User:BudjarnLambeth/Equalizer subgroup: Difference between revisions

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__NEWSECTIONLINK__

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 ~~even~~ most people.

'''Disclaimer from the author'''

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.

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'''Assertive harmonics''' means harmonics 5 through 12, inclusive. These harmonics have very strong personalities, tending to define and shape the overall flavor of the scale.

'''Ethereal harmonics''' means harmonics 13, 14, 15, 16, 17 and so on. These harmonics usually tend to fade into the background, but they subtly wield their influence, adding consonances and dissonances undetectable on their own, ~~bit~~ influential together.

'''Ethereal harmonics''' means harmonics 13, 14, 15, 16, 17 and so on. These harmonics usually tend to fade into the background, but they subtly wield their influence, adding consonances and dissonances undetectable on their own, but influential together.

5/1 can act as either a structural or an assertive harmonic depending on context.

[[5/1]] can act as either a structural or an assertive harmonic depending on context.

== Aim of equalizer subgroups ==

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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 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 ~~(not ready audibly)~~ similar to an equalizer subgroup.

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.

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'''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]]

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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

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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

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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

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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

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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

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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

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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 ====

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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

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==== 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):

* 2.3.13.14.17

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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

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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

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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

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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

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'''~~Semiamulet~~'''

'''Semihaunt'''

Subgroup: 2.3.13.17.19

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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

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

'''Semihaunt (+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]

Adjusted ~~Error~~ (cents): 3.417836

Adjusted error (cents): 3.417836

Complexity: 2.661109

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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

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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

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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

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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

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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

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== 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 1: / Line 1: @@
 <div style="border: 1px green solid; background-color: #efe; padding: 0.5em 1em; margin-bottom: 1em">
 __NEWSECTIONLINK__
-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 even most people.
+'''Disclaimer from the author'''
+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 16: / Line 18: @@
 '''Assertive harmonics''' means harmonics 5 through 12, inclusive. These harmonics have very strong personalities, tending to define and shape the overall flavor of the scale.
-'''Ethereal harmonics''' means harmonics 13, 14, 15, 16, 17 and so on. These harmonics usually tend to fade into the background, but they subtly wield their influence, adding consonances and dissonances undetectable on their own, bit influential together.
+'''Ethereal harmonics''' means harmonics 13, 14, 15, 16, 17 and so on. These harmonics usually tend to fade into the background, but they subtly wield their influence, adding consonances and dissonances undetectable on their own, but influential together.
-/1 can act as either a structural or an assertive harmonic depending on context.
+[[5/1]] can act as either a structural or an assertive harmonic depending on context.
 == Aim of equalizer subgroups ==
@@ Line 26: / Line 28: @@
 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 (not ready audibly) similar to an equalizer subgroup.
+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.
@@ Line 40: / 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 74: / 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 96: / 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 118: / 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 140: / 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 162: / 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 184: / 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 206: / 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 241: / 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 288: / 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
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 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 332: / 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 354: / 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 376: / 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 384: / Line 387: @@
-'''Semiamulet'''
+'''Semihaunt'''
 Subgroup: 2.3.13.17.19
@@ Line 398: / 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 406: / Line 409: @@
-'''Semiamulet (+23)'''
+'''Semihaunt (+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]
-Adjusted Error (cents): 3.417836
+Adjusted error (cents): 3.417836
 Complexity: 2.661109
@@ Line 442: / 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 464: / 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 486: / 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 508: / 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 551: / 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 647: / 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]]