User:BudjarnLambeth/Substitute harmonic: Difference between revisions
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Why do this? It could allow for a whole array of subtly different harmonic flavours of existing tunings, while preserving their basic melodic and harmonic structure. | Why do this? It could allow for a whole array of subtly different harmonic flavours of existing tunings, while preserving their basic melodic and harmonic structure. | ||
You can also substitute a simpler harmonic ''n'' for two more complex harmonics, to make a dual-substitute-n temperament{{idiosyncratic}}. | You can also substitute a simpler harmonic ''n'' for two more complex harmonics, to make a dual-substitute-n temperament{{idiosyncratic}}, with similar aims (but different tactics) to a [[dual-fifth]] temperament. | ||
= List of substitute harmonics = | |||
Each harmonic is given in octave-reduced cents. This list is not exhaustive. | Each harmonic is given in octave-reduced cents. This list is not exhaustive. | ||
== Substitutes for the 3rd harmonic (~702) == | |||
*the 381st harmonic (~688) | *the 381st harmonic (~688) | ||
*the 763rd harmonic (~691) | *the 763rd harmonic (~691) | ||
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*the 387th harmonic (~715) | *the 387th harmonic (~715) | ||
== Substitutes for the 5th harmonic (~386) == | |||
*the 317th harmonic (~370) | *the 317th harmonic (~370) | ||
*the 635th harmonic (~373) | *the 635th harmonic (~373) | ||
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*the 323rd harmonic (~402) | *the 323rd harmonic (~402) | ||
== Substitutes for the 7th harmonic (~969) == | |||
*the 111th harmonic (~953) | *the 111th harmonic (~953) | ||
*the 889th harmonic (~955) | *the 889th harmonic (~955) | ||
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*the 113th harmonic (~984) | *the 113th harmonic (~984) | ||
== Substitutes for the 11th harmonic (~551) == | |||
*the 349th harmonic (~537) | *the 349th harmonic (~537) | ||
*the 699th harmonic (~539) | *the 699th harmonic (~539) | ||
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*the 709th harmonic (~564) | *the 709th harmonic (~564) | ||
*the 355th harmonic (~566) | *the 355th harmonic (~566) | ||
= Dual-substitute-n temperaments = | |||
== Dual-substitute-2 temperaments == | |||
== Dual-substitute-3 temperaments == | |||
=== 2.5.767.769 subgroup temperaments === | |||
=== 2.5.383.385 subgroup temperaments === | |||
=== 2.5.765.771 subgroup temperaments === | |||
=== 2.5.191.193 subgroup temperaments === | |||
=== 2.5.7.767.769 subgroup temperaments === | |||
=== 2.5.7.383.385 subgroup temperaments === | |||
=== 2.5.7.765.771 subgroup temperaments === | |||
=== 2.5.7.191.193 subgroup temperaments === | |||
=== 2.5.7.11.767.769 subgroup temperaments === | |||
=== 2.5.7.11.383.385 subgroup temperaments === | |||
=== 2.5.7.11.765.771 subgroup temperaments === | |||
=== 2.5.7.11.191.193 subgroup temperaments === | |||
=== 2.5.11.767.769 subgroup temperaments === | |||
=== 2.5.11.383.385 subgroup temperaments === | |||
=== 2.5.11.765.771 subgroup temperaments === | |||
=== 2.5.11.191.193 subgroup temperaments === | |||
== Dual-substitute-5 temperaments == | |||
== Dual-substitute-7 temperaments == | |||
== Dual-substitute-11 temperaments == | |||
== See also == | == See also == | ||
* [[List of octave-reduced harmonics]] | * [[List of octave-reduced harmonics]] | ||
* [[Naughty and nice harmonics]] | |||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||
[[Category:Octave-reduced harmonics]] | [[Category:Octave-reduced harmonics]] | ||