User:BudjarnLambeth/Equalizer subgroup: Difference between revisions
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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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The hope is that there might be subtle harmonies and consonances involving ethereal harmonics that can allow for novel new sounds to be discovered, if we give them the space to show themselves. | The hope is that there might be subtle harmonies and consonances involving ethereal harmonics that can allow for novel new sounds to be discovered, if we give them the space to show themselves. | ||
The reason for the name is that when music producers or listeners use an equalizer, they often turn down the middle pitches, while boosting the low and high end, which is visually | The reason for the name is that when music producers or listeners use an equalizer, they often turn down the middle pitches, while boosting the low and high end, which is visually similar to an equalizer subgroup. (These are very much not the same thing though, don’t read too deep into the analogy.) | ||
The sections of this article will showcase temperaments and scales from different equalizer subgroups. Feel free to add more. | The sections of this article will showcase temperaments and scales from different equalizer subgroups. Feel free to add more. | ||
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'''Fifigeist''' | '''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 | 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 | Adjusted [[error]] (cents): 4.477868 | ||
Complexity: 2.503140 | [[Complexity]]: 2.503140 | ||
Related temperaments: [[fifive]] | Related temperaments: [[fifive]] | ||
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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 | ||
Related temperaments: [[decimal]] | Related temperaments: [[decimal]] | ||
==== Scales ==== | ==== Scales ==== | ||
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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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==== Scales ==== | ==== Scales ==== | ||
== 2.3.n subgroups | == 2.3.n subgroups == | ||
2.3.13.n subgroups === | === 2.3.13.n subgroups === | ||
Examples of valid equalizer subgroups in this category (not exhaustive): | Examples of valid equalizer subgroups in this category (not exhaustive): | ||
* 2.3.13.14.17 | * 2.3.13.14.17 | ||
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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]] | ||