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 | 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 |
| 13 | 730.001 | |
| 14 | 232.308 | 8/7 |
| 15 | 934.616 | |
| 16 | 436.924 | |
| 17 | 1139.232 | |
| 18 | 641.539 | |
| 19 | 143.847 | |
| 20 | 846.155 | |
| 21 | 348.463 | |
| 22 | 1050.770 | |
| 23 | 553.078 | 11/8 |
| 24 | 55.386 | |
| 25 | 757.694 | |
| 26 | 260.001 | |
| 27 | 962.309 | |
| 28 | 464.617 | |
| 29 | 1166.925 | |
| 30 | 669.232 | |
| 31 | 171.540 | |
| 32 | 873.848 | |
| 33 | 376.156 | |
| 34 | 1078.463 | |
| 35 | 580.771 | 7/5 |
| 36 | 83.079 | 21/20, 22/21 |
| 37 | 785.387 | 11/7 |
| 38 | 287.694 | |
| 39 | 990.002 | |
| 40 | 492.310 | |
| 41 | 1194.618 | |
| 42 | 696.925 | |
| 43 | 199.233 | |
| 44 | 901.541 | |
| 45 | 403.849 | |
| 46 | 1106.156 | |
| 47 | 608.464 | |
| 48 | 110.772 | |
| 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 | |
| 63 | 1045.388 | |
| 64 | 547.696 | |
| 65 | 50.003 | |
| 66 | 752.311 | |
| 67 | 254.619 | |
| 68 | 956.927 | |
| 69 | 459.234 | |
| 70 | 1161.542 | 88/45 |
| 71 | 663.850 | 22/15 |
| 72 | 166.158 | 11/10 |
| 73 | 868.465 | |
| 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 | |
| 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 | |
| 99 | 1128.467 | |
| 100 | 630.775 | |
| 101 | 133.082 | 27/25 |
| 102 | 835.390 | |
| 103 | 337.698 | |
| 104 | 1040.005 | |
| 105 | 542.313 | |
| 106 | 44.621 | |
| 107 | 746.929 | |
| 108 | 249.236 | |
| 109 | 951.544 | |
| 110 | 453.852 | |
| 111 | 1156.160 | |
| 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 | |
| 122 | 481.545 | |
| 123 | 1183.853 | |
| 124 | 686.160 | |
| 125 | 188.468 | |
| 126 | 890.776 | |
| 127 | 393.084 | |
| 128 | 1095.391 | |
| 129 | 597.699 | |
| 130 | 100.007 | |
| 131 | 802.315 | |
| 132 | 304.622 | |
| 133 | 1006.930 | |
| 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
| 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 |