User:BudjarnLambeth/Equalizer subgroup: Difference between revisions

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 '''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 42: / Line 42: @@
 '''Fifigeist'''
-Subgroup: 2.3.5.13.17.19
+[[Subgroup]]: 2.3.5.13.17.19
-Comma list: 153/152, 170/169, 250/247, 289/288, 324/323, 325/323, 325/324, 729/722
+[[Comma list]]: 153/152, 170/169, 250/247, 289/288, 324/323, 325/323, 325/324, 729/722
-Mapping: {{mapping| 2 2 3 6 7 5 | 0 5 7 6 5 15 }}
+[[Mapping]]: {{mapping| 2 2 3 6 7 5 | 0 5 7 6 5 15 }}
-Optimal tuning (TE): ~1\2 = 600.1848, ~13/12 = 140.2424
+[[Optimal tuning]] ([[TE]]): ~1\2 = 600.1848, ~13/12 = 140.2424
-Recommended EDOs: {{EDOs|10, 18, 26, 34, 60, 94}}
+Recommended [[EDO]]s: {{EDOs|10, 18, 26, 34, 60, 94}}
-TE mistunings (cents): ⟨0.370, -0.373, -4.062, 2.036, -2.450, 7.048]
+TE mistunings ([[cents]]): ⟨0.370, -0.373, -4.062, 2.036, -2.450, 7.048]
-Adjusted Error (cents): 4.477868
+Adjusted [[error]] (cents): 4.477868
-Complexity: 2.503140
+[[Complexity]]: 2.503140
 Related temperaments: [[fifive]]
@@ Line 76: / Line 76: @@
 TE mistunings (cents): ⟨0.364, -0.082, -3.655, 2.375, -2.172, 7.925, -3.258]
-Adjusted Error (cents): 4.621471
+Adjusted error (cents): 4.621471
 Complexity: 2.381333
@@ Line 98: / Line 98: @@
 TE mistunings (cents): ⟨-1.494, -0.272, 2.103, 1.908, -7.007, 8.284]
-Adjusted Error (cents): 5.508389
+Adjusted error (cents): 5.508389
 Complexity: 2.106437
@@ Line 120: / Line 120: @@
 TE mistunings (cents): ⟨-1.647, -0.222, 1.159, 1.192, -7.340, 8.511, 3.389]
-Adjusted Error (cents): 5.641385
+Adjusted error (cents): 5.641385
 Complexity: 2.152852
@@ Line 142: / Line 142: @@
 TE mistunings (cents): ⟨-1.361, 1.117, 0.058, -3.706, -5.286, 12.382]
-Adjusted Error (cents): 6.376950
+Adjusted error (cents): 6.376950
 Complexity: 1.825578
@@ Line 164: / Line 164: @@
 TE mistunings (cents): ⟨-1.317, 1.273, -0.015, -2.849, -5.021, 12.829, -2.320]
-Adjusted Error (cents): 6.366626
+Adjusted error (cents): 6.366626
 Complexity: 1.791017
@@ Line 186: / Line 186: @@
 TE mistunings (cents): ⟨1.509, -3.502, 1.464, 5.229, -2.729, -2.907]
-Adjusted Error (cents): 5.610433
+Adjusted error (cents): 5.610433
 Complexity: 2.151739
@@ Line 208: / Line 208: @@
 TE mistunings (cents): ⟨1.565, -3.608, 0.815, 4.950, -2.695, -3.253, 1.983]
-Adjusted Error (cents): 5.607494
+Adjusted error (cents): 5.607494
 Complexity: 2.266610
 Related temperaments: [[decimal]]
 ==== Scales ====
@@ Line 243: / Line 244: @@
 TE mistunings (cents): ⟨-0.192, -0.709, 0.845, 5.107, -2.975, -1.249]
-Adjusted Error (cents): 2.918377
+Adjusted error (cents): 2.918377
 Complexity: 2.264161
@@ Line 290: / Line 291: @@
 ==== Scales ====
-== 2.3.n subgroups =====
+== 2.3.n subgroups ==
-.3.13.n subgroups ===
+=== 2.3.13.n subgroups ===
 Examples of valid equalizer subgroups in this category (not exhaustive):
 * 2.3.13.14.17
@@ Line 312: / Line 313: @@
 TE mistunings (cents): ⟨0.368, -0.506, -3.814, 2.609, 1.454]
-Adjusted Error (cents): 2.565939
+Adjusted error (cents): 2.565939
 Complexity: 2.398767
@@ Line 334: / Line 335: @@
 TE mistunings (cents): ⟨0.052, -0.860, -4.638, 2.351, -0.335, 5.630]
-Adjusted Error (cents): 3.578280
+Adjusted error (cents): 3.578280
 Complexity: 2.231135
@@ Line 356: / Line 357: @@
 TE mistunings (cents): ⟨0.465, -1.219, 0.000, -3.058, 4.462]
-Adjusted Error (cents): 2.986065
+Adjusted error (cents): 2.986065
 Complexity: 1.296641
@@ Line 378: / Line 379: @@
 TE mistunings (cents): ⟨0.388, -1.341, -5.042, -3.371, 4.136, 7.535]
-Adjusted Error (cents): 4.929473
+Adjusted error (cents): 4.929473
 Complexity: 1.399563
@@ Line 386: / Line 387: @@
-'''Semiamulet'''
+'''Semihaunt'''
 Subgroup: 2.3.13.17.19
@@ Line 400: / Line 401: @@
 TE mistunings (cents): ⟨-1.189, -0.259, 3.274, 0.926, 1.013]
-Adjusted Error (cents): 2.900547
+Adjusted error (cents): 2.900547
 Complexity: 0.682815
@@ Line 408: / Line 409: @@
-'''Semiamulet (+23)'''
+'''Semihaunt (+23)'''
 Subgroup: 2.3.13.17.19.23
@@ Line 422: / Line 423: @@
 TE mistunings (cents): ⟨-1.609, 0.052, 1.229, 2.137, 0.203, 3.034]
-Adjusted Error (cents): 3.417836
+Adjusted error (cents): 3.417836
 Complexity: 2.661109
@@ Line 444: / Line 445: @@
 TE mistunings (cents): ⟨0.201, 0.560, 2.530, -1.939, -3.248]
-Adjusted Error (cents): 2.281355
+Adjusted error (cents): 2.281355
 Complexity: 2.352952
@@ Line 466: / Line 467: @@
 TE mistunings (cents): ⟨0.068, 1.122, -0.666, -1.708, -6.130, 5.706]
-Adjusted Error (cents): 3.867737
+Adjusted error (cents): 3.867737
 Complexity: 2.667192
@@ Line 488: / Line 489: @@
 TE mistunings (cents): ⟨-0.113, -1.014, 1.767, 2.427, -1.357]
-Adjusted Error (cents): 1.996594
+Adjusted error (cents): 1.996594
 Complexity: 2.351780
@@ Line 510: / Line 511: @@
 TE mistunings (cents): ⟨-0.096, -1.048, 2.231, 2.068, -1.099, -0.426]
-Adjusted Error (cents): 1.972909
+Adjusted error (cents): 1.972909
 Complexity: 3.987557
@@ Line 553: / Line 554: @@
 TE mistunings (cents): ⟨0.465, -1.219, -3.058, 4.462, -0.000]
-Adjusted Error (cents): 3.179821
+Adjusted error (cents): 3.179821
 Complexity: 1.060700
@@ Line 649: / 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]]