User:BudjarnLambeth/Substitute harmonic: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
→...with mostly sharp substitutes: Added Compton substitute templates
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*[-9, -2, 0, 1, 2⟩ (6593073:6537728)
*[-9, -2, 0, 1, 2⟩ (6593073:6537728)
*[8, 0, 2, -1, -2⟩ (6635776:6593073)
*[8, 0, 2, -1, -2⟩ (6635776:6593073)
==== Narrowed Compton ====
These temperaments are like [[compton]] but with a smaller generator. They reduce the incidence of [[wolf]] fifths, and allow the melodic shape of [[compton]] to be used in tunings (especially [[edo]]s that might not otherwise support it.
These temperaments work by replacing the 5th harmonic with a slightly sharper substitute harmonic. These temperaments do not follow the naming conventions of other sharp-substitute temperaments. Instead these should be named using words that end with “com” or “come”.
===== Dotcom =====
Equal Temperament Mappings
2 3 43
[ ⟨ 12 19 65 ]
⟨ 48 76 261 ] ⟩
Reduced Mapping
2 3 43
[ ⟨ 12 19 65 ]
⟨ 0 0 1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 8.1729]
POTE Step Tunings (cents)
⟨67.30854, 8.17286]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 6508.173]
POTE Mistunings (cents)
⟨0.000, -1.955, -3.345]
Complexity 1.041959
Adjusted Error 2.733862 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Sitcom =====
Equal Temperament Mappings
2 3 85
[ ⟨ 12 19 77 ]
⟨ 48 76 307 ] ⟩
Reduced Mapping
2 3 85
[ ⟨ 12 19 77 ]
⟨ 0 0 -1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 12.6817]
POTE Step Tunings (cents)
⟨49.27306, 12.68173]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 7687.318]
POTE Mistunings (cents)
⟨0.000, -1.955, -3.951]
Complexity 0.882135
Adjusted Error 3.229180 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Romcom =====
Equal Temperament Mappings
2 3 91
[ ⟨ 12 19 78 ]
⟨ 36 57 235 ] ⟩
Reduced Mapping
2 3 91
[ ⟨ 12 19 78 ]
⟨ 0 0 1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 5.3421]
POTE Step Tunings (cents)
⟨83.97384, 5.34205]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 7805.342]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.012]
Complexity 0.868796
Adjusted Error 3.278758 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Income =====
Equal Temperament Mappings
2 3 135
[ ⟨ 12 19 85 ]
⟨ 48 76 339 ] ⟩
Reduced Mapping
2 3 135
[ ⟨ 12 19 85 ]
⟨ 0 0 -1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 12.1836]
POTE Step Tunings (cents)
⟨51.26579, 12.18355]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 8487.816]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.362]
Complexity 0.798940
Adjusted Error 3.565442 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Outcome =====
Equal Temperament Mappings
2 3 143
[ ⟨ 12 19 86 ]
⟨ 48 76 343 ] ⟩
Reduced Mapping
2 3 143
[ ⟨ 12 19 86 ]
⟨ 0 0 -1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 12.5679]
POTE Step Tunings (cents)
⟨49.72855, 12.56786]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 8587.432]
POTE Mistunings (cents)
⟨-0.000, -1.955, -4.413]
Complexity 0.789672
Adjusted Error 3.607288 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Telecom =====
Equal Temperament Mappings
2 3 191
[ ⟨ 12 19 91 ]
⟨ 48 76 363 ] ⟩
Reduced Mapping
2 3 191
[ ⟨ 12 19 91 ]
⟨ 0 0 -1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 11.7563]
POTE Step Tunings (cents)
⟨52.97495, 11.75626]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 9088.244]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.671]
Complexity 0.746156
Adjusted Error 3.817661 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Intercom =====
Equal Temperament Mappings
2 3 193
[ ⟨ 12 19 91 ]
⟨ 36 57 274 ] ⟩
Reduced Mapping
2 3 193
[ ⟨ 12 19 91 ]
⟨ 0 0 1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 6.2683]
POTE Step Tunings (cents)
⟨81.19502, 6.26833]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 9106.268]
POTE Mistunings (cents)
⟨-0.000, -1.955, -4.680]
Complexity 0.744680
Adjusted Error 3.825233 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Newcome =====
Equal Temperament Mappings
2 3 217
[ ⟨ 12 19 93 ]
⟨ 36 57 280 ] ⟩
Reduced Mapping
2 3 217
[ ⟨ 12 19 93 ]
⟨ 0 0 1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 9.0771]
POTE Step Tunings (cents)
⟨72.76862, 9.07713]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 9309.077]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.784]
Complexity 0.728456
Adjusted Error 3.910426 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Satcom =====
Equal Temperament Mappings
2 3 227
[ ⟨ 12 19 94 ]
⟨ 48 76 375 ] ⟩
Reduced Mapping
2 3 227
[ ⟨ 12 19 94 ]
⟨ 0 0 -1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 12.9662]
POTE Step Tunings (cents)
⟨48.13507, 12.96623]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 9387.034]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.824]
Complexity 0.722406
Adjusted Error 3.943173 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Minicom =====
Equal Temperament Mappings
2 3 243
[ ⟨ 12 19 95 ]
⟨ 24 38 191 ] ⟩
Reduced Mapping
2 3 243
[ ⟨ 12 19 95 ]
⟨ 0 0 1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 4.8900]
POTE Step Tunings (cents)
⟨90.21997, 4.89002]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 9504.890]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.885]
Complexity 0.713449
Adjusted Error 3.992680 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)
===== Glycome =====
Equal Temperament Mappings
2 3 255
[ ⟨ 12 19 96 ]
⟨ 48 76 383 ] ⟩
Reduced Mapping
2 3 255
[ ⟨ 12 19 96 ]
⟨ 0 0 -1 ] ⟩
POTE Generator Tunings (cents)
⟨100.0000, 11.7037]
POTE Step Tunings (cents)
⟨53.18508, 11.70373]
POTE Tuning Map (cents)
⟨1200.000, 1900.000, 9588.296]
POTE Mistunings (cents)
⟨0.000, -1.955, -4.928]
Complexity 0.707243
Adjusted Error 4.027716 cents
TE Error 0.503820 cents/octave
Unison Vector
[-19, 12, 0⟩ (531441:524288)


===...with mostly flat substitutes===
===...with mostly flat substitutes===