User:BudjarnLambeth/Equalizer subgroup: Difference between revisions

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BudjarnLambeth (talk | contribs)
m BudjarnLambeth moved page Equalizer subgroup to User:BudjarnLambeth/Equalizer subgroup: Subjective opinion
 
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'''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.
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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
Line 76: Line 76:
TE mistunings (cents): ⟨0.364, -0.082, -3.655, 2.375, -2.172, 7.925, -3.258]
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
Complexity: 2.381333
Line 98: Line 98:
TE mistunings (cents): ⟨-1.494, -0.272, 2.103, 1.908, -7.007, 8.284]
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
Complexity: 2.106437
Line 120: Line 120:
TE mistunings (cents): ⟨-1.647, -0.222, 1.159, 1.192, -7.340, 8.511, 3.389]
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
Complexity: 2.152852
Line 142: Line 142:
TE mistunings (cents): ⟨-1.361, 1.117, 0.058, -3.706, -5.286, 12.382]
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
Complexity: 1.825578
Line 164: Line 164:
TE mistunings (cents): ⟨-1.317, 1.273, -0.015, -2.849, -5.021, 12.829, -2.320]
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
Complexity: 1.791017
Line 186: Line 186:
TE mistunings (cents): ⟨1.509, -3.502, 1.464, 5.229, -2.729, -2.907]
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
Complexity: 2.151739
Line 208: Line 208:
TE mistunings (cents): ⟨1.565, -3.608, 0.815, 4.950, -2.695, -3.253, 1.983]
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
Complexity: 2.266610
Line 244: Line 244:
TE mistunings (cents): ⟨-0.192, -0.709, 0.845, 5.107, -2.975, -1.249]
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
Complexity: 2.264161
Line 313: Line 313:
TE mistunings (cents): ⟨0.368, -0.506, -3.814, 2.609, 1.454]
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
Complexity: 2.398767
Line 335: Line 335:
TE mistunings (cents): ⟨0.052, -0.860, -4.638, 2.351, -0.335, 5.630]
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
Complexity: 2.231135
Line 357: Line 357:
TE mistunings (cents): ⟨0.465, -1.219, 0.000, -3.058, 4.462]
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
Complexity: 1.296641
Line 379: Line 379:
TE mistunings (cents): ⟨0.388, -1.341, -5.042, -3.371, 4.136, 7.535]
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
Complexity: 1.399563
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'''Semiamulet'''
'''Semihaunt'''


Subgroup: 2.3.13.17.19
Subgroup: 2.3.13.17.19
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TE mistunings (cents): ⟨-1.189, -0.259, 3.274, 0.926, 1.013]
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
Complexity: 0.682815
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'''Semiamulet (+23)'''
'''Semihaunt (+23)'''


Subgroup: 2.3.13.17.19.23
Subgroup: 2.3.13.17.19.23
Line 423: Line 423:
TE mistunings (cents): ⟨-1.609, 0.052, 1.229, 2.137, 0.203, 3.034]
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
Complexity: 2.661109
Line 445: Line 445:
TE mistunings (cents): ⟨0.201, 0.560, 2.530, -1.939, -3.248]
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
Complexity: 2.352952
Line 467: Line 467:
TE mistunings (cents): ⟨0.068, 1.122, -0.666, -1.708, -6.130, 5.706]
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
Complexity: 2.667192
Line 489: Line 489:
TE mistunings (cents): ⟨-0.113, -1.014, 1.767, 2.427, -1.357]
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
Complexity: 2.351780
Line 511: Line 511:
TE mistunings (cents): ⟨-0.096, -1.048, 2.231, 2.068, -1.099, -0.426]
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
Complexity: 3.987557
Line 554: Line 554:
TE mistunings (cents): ⟨0.465, -1.219, -3.058, 4.462, -0.000]
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
Complexity: 1.060700
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== Related concepts ==
== 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
* [[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]]
[[Category:Subgroup]][[Category:Subgroup temperaments]]