Cotoneum: Difference between revisions

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Revision as of 22:24, 29 May 2021

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
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