Xenharmonic Wiki

User:BudjarnLambeth/Equalizer subgroup: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,819 edits
m Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "
 
(7 intermediate revisions by one other user not shown)
Line 3: Line 3:
'''Disclaimer from the author'''
'''Disclaimer from the author'''


Note that everything written on this page is the authors’ personal opinion based on how they subjectively experience harmony and will not be psychoacoustically true for everyone, and may not even be true for most people.  
Note that everything written on this page is the author’s personal opinion based on how they subjectively experience harmony and will not be psychoacoustically true for everyone, and may not even be true for most people.  


Nothing on this page is science. It's just one of many possible frameworks for looking at things, and it's not even a very well-tested one. So take it all with a grain of salt.
Nothing on this page is science. It's just one of many possible frameworks for looking at things, and it's not even a very well-tested one. So take it all with a grain of salt.
Line 68: Line 68:
Comma list: 115/114, 153/152, 300/299, 391/390, 1105/1104, 8075/8073
Comma list: 115/114, 153/152, 300/299, 391/390, 1105/1104, 8075/8073


Mapping: {{mapping| 2 2 3 6 7 5 6 | 0 5 7 6 5 15 13 }}
{{Mapping|legend=0| 2 2 3 6 7 5 6 | 0 5 7 6 5 15 13 }}


Optimal tuning (TE): ~1\2 = 600.1820, ~13/12 = 140.3019
Optimal tuning (TE): ~1\2 = 600.1820, ~13/12 = 140.3019
Line 90: Line 90:
Comma list: 96/95, 136/135, 153/152, 170/169, 256/255, 289/285, 289/288, 324/323
Comma list: 96/95, 136/135, 153/152, 170/169, 256/255, 289/285, 289/288, 324/323


Mapping: {{mapping| 2 4 3 7 9 11 | 0 -2 4 1 -2 -6 }}
{{Mapping|legend=0| 2 4 3 7 9 11 | 0 -2 4 1 -2 -6 }}


Optimal tuning (TE): ~1\2 = 599.2530, ~15/13 = 247.6643
Optimal tuning (TE): ~1\2 = 599.2530, ~15/13 = 247.6643
Line 112: Line 112:
Comma list: 96/95, 136/135, 153/152, 300/299, 391/390
Comma list: 96/95, 136/135, 153/152, 300/299, 391/390


Mapping: {{mapping| 2 4 3 7 9 11 7 | 0 -2 4 1 -2 -6 5 }}
{{Mapping|legend=0| 2 4 3 7 9 11 7 | 0 -2 4 1 -2 -6 5 }}


Optimal tuning (TE): ~1\2 = 599.1763, ~15/13 = 247.4859
Optimal tuning (TE): ~1\2 = 599.1763, ~15/13 = 247.4859
Line 134: Line 134:
Comma list: 96/95, 136/135, 153/152, 256/255, 289/285, 289/288, 324/323, 325/323
Comma list: 96/95, 136/135, 153/152, 256/255, 289/285, 289/288, 324/323, 325/323


Mapping: {{mapping| 2 3 5 6 8 8 | 0 1 -2 8 1 3 }}
{{Mapping|legend=0| 2 3 5 6 8 8 | 0 1 -2 8 1 3 }}


Optimal tuning (TE): ~1\2 = 599.3195, ~17/16 = 105.1130
Optimal tuning (TE): ~1\2 = 599.3195, ~17/16 = 105.1130
Line 156: Line 156:
Comma list: 96/95, 115/114, 136/135, 153/152, 325/324, 442/437
Comma list: 96/95, 115/114, 136/135, 153/152, 325/324, 442/437


Mapping: {{mapping| 2 3 5 6 8 8 | 0 1 -2 8 1 3 }}
{{Mapping|legend=0| 2 3 5 6 8 8 | 0 1 -2 8 1 3 }}


Optimal tuning (TE): ~1\2 = 599.3413, ~17/16 = 105.2039
Optimal tuning (TE): ~1\2 = 599.3413, ~17/16 = 105.2039
Line 178: Line 178:
Comma list: 81/80, 153/152, 170/169, 171/169, 171/170, 289/288, 323/320, 324/323
Comma list: 81/80, 153/152, 170/169, 171/169, 171/170, 289/288, 323/320, 324/323


Mapping: {{mapping| 2 3 4 7 8 8 | 0 2 8 5 2 6 }}
{{Mapping|legend=0| 2 3 4 7 8 8 | 0 2 8 5 2 6 }}


Optimal tuning (TE): ~1\2 = 600.7546, ~27/26 = 48.0949
Optimal tuning (TE): ~1\2 = 600.7546, ~27/26 = 48.0949
Line 200: Line 200:
Comma list: 153/152, 171/170, 300/299, 391/390, 741/736, 1105/1104, 1311/1300, 9747/9568
Comma list: 153/152, 171/170, 300/299, 391/390, 741/736, 1105/1104, 1311/1300, 9747/9568


