User:BudjarnLambeth/Equalizer subgroup: Difference between revisions
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 | 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 [[ | Adjusted [[error]] (cents): 4.477868 | ||
[[Complexity]]: 2.503140 | [[Complexity]]: 2.503140 | ||
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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 | Adjusted error (cents): 4.621471 | ||
Complexity: 2.381333 | Complexity: 2.381333 | ||
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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 | Adjusted error (cents): 5.508389 | ||
Complexity: 2.106437 | Complexity: 2.106437 | ||
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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 | Adjusted error (cents): 5.641385 | ||
Complexity: 2.152852 | Complexity: 2.152852 | ||
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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 | Adjusted error (cents): 6.376950 | ||
Complexity: 1.825578 | Complexity: 1.825578 | ||
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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 | Adjusted error (cents): 6.366626 | ||
Complexity: 1.791017 | Complexity: 1.791017 | ||
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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 | Adjusted error (cents): 5.610433 | ||
Complexity: 2.151739 | Complexity: 2.151739 | ||
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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 | Adjusted error (cents): 5.607494 | ||
Complexity: 2.266610 | Complexity: 2.266610 | ||
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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 | Adjusted error (cents): 2.918377 | ||
Complexity: 2.264161 | Complexity: 2.264161 | ||
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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 | Adjusted error (cents): 2.565939 | ||
Complexity: 2.398767 | Complexity: 2.398767 | ||
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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 | Adjusted error (cents): 3.578280 | ||
Complexity: 2.231135 | Complexity: 2.231135 | ||
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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 | Adjusted error (cents): 2.986065 | ||
Complexity: 1.296641 | Complexity: 1.296641 | ||
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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 | Adjusted error (cents): 4.929473 | ||
Complexity: 1.399563 | Complexity: 1.399563 | ||
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''' | '''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 | Adjusted error (cents): 2.900547 | ||
Complexity: 0.682815 | Complexity: 0.682815 | ||
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''' | '''Semihaunt (+23)''' | ||
Subgroup: 2.3.13.17.19.23 | Subgroup: 2.3.13.17.19.23 | ||
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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 | Adjusted error (cents): 3.417836 | ||
Complexity: 2.661109 | Complexity: 2.661109 | ||
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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 | Adjusted error (cents): 2.281355 | ||
Complexity: 2.352952 | Complexity: 2.352952 | ||
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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 | Adjusted error (cents): 3.867737 | ||
Complexity: 2.667192 | Complexity: 2.667192 | ||
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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 | Adjusted error (cents): 1.996594 | ||
Complexity: 2.351780 | Complexity: 2.351780 | ||
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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 | Adjusted error (cents): 1.972909 | ||
Complexity: 3.987557 | Complexity: 3.987557 | ||
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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 | 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]] | ||