User:BudjarnLambeth/Substitute harmonic: Difference between revisions
→...with mostly sharp substitutes: Added Compton substitute templates |
|||
| Line 277: | Line 277: | ||
*[-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=== | ||