User:BudjarnLambeth/Equalizer subgroup: Difference between revisions

(8 intermediate revisions by one other user not shown)

Line 3:

'''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.

Line 68:

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 }}

Optimal tuning (TE): ~1\2 = 600.1820, ~13/12 = 140.3019

Line 90:

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 }}

Optimal tuning (TE): ~1\2 = 599.2530, ~15/13 = 247.6643

Line 112:

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 }}

Optimal tuning (TE): ~1\2 = 599.1763, ~15/13 = 247.4859

Line 134:

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 }}

Optimal tuning (TE): ~1\2 = 599.3195, ~17/16 = 105.1130

Line 156:

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 }}

Optimal tuning (TE): ~1\2 = 599.3413, ~17/16 = 105.2039

Line 178:

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 }}

Optimal tuning (TE): ~1\2 = 600.7546, ~27/26 = 48.0949

Line 200:

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 }}

Optimal tuning (TE): ~1\2 = 600.7827, ~27/26 = 47.9997

Line 236:

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 }}

Optimal tuning (TE): ~2/1 = 1199.8084, ~4/3 = 498.3709

Line 305:

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 }}

Optimal tuning (TE): ~2/1 = 1200.3681, ~18/13 = 566.5519

Line 327:

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 }}

Optimal tuning (TE): ~2/1 = 1200.0516, ~18/13 = 566.3531

Line 349:

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 }}

Optimal tuning (TE): ~1\12 = 100.0387, ~27/26 = 61.2152

Line 371:

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 }}

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

Line 387:

'''~~Semiamulet~~'''

'''Semihaunt'''

Subgroup: 2.3.13.17.19

Line 393:

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 }}

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

Line 409:

'''~~Semiamulet~~ (+23)'''

'''Semihaunt (+23)'''

Subgroup: 2.3.13.17.19.23

Line 415:

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 }}

Optimal tuning (TE): ~1\3 = 399.4637, ? = 47.6560

Line 437:

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 }}

Optimal tuning (TE): ~1\2 = 600.1004, ? = 51.1066

Line 459:

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 }}

Optimal tuning (TE): ~1\2 = 600.0341, ? = 51.4873

Line 481:

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 }}

Optimal tuning (TE): ~2/1 = 1199.8867, ~? = 249.4160

Line 503:

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 }}

Optimal tuning (TE): ~2/1 = 1199.9040, ~? = 249.4504

Line 546:

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 }}

Optimal tuning (TE): ~1\12 = 100.0387, ~? = 26.1830

Line 650:

== Related concepts ==

* [[No-twos subgroup temperaments]]

* [[Subgroup temperaments]]

* [[No-threes subgroup temperaments]]

** [[No-twos subgroup temperaments]]

* [[No-fives subgroup temperaments]]

** [[No-threes subgroup temperaments]]

* [[No-sevens subgroup temperaments]]

** [[No-fives subgroup temperaments]]

** [[No-sevens subgroup temperaments]]

** [[Half-prime subgroup]]

* [[Substitute harmonic]]s

* [[Dual-fifth temperaments]]

* [[Sooty fox scale]]s: many of these tunings are especially great at approximating equalizer subgroups

[[Category:Subgroup]][[Category:Subgroup temperaments]]

@@ Line 3: / Line 3: @@
 '''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.
@@ Line 68: / Line 68: @@
 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
@@ Line 90: / Line 90: @@
 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
@@ Line 112: / Line 112: @@
 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
@@ Line 134: / Line 134: @@
 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
@@ Line 156: / Line 156: @@
 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
@@ Line 178: / Line 178: @@
 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
@@ Line 200: / Line 200: @@
 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
@@ Line 236: / Line 236: @@
 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
@@ Line 305: / Line 305: @@
 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
@@ Line 327: / Line 327: @@
 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
@@ Line 349: / Line 349: @@
 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
@@ Line 371: / Line 371: @@
 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
@@ Line 387: / Line 387: @@
-'''Semiamulet'''
+'''Semihaunt'''
 Subgroup: 2.3.13.17.19
@@ Line 393: / Line 393: @@
 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
@@ Line 409: / Line 409: @@
-'''Semiamulet (+23)'''
+'''Semihaunt (+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
-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
@@ Line 437: / Line 437: @@
 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
@@ Line 459: / Line 459: @@
 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
@@ Line 481: / Line 481: @@
 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
@@ Line 503: / Line 503: @@
 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
@@ Line 546: / Line 546: @@
 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
@@ Line 650: / Line 650: @@
 == Related concepts ==
-* [[No-twos subgroup temperaments]]
+* [[Subgroup temperaments]]
-* [[No-threes subgroup temperaments]]
+** [[No-twos subgroup temperaments]]
-* [[No-fives subgroup temperaments]]
+** [[No-threes subgroup temperaments]]
-* [[No-sevens subgroup temperaments]]
+** [[No-fives subgroup temperaments]]
+** [[No-sevens subgroup temperaments]]
+** [[Half-prime subgroup]]
 * [[Substitute harmonic]]s
+* [[Dual-fifth temperaments]]
+* [[Sooty fox scale]]s: many of these tunings are especially great at approximating equalizer subgroups
 [[Category:Subgroup]][[Category:Subgroup temperaments]]