Mapping: {{mapping| 2 3 4 7 8 8 8 | 0 2 8 5 2 6 13 }}
{{Mapping|legend=0| 2 3 4 7 8 8 8 | 0 2 8 5 2 6 13 }}


Optimal tuning (TE): ~1\2 = 600.7827, ~27/26 = 47.9997
Optimal tuning (TE): ~1\2 = 600.7827, ~27/26 = 47.9997
Line 236: Line 236:
Comma list: 171/170, 256/255, 324/323, 361/360, 460/459, 513/512, 576/575, 874/867
Comma list: 171/170, 256/255, 324/323, 361/360, 460/459, 513/512, 576/575, 874/867


Mapping: {{mapping| 1 2 -1 7 3 12 | 0 -1 8 -7 3 -18 }}
{{Mapping|legend=0| 1 2 -1 7 3 12 | 0 -1 8 -7 3 -18 }}


Optimal tuning (TE): ~2/1 = 1199.8084, ~4/3 = 498.3709
Optimal tuning (TE): ~2/1 = 1199.8084, ~4/3 = 498.3709
Line 305: Line 305:
Comma list: 324/323, 513/512, 2187/2176, 2197/2176, 2197/2187, 6144/6137
Comma list: 324/323, 513/512, 2187/2176, 2197/2176, 2197/2187, 6144/6137


Mapping: {{mapping| 1 3 7 14 0 | 0 -3 -7 -21 9 }}
{{Mapping|legend=0| 1 3 7 14 0 | 0 -3 -7 -21 9 }}


Optimal tuning (TE): ~2/1 = 1200.3681, ~18/13 = 566.5519
Optimal tuning (TE): ~2/1 = 1200.3681, ~18/13 = 566.5519
Line 327: Line 327:
Comma list: 208/207, 324/323, 513/512, 741/736, 2187/2176, 2197/2176, 2197/2187, 3159/3128
Comma list: 208/207, 324/323, 513/512, 741/736, 2187/2176, 2197/2176, 2197/2187, 3159/3128


Mapping: {{mapping| 1 3 7 14 0 5 | 0 -3 -7 -21 9 -1 }}
{{Mapping|legend=0| 1 3 7 14 0 5 | 0 -3 -7 -21 9 -1 }}


Optimal tuning (TE): ~2/1 = 1200.0516, ~18/13 = 566.3531
Optimal tuning (TE): ~2/1 = 1200.0516, ~18/13 = 566.3531
Line 349: Line 349:
Comma list: 153/152, 289/288, 324/323, 513/512, 729/722, 1088/1083
Comma list: 153/152, 289/288, 324/323, 513/512, 729/722, 1088/1083


Mapping: {{mapping| 12 19 45 49 51 | 0 0 -1 0 0 }}
{{Mapping|legend=0| 12 19 45 49 51 | 0 0 -1 0 0 }}


Optimal tuning (TE): ~1\12 = 100.0387, ~27/26 = 61.2152
Optimal tuning (TE): ~1\12 = 100.0387, ~27/26 = 61.2152
Line 371: Line 371:
Comma list: 153/152, 208/207, 289/288, 324/323, 442/437, 513/512, 729/722, 741/736
Comma list: 153/152, 208/207, 289/288, 324/323, 442/437, 513/512, 729/722, 741/736


Mapping: {{mapping| 12 19 45 49 51 54 | 0 0 -1 0 0 1 }}
{{Mapping|legend=0| 12 19 45 49 51 54 | 0 0 -1 0 0 1 }}


Optimal tuning (TE): ~1\12 = 100.0323, ~27/26 = 34.0630
Optimal tuning (TE): ~1\12 = 100.0323, ~27/26 = 34.0630
Line 387: Line 387:




'''Semiamulet'''
'''Semihaunt'''


Subgroup: 2.3.13.17.19
Subgroup: 2.3.13.17.19
Line 393: Line 393:
Comma list: 324/323, 512/507, 1088/1083, 2888/2873, 4624/4617, 6912/6859
Comma list: 324/323, 512/507, 1088/1083, 2888/2873, 4624/4617, 6912/6859


Mapping: {{mapping| 3 5 11 13 13 | 0 -2 1 -6 -2 }}
{{Mapping|legend=0| 3 5 11 13 13 | 0 -2 1 -6 -2 }}


Optimal tuning (TE): ~1\3 = 399.6037, ? = 48.1611
Optimal tuning (TE): ~1\3 = 399.6037, ? = 48.1611
Line 409: Line 409:




'''Semiamulet (+23)'''
'''Semihaunt (+23)'''


Subgroup: 2.3.13.17.19.23
Subgroup: 2.3.13.17.19.23
Line 415: Line 415:
Comma list: 208/207, 324/323, 512/507, 1088/1083, 2208/2197, 2888/2873, 4624/4617, 4693/4692
Comma list: 208/207, 324/323, 512/507, 1088/1083, 2208/2197, 2888/2873, 4624/4617, 4693/4692


Mapping: {{mapping| 3 5 11 13 13 13 | 0 -2 1 -6 -2 5 }}
{{Mapping|legend=0| 3 5 11 13 13 13 | 0 -2 1 -6 -2 5 }}


Optimal tuning (TE): ~1\3 = 399.4637, ? = 47.6560
Optimal tuning (TE): ~1\3 = 399.4637, ? = 47.6560
Line 437: Line 437:
Comma list: 289/288, 513/512, 2888/2873, 4624/4617, 6137/6084, 16473/16384
Comma list: 289/288, 513/512, 2888/2873, 4624/4617, 6137/6084, 16473/16384


Mapping: {{mapping| 2 3 8 8 9 | 0 2 -7 2 -6 }}
{{Mapping|legend=0| 2 3 8 8 9 | 0 2 -7 2 -6 }}


Optimal tuning (TE): ~1\2 = 600.1004, ? = 51.1066
Optimal tuning (TE): ~1\2 = 600.1004, ? = 51.1066
Line 459: Line 459:
Comma list: 208/207, 289/288, 513/512, 741/736, 2888/2873, 3211/3174, 3757/3726, 4624/4617
Comma list: 208/207, 289/288, 513/512, 741/736, 2888/2873, 3211/3174, 3757/3726, 4624/4617


Mapping: {{mapping| 2 3 8 8 9 10 | 0 2 -7 2 -6 -11 }}
{{Mapping|legend=0| 2 3 8 8 9 10 | 0 2 -7 2 -6 -11 }}


Optimal tuning (TE): ~1\2 = 600.0341, ? = 51.4873
Optimal tuning (TE): ~1\2 = 600.0341, ? = 51.4873
Line 481: Line 481:
Comma list: 324/323, 513/512, 2187/2176, 2888/2873, 6144/6137, 13718/13689
Comma list: 324/323, 513/512, 2187/2176, 2888/2873, 6144/6137, 13718/13689


Mapping: {{mapping| 1 2 1 7 3 | 0 -2 13 -14 6 }}
{{Mapping|legend=0| 1 2 1 7 3 | 0 -2 13 -14 6 }}


Optimal tuning (TE): ~2/1 = 1199.8867, ~? = 249.4160
Optimal tuning (TE): ~2/1 = 1199.8867, ~? = 249.4160
Line 503: Line 503:
Comma list: 324/323, 513/512, 2187/2176, 2208/2197, 2888/2873, 4693/4692, 6144/6137, 6656/6647
Comma list: 324/323, 513/512, 2187/2176, 2208/2197, 2888/2873, 4693/4692, 6144/6137, 6656/6647


Mapping: {{mapping| 1 2 1 7 3 -4 | 0 -2 13 -14 6 41 }}
{{Mapping|legend=0| 1 2 1 7 3 -4 | 0 -2 13 -14 6 41 }}


Optimal tuning (TE): ~2/1 = 1199.9040, ~? = 249.4504
Optimal tuning (TE): ~2/1 = 1199.9040, ~? = 249.4504
Line 546: Line 546:
Comma list: 153/152, 289/288, 324/323, 513/512, 729/722, 1088/1083
Comma list: 153/152, 289/288, 324/323, 513/512, 729/722, 1088/1083


Mapping: {{mapping| 12 19 49 51 54 | 0 0 0 0 0 }}
{{Mapping|legend=0| 12 19 49 51 54 | 0 0 0 0 0 }}


Optimal tuning (TE): ~1\12 = 100.0387, ~? = 26.1830
Optimal tuning (TE): ~1\12 = 100.0387, ~? = 26.1830
Line 655: Line 655:
** [[No-fives subgroup temperaments]]
** [[No-fives subgroup temperaments]]
** [[No-sevens subgroup temperaments]]
** [[No-sevens subgroup temperaments]]
** [[Half-prime subgroup]]
* [[Substitute harmonic]]s
* [[Substitute harmonic]]s
* [[Dual-fifth temperaments]]
* [[Dual-fifth temperaments]]
* [[Sooty fox scale]]s: many of these tunings are especially great at approximating equalizer subgroups


[[Category:Subgroup]][[Category:Subgroup temperaments]]
[[Category:Subgroup]][[Category:Subgroup temperaments]]
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Equalizer_subgroup"