User:BudjarnLambeth/Substitute harmonic: Difference between revisions
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A '''substitute harmonic'''{{idiosyncratic}} is a more complex [[harmonic]] which is used to substitute for a simpler one. | A '''substitute harmonic'''{{idiosyncratic}} is a more complex [[harmonic]] which is used to substitute for a simpler one. | ||
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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. | ||
The use of substitute harmonics is one kind of [[fudging]]. | |||
== List of substitute harmonics == | == List of substitute harmonics == | ||
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=== Substitutes for the 3rd harmonic (~702) === | === Substitutes for the 3rd harmonic (~702) === | ||
*the 381st harmonic (~688) | * the 381st harmonic (~688) | ||
*the 763rd harmonic (~691) | * the 763rd harmonic (~691) | ||
*the 191st harmonic (~693) | * the 191st harmonic (~693) | ||
*the 765th harmonic (~695) | * the 765th harmonic (~695) | ||
*the 383rd harmonic (~697) | * the 383rd harmonic (~697) | ||
*the 767th harmonic (~700) | * the 767th harmonic (~700) | ||
*the 769th harmonic (~704) | * the 769th harmonic (~704) | ||
*the 385th harmonic (~706) | * the 385th harmonic (~706) | ||
*the 771st harmonic (~709) | * the 771st harmonic (~709) | ||
*the 193rd harmonic (~711) | * the 193rd harmonic (~711) | ||
*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) === | ||
*the 317th harmonic (~370) | * the 317th harmonic (~370) | ||
*the 635th harmonic (~373) | * the 635th harmonic (~373) | ||
*the 159th harmonic (~375) | * the 159th harmonic (~375) | ||
*the 637th harmonic (~378) | * the 637th harmonic (~378) | ||
*the 319th harmonic (~381) | * the 319th harmonic (~381) | ||
*the 639th harmonic (~384) | * the 639th harmonic (~384) | ||
*the 641st harmonic (~389) | * the 641st harmonic (~389) | ||
*the 321st harmonic (~392) | * the 321st harmonic (~392) | ||
*the 643rd harmonic (~394) | * the 643rd harmonic (~394) | ||
*the 161st harmonic (~397) | * the 161st harmonic (~397) | ||
*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) === | ||
*the 111th harmonic (~953) | * the 111th harmonic (~953) | ||
*the 889th harmonic (~955) | * the 889th harmonic (~955) | ||
*the 445th harmonic (~957) | * the 445th harmonic (~957) | ||
*the 891st harmonic (~959) | * the 891st harmonic (~959) | ||
*the 223rd harmonic (~961) | * the 223rd harmonic (~961) | ||
*the 893rd harmonic (~963) | * the 893rd harmonic (~963) | ||
*the 447th harmonic (~965) | * the 447th harmonic (~965) | ||
*the 895th harmonic (~967) | * the 895th harmonic (~967) | ||
*the 897th harmonic (~971) | * the 897th harmonic (~971) | ||
*the 449th harmonic (~973) | * the 449th harmonic (~973) | ||
*the 899th harmonic (~975) | * the 899th harmonic (~975) | ||
*the 225th harmonic (~977) | * the 225th harmonic (~977) | ||
*the 901st harmonic (~978) | * the 901st harmonic (~978) | ||
*the 451st harmonic (~980) | * the 451st harmonic (~980) | ||
*the 903rd harmonic (~982) | * the 903rd harmonic (~982) | ||
*the 113th harmonic (~984) | * the 113th harmonic (~984) | ||
=== Substitutes for the 11th harmonic (~551) === | === Substitutes for the 11th harmonic (~551) === | ||
*the 349th harmonic (~537) | * the 349th harmonic (~537) | ||
*the 699th harmonic (~539) | * the 699th harmonic (~539) | ||
*the 175th harmonic (~541) | * the 175th harmonic (~541) | ||
*the 701st harmonic (~544) | * the 701st harmonic (~544) | ||
*the 351st harmonic (~546) | * the 351st harmonic (~546) | ||
*the 703rd harmonic (~549) | * the 703rd harmonic (~549) | ||
*the 705th harmonic (~554) | * the 705th harmonic (~554) | ||
*the 353rd harmonic (~556) | * the 353rd harmonic (~556) | ||
*the 707th harmonic (~559) | * the 707th harmonic (~559) | ||
*the 177th harmonic (~561) | * the 177th harmonic (~561) | ||
*the 709th harmonic (~564) | * the 709th harmonic (~564) | ||
*the 355th harmonic (~566) | * the 355th harmonic (~566) | ||
== Temperaments using substitute harmonics == | == Temperaments using substitute harmonics == | ||
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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 ==== | ||
Same melodic shape as [[diminished]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | Same melodic shape as [[diminished]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | ||
Subgroup | Subgroup | ||
2.113.161.177.193 | 2.113.161.177.193 | ||
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====Pajaraxe ==== | ==== Pajaraxe ==== | ||
Same melodic shape as [[pajara]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | Same melodic shape as [[pajara]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | ||
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*[8, 0, 2, -1, -2⟩ (6635776:6593073) | *[8, 0, 2, -1, -2⟩ (6635776:6593073) | ||
==== Narrowed | |||
==== Narrowed compton ==== | |||
These temperaments are like [[compton]] but with a smaller generator. They reduce the incidence of [[Wolf interval|wolf]] fifths, especially in the smaller 24- and 36-tone [[MOS scale]]s, and allow the melodic shape of [[compton]] to be used in tunings (especially [[edo]]s) that might not otherwise support it. | These temperaments are like [[compton]] but with a smaller generator. They reduce the incidence of [[Wolf interval|wolf]] fifths, especially in the smaller 24- and 36-tone [[MOS scale]]s, 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”. | 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