9/8
3	906.923	27/16
4	409.231	19/15
5	1111.539	19/10
6	613.846
7	116.154
8	818.462
9	320.770
10	1023.077
11	525.385
12	27.693	64/63, 65/64, 66/65
13	730.001	32/21
14	232.308	8/7
15	934.616	12/7
16	436.924	9/7
17	1139.232	27/14
18	641.539
19	143.847
20	846.155
21	348.463	11/9
22	1050.770	11/6
23	553.078	11/8
24	55.386	33/32, 65/63
25	757.694
26	260.001
27	962.309
28	464.617	17/13
29	1166.925	51/26, 96/49, 112/57
30	669.232	28/19
31	171.540	21/19
32	873.848
33	376.156
34	1078.463	28/15
35	580.771	7/5
36	83.079	21/20, 22/21
37	785.387	11/7
38	287.694	13/11
39	990.002	39/22
40	492.310
41	1194.618
42	696.925
43	199.233
44	901.541	32/19
45	403.849	24/19
46	1106.156	36/19
47	608.464	27/19, 64/45
48	110.772	16/15
49	813.080	8/5
50	315.387	6/5
51	1017.695	9/5
52	520.003	27/20
53	22.310	81/80
54	724.618
55	226.926
56	929.234
57	431.541
58	1133.849	52/27
59	636.157	13/9
60	138.465	13/12
61	840.772	13/8
62	343.080	39/32
63	1045.388	64/35
64	547.696	48/35
65	50.003	34/33, 36/35
66	752.311	17/11
67	254.619	22/19
68	956.927	33/19
69	459.234
70	1161.542	88/45
71	663.850	22/15
72	166.158	11/10
73	868.465	33/20
74	370.773
75	1073.081
76	575.389
77	77.696
78	780.004
79	282.312
80	984.620
81	486.927
82	1189.235
83	691.543
84	193.851
85	896.158
86	398.466	34/27
87	1100.774	17/9
88	603.082	17/12
89	105.389	17/16
90	807.697
91	310.005
92	1012.313
93	514.620
94	16.928
95	719.236
96	221.544
97	923.851
98	426.159	32/25
99	1128.467	48/25
100	630.775	36/25
101	133.082	27/25
102	835.390
103	337.698
104	1040.005
105	542.313	26/19
106	44.621	39/38
107	746.929
108	249.236	52/45
109	951.544	26/15
110	453.852	13/10
111	1156.160	39/20
112	658.467
113	160.775
114	863.083
115	365.391
116	1067.698
117	570.006
118	72.314
119	774.622
120	276.929
121	979.237	44/25
122	481.545	33/25
123	1183.853	99/50
124	686.160	52/35
125	188.468	39/35
126	890.776
127	393.084
128	1095.391
129	597.699
130	100.007
131	802.315
132	304.622
133	1006.930	34/19
134	509.238
135	11.546
136	713.853
137	216.161	17/15
138	918.469	17/10

* in 19-limit POTE tuning

Tuning spectrum

Gencom: [2 4/3; 343/342 364/363 441/440 595/594 1216/1215 1729/1728]

Gencom map: [⟨1 2 -18 -3 13 29 41 -14], ⟨0 -1 49 14 -23 -61 -89 44]]

Eigenmonzo	Fifth generator	Comments
4/3	701.9550
9/7	702.1928
7/6	702.2086
8/7	702.2267
14/11	702.2295
11/8	702.2312
22/21	702.2371
20/19	702.2399
12/11	702.2438
21/16	702.2476
11/9	702.2575
14/13	702.2894
11/10	702.2917	11 and 13-odd-limit minimax
17/14	702.2925
26/21	702.2939
22/19	702.2956
21/17	702.2958
15/11	702.2965	15, 17, 19, and 21-odd-limit minimax
17/13	702.3010
17/16	702.3029
16/13	702.3037
10/9	702.3058	9-odd-limit minimax
24/17	702.3068
20/17	702.3090
13/12	702.3095
18/17	702.3109
13/10	702.3110
19/15	702.3111
17/15	702.3116
19/17	702.3116
6/5	702.3128	5 and 7-odd-limit minimax
19/18	702.3130
15/13	702.3143
26/19	702.3144
18/13	702.3156
5/4	702.3201
24/19	702.3209
16/15	702.3277
22/17	702.3278
19/16	702.3292
21/20	702.3463
13/11	702.3476
7/5	702.3575
21/19	702.3635
15/14	702.3693
19/14	702.3771