User:BudjarnLambeth/Substitute harmonic: Difference between revisions
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You could also substitute a simpler harmonic ''n'' in a dual-n temperament for two more complex harmonics, to make a '''dual-substitute-n temperament'''{{idiosyncratic}}. For example, you could convert a [[Dual-fifth temperaments|2.3-.3+.5 subgroup temperament]] into a 2.5.767.769 subgroup temperament. | You could also substitute a simpler harmonic ''n'' in a dual-n temperament for two more complex harmonics, to make a '''dual-substitute-n temperament'''{{idiosyncratic}}. For example, you could convert a [[Dual-fifth temperaments|2.3-.3+.5 subgroup temperament]] into a 2.5.767.769 subgroup temperament. | ||
== List of substitute harmonics == | == List of substitute harmonics == | ||
Each harmonic is given in octave-reduced [[cent]]s. This list is not exhaustive. | Each harmonic is given in octave-reduced [[cent]]s. This list is not exhaustive. | ||
=== Substitutes for the 2nd harmonic (1200) === | === Substitutes for the 2nd harmonic (1200) === | ||
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* the 515th harmonic (~10) | * the 515th harmonic (~10) | ||
* the 1031st harmonic (~12) | * the 1031st harmonic (~12) | ||
=== Substitutes for the 3rd harmonic (~702) === | === Substitutes for the 3rd harmonic (~702) === | ||
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*the 773rd harmonic (~713) | *the 773rd harmonic (~713) | ||
*the 387th harmonic (~715) | *the 387th harmonic (~715) | ||
=== Substitutes for the 5th harmonic (~386) === | === Substitutes for the 5th harmonic (~386) === | ||
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*the 645th harmonic (~400) | *the 645th harmonic (~400) | ||
*the 323rd harmonic (~402) | *the 323rd harmonic (~402) | ||
=== Substitutes for the 7th harmonic (~969) === | === Substitutes for the 7th harmonic (~969) === | ||
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*the 709th harmonic (~564) | *the 709th harmonic (~564) | ||
*the 355th harmonic (~566) | *the 355th harmonic (~566) | ||
== Temperaments using substitute harmonics == | == Temperaments using substitute harmonics == | ||
===...with mostly sharp substitutes=== | ===...with mostly sharp substitutes=== | ||
Name these after sharp weapons. If they closely resemble another temperament, reference that temperament in the name. | Name these after sharp weapons. If they closely resemble another temperament, reference that temperament in the name. | ||
====Daggerminished==== | ====Daggerminished==== | ||
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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 ==== | ==== Narrowed Compton ==== | ||
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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”. | 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 ===== | ===== Dotcom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Sitcom ===== | ===== Sitcom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Romcom ===== | ===== Romcom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Income ===== | ===== Income ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Outcome ===== | ===== Outcome ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Telecom ===== | ===== Telecom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Intercom ===== | ===== Intercom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Newcome ===== | ===== Newcome ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Satcom ===== | ===== Satcom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Minicom ===== | ===== Minicom ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Glycome ===== | ===== Glycome ===== | ||
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[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===...with mostly flat substitutes=== | ===...with mostly flat substitutes=== | ||
Name these after flat regions like deserts. If they closely resemble another temperament, reference that temperament in the name. | Name these after flat regions like deserts. If they closely resemble another temperament, reference that temperament in the name. | ||
====Sahara==== | ====Sahara==== | ||
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*[2, 3, -1, -1, -1⟩ (1823508:1771525) | *[2, 3, -1, -1, -1⟩ (1823508:1771525) | ||
*[-15, 0, 1, -1, 2⟩ (5800479:5734400) | *[-15, 0, 1, -1, 2⟩ (5800479:5734400) | ||
'''Sahara Septatonic scale''': A nice subset of Sahara[9]. Try noodling with it in Scale Workshop: | '''Sahara Septatonic scale''': A nice subset of Sahara[9]. Try noodling with it in Scale Workshop: | ||
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*1071.881 | *1071.881 | ||
*1200. | *1200. | ||
===...with an even mix of both=== | ===...with an even mix of both=== | ||
Name these after dishes which involve mixing things (e.g. stirfry, salad). If they closely resemble another temperament, reference that temperament in the name. | Name these after dishes which involve mixing things (e.g. stirfry, salad). If they closely resemble another temperament, reference that temperament in the name. | ||
==See also== | ==See also== | ||