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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.
{{Breadcrumb|Ploidacot|Tetracot}}
 
For most of its generator range, [[7L 6s]], [[7L 13s]], and [[13L 7s]] are the chromatic scales of [[Ploidacot/Tetracot|tetracot]] temperaments. thus finding a small diesis +7 or −13 generators. In fact, this comma, which may be inflated to as much as 60{{c}}, 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}}
 


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