Ploidacot/Tetracot/Generator tunings: Difference between revisions

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For most of its generator range, this MOS is the chromatic scale of the family of temperaments which divide the perfect fifth into four equal parts, thus representing 81:80 (the syntonic comma) by +7 or −13 generators. In fact, this comma, which may be exaggerated until the point where it is 60¢, appears as the difference between the generator and the disjunct tone and as the small step when the generator is flatter than 3/20edo.{{todo|cleanup}}
For most of its generator range, [[7L 6s]], [[7L 13s]], and [[13L 7s]] are the chromatic scales of the family of temperaments which divide the perfect fifth into four equal parts, thus representing 81:80 (the syntonic comma) by +7 or −13 generators. In fact, this comma, which may be inflated to as much as 60¢, appears as the difference between the generator and the disjunct tone and as the small step when the generator is flatter than 3/20edo.{{todo|cleanup}}


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Revision as of 15:52, 3 March 2025

For most of its generator range, 7L 6s, 7L 13s, and 13L 7s are the chromatic scales of the family of temperaments which divide the perfect fifth into four equal parts, thus representing 81:80 (the syntonic comma) by +7 or −13 generators. In fact, this comma, which may be inflated to as much as 60¢, appears as the difference between the generator and the disjunct tone and as the small step when the generator is flatter than 3/20edo.

Generator Cents Syntonic comma Cents Generator
1/7 171.429 0 184.615 2/13
6/41 175.61 29.268 20.339 183.051 9/59
23/157 175.796 30.573 21.525 182.96 34/223
17/116 175.862 31.0345 21.951 182.927 25/164
11/75 176 32 22.857 182.857 16/105
16/109 176.147 33.0275 23.841 182.7815 23/151
21/143 176.224 33.5665 24.3655 182.721 30/197
26/177 176.271 33.8983 24.691 182.741 37/243
31/211 176.303 34.171 24.9135 182.72 44/289
36/245 176.3265 34.286 25.075 182.687 51/335
176.328 34.294 25.083 182.686
5/34 176.471 35.294 26.0345 182.609 7/46
24/163 176.687 36.872 27.843 182.4885 33/217
19/129 176.744 37.209 28.07 182.456 26/171
176.781 37.467 28.344 182.435
14/95 176.842 37.895 28.8 182.4 19/125
176.901 38.3065 29.244 182.366
23/156 176.923 38.4615 29.412 182.353 31/204
9/61 177.049 39.344 30.38 182.2875 12/79
22/149 177.181 40.2685 31.414 182.199 29/191
13/88 177.273 40.909 32.143 182.143 17/112
17/115 177.391 41.739 33.103 182.069 22/145
21/142 177.465 42.2535 33.708 182.0225 27/178
25/169 177.515 42.604 33.825 181.9905 32/211
29/196 177.551 42.857 34.426 181.967 37/244
177.553 42.871 34.542 181.958
33/223 177.5785 43.049 34.657 181.9495 42/277
37/250 177.6 43.2 34.839 181.9355 47/310
41/277 177.617 43.321 34.985 181.924 52/343
45/304 177.632 43.421 35.106 181.915 57/376
4/27 177.778 44.444 36.364 181.818 5/33
39/263 177.947 45.585 37.539 181.7035 48/317
35/236 177.966 45.763 38.028 181.69 43/284
31/209 177.99 45.933 38.247 181.673 38/251
27/182 178.022 46.154 38.514 181.651 33/218
23/155 178.0645 46.452 38.919 181.621 28/185
19/128 178.125 46.875 39.474 181.579 23/152
15/101 178.218 47.525 40.336 181.513 18/119
178.252 47.762 40.655 181.488
11/74 178.378 48.649 41.8605 181.395 13/86
29/195 178.4615 49.231 42.667 181.333 34/225
178.476 49.3295 42.8045 181.323
18/121 178.512 49.587 43.1655 181.295 21/139
25/168 178.571 50 43.75 181.25 29/192
178.573 50.009 43.763 181.249
32/215 178.605 50.233 44.082 181.2245 37/245
7/47 178.723 51.063 45.283 181.132 8/53
24/161 178.882 52.174 46.927 181.006 27/179
17/114 178.947 52.632 47.619 180.952 19/126
27/181 179.0055 53.039 48.241 180.814 30/199
10/67 179.1045 53.732 49.315 180.575 11/73
23/154 179.221 54.5455 50.602 180.506 25/166
13/87 179.31 55.172 51.613 180.452 14/93
3/20 180 60 180 3/20
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