No-fives subgroup temperaments: Difference between revisions

m Text replacement - "Gencom mapping: {{mapping| " to "{{Mapping|legend=4| "
m Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "
Tags: Mobile edit Mobile web edit
 
Line 75: Line 75:
Comma list: 1331/1323, 19712/19683
Comma list: 1331/1323, 19712/19683


Subgroup-val mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}
{{Mapping|legend=2| 1 1 0 1 | 0 5 24 21 }}


Optimal tunings:  
Optimal tunings:  
Line 90: Line 90:
Comma list: 352/351, 729/728, 1331/1323
Comma list: 352/351, 729/728, 1331/1323


Subgroup-val mapping: {{mapping| 1 1 0 1 3 | 0 5 24 21 6 }}
{{Mapping|legend=2| 1 1 0 1 3 | 0 5 24 21 6 }}


Optimal tunings:  
Optimal tunings:  
Line 150: Line 150:
Comma list: 243/242, 896/891
Comma list: 243/242, 896/891


Subgroup-val mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}
{{Mapping|legend=2| 1 1 -1 2 | 0 2 13 5 }}


{{Mapping|legend=4| 1 1 0 -1 2 | 0 2 0 13 5 }}
{{Mapping|legend=4| 1 1 0 -1 2 | 0 2 0 13 5 }}
Line 188: Line 188:
Comma list: 243/242, 896/891, 1083/1078
Comma list: 243/242, 896/891, 1083/1078


Subgroup-val mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}
{{Mapping|legend=2| 1 1 -1 2 0 | 0 4 26 10 29 }}
: mapping generators: ~2, ~21/19
: mapping generators: ~2, ~21/19


Line 226: Line 226:
Comma list: 243/242, 65536/65219
Comma list: 243/242, 65536/65219


Subgroup-val mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}
{{Mapping|legend=2| 1 1 5 2 | 0 4 -15 10 }}


Optimal tunings:  
Optimal tunings:  
Line 241: Line 241:
Comma list: 243/242, 513/512, 1083/1078
Comma list: 243/242, 513/512, 1083/1078


Subgroup-val mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}
{{Mapping|legend=2| 1 1 5 2 6 | 0 4 -15 10 -12 }}


Optimal tunings:  
Optimal tunings:  
Line 276: Line 276:
Comma list: 896/891, 26411/26244
Comma list: 896/891, 26411/26244


Subgroup-val mapping: {{mapping| 1 0 -1 6 | 0 5 12 -8 }}
{{Mapping|legend=2| 1 0 -1 6 | 0 5 12 -8 }}


Optimal tunings:  
Optimal tunings:  
Line 291: Line 291:
Comma list: 144/143, 343/338, 729/728
Comma list: 144/143, 343/338, 729/728


Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 | 0 5 12 -8 18 }}
{{Mapping|legend=2| 1 0 -1 6 -2 | 0 5 12 -8 18 }}


Optimal tunings:  
Optimal tunings:  
Line 306: Line 306:
Comma list: 144/143, 232/231, 343/338, 729/728
Comma list: 144/143, 232/231, 343/338, 729/728


Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}
{{Mapping|legend=2| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}


Optimal tunings:  
Optimal tunings:  
Line 321: Line 321:
Comma list: 352/351, 364/363, 26411/26244
Comma list: 352/351, 364/363, 26411/26244


Subgroup-val mapping: {{mapping| 1 0 -1 6 11 | 0 5 12 -8 -23 }}
{{Mapping|legend=2| 1 0 -1 6 11 | 0 5 12 -8 -23 }}


Optimal tunings:  
Optimal tunings:  
Line 336: Line 336:
Comma list: 169/168, 896/891, 26411/26244
Comma list: 169/168, 896/891, 26411/26244


Subgroup-val mapping: {{mapping| 1 0 -1 6 1 | 0 10 24 -16 17 }}
{{Mapping|legend=2| 1 0 -1 6 1 | 0 10 24 -16 17 }}
: mapping generators: ~2, ~143/128
: mapping generators: ~2, ~143/128


Line 352: Line 352:
Comma list: 784/783, 5887/5832
Comma list: 784/783, 5887/5832


Subgroup-val mapping: {{mapping| 1 0 -1 2 | 0 5 12 9 }}
{{Mapping|legend=2| 1 0 -1 2 | 0 5 12 9 }}


Optimal tunings:  
Optimal tunings:  
Line 391: Line 391:
Comma list: 99/98, 243/242
Comma list: 99/98, 243/242


Subgroup-val mapping: {{mapping| 1 -1 -3 -3 | 0 4 9 10 }}
{{Mapping|legend=2| 1 -1 -3 -3 | 0 4 9 10 }}


{{Mapping|legend=4| 1 -1 0 -3 -3 | 0 4 0 9 10 }}
{{Mapping|legend=4| 1 -1 0 -3 -3 | 0 4 0 9 10 }}
Line 408: Line 408:
Comma list: 78/77, 99/98, 243/242
Comma list: 78/77, 99/98, 243/242


Subgroup-val mapping: {{mapping| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}
{{Mapping|legend=2| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}


{{Mapping|legend=4| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}
{{Mapping|legend=4| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}
Line 425: Line 425:
Comma list: 99/98, 144/143, 243/242
Comma list: 99/98, 144/143, 243/242


Subgroup-val mapping: {{mapping| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}
{{Mapping|legend=2| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}


{{Mapping|legend=4| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}
{{Mapping|legend=4| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}
Line 444: Line 444:
Comma list: 99/98, 243/242, 363/361
Comma list: 99/98, 243/242, 363/361


Subgroup-val mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}
{{Mapping|legend=2| 2 2 3 4 5 | 0 4 9 10 12 }}
: mapping generators: ~209/147, ~21/19
: mapping generators: ~209/147, ~21/19


Line 504: Line 504:
Comma list: 99/98, 864/847
Comma list: 99/98, 864/847


Subgroup-val mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}
{{Mapping|legend=2| 1 1 2 3 | 0 5 7 4 }}


{{Mapping|legend=4| 1 1 0 2 3 | 0 5 0 7 4 }}
{{Mapping|legend=4| 1 1 0 2 3 | 0 5 0 7 4 }}
Line 521: Line 521:
Comma list: 78/77, 99/98, 144/143
Comma list: 78/77, 99/98, 144/143


Subgroup-val mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}
{{Mapping|legend=2| 1 1 2 3 3 | 0 5 7 4 6 }}


{{Mapping|legend=4| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}
{{Mapping|legend=4| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}
Line 563: Line 563:
Comma list: 243/242, 2401/2376
Comma list: 243/242, 2401/2376


Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}
{{Mapping|legend=2| 1 1 2 2 | 0 8 11 20 }}


Optimal tunings:  
Optimal tunings:  
Line 578: Line 578:
Comma list: 133/132, 243/242, 343/342
Comma list: 133/132, 243/242, 343/342


Subgroup-val mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}
{{Mapping|legend=2| 1 1 2 2 3 | 0 8 11 20 17 }}


Optimal tunings:  
Optimal tunings:  
Line 633: Line 633:
Comma list: 43923/43904, 5767168/5764801
Comma list: 43923/43904, 5767168/5764801


Subgroup-val mapping: {{mapping| 1 -4 3 5 | 0 29 -1 -8 }}
{{Mapping|legend=2| 1 -4 3 5 | 0 29 -1 -8 }}


Optimal tunings:  
Optimal tunings:  
Line 676: Line 676:
Comma list: 896/891, 1331/1323
Comma list: 896/891, 1331/1323


Subgroup-val mapping: {{mapping| 1 0 -21 -14 | 0 1 15 11 }}
{{Mapping|legend=2| 1 0 -21 -14 | 0 1 15 11 }}


{{Mapping|legend=4| 1 0 0 -21 -14 | 0 1 0 15 11 }}
{{Mapping|legend=4| 1 0 0 -21 -14 | 0 1 0 15 11 }}
Line 693: Line 693:
Comma list: 169/168, 352/351, 364/363
Comma list: 169/168, 352/351, 364/363


Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
{{Mapping|legend=2| 1 0 -21 -14 -9 | 0 1 15 11 8 }}


{{Mapping|legend=4| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
{{Mapping|legend=4| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
Line 710: Line 710:
Comma list: 169/168, 208/207, 352/351, 364/363
Comma list: 169/168, 208/207, 352/351, 364/363


Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
{{Mapping|legend=2| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}


{{Mapping|legend=4| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
{{Mapping|legend=4| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
Line 727: Line 727:
Comma list: 169/168, 208/207, 232/231, 352/351, 364/363
Comma list: 169/168, 208/207, 232/231, 352/351, 364/363


Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
{{Mapping|legend=2| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}


{{Mapping|legend=4| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}
{{Mapping|legend=4| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}
Line 794: Line 794:
Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }}
Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }}


Subgroup-val mapping: {{mapping| 1 -126 -214 -80 | 0 439 746 288 }}
{{Mapping|legend=2| 1 -126 -214 -80 | 0 439 746 288 }}


Optimal tunings:  
Optimal tunings:  
Line 809: Line 809:
Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }}
Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }}


Subgroup-val mapping: {{mapping| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}
{{Mapping|legend=2| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}


Optimal tunings:  
Optimal tunings:  
Line 824: Line 824:
Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256
Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256


Subgroup-val mapping: {{mapping| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}
{{Mapping|legend=2| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}


Optimal tunings:  
Optimal tunings:  
Line 963: Line 963:
Comma list: 144/143, 729/704
Comma list: 144/143, 729/704


Subgroup-val mapping: {{mapping| 1 0 -6 10 | 0 1 6 -4 }}
{{Mapping|legend=2| 1 0 -6 10 | 0 1 6 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 978: Line 978:
Comma list: 363/361, 729/704
Comma list: 363/361, 729/704


Subgroup-val mapping: {{mapping| 1 0 -6 -6 | 0 2 12 13 }}
{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }}
: mapping generators: ~2, ~19/11
: mapping generators: ~2, ~19/11


Line 1,016: Line 1,016:
Comma list: 512/507, 1352/1331
Comma list: 512/507, 1352/1331


Subgroup-val mapping: {{mapping| 1 -3 5 6 | 0 6 -2 -3 }}
{{Mapping|legend=2| 1 -3 5 6 | 0 6 -2 -3 }}
: mapping generators: ~2, ~22/13
: mapping generators: ~2, ~22/13


Line 1,052: Line 1,052:
Comma list: 352/351, 531674/531441
Comma list: 352/351, 531674/531441


Subgroup-val mapping: {{mapping| 1 1 0 3 | 0 5 21 6 }}
{{Mapping|legend=2| 1 1 0 3 | 0 5 21 6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,186: Line 1,186:
Comma list: 3888/3887, 12168/12167
Comma list: 3888/3887, 12168/12167


Subgroup-val mapping: {{mapping| 1 -5 -7 -7 | 0 8 13 14 }}
{{Mapping|legend=2| 1 -5 -7 -7 | 0 8 13 14 }}


Optimal tunings:  
Optimal tunings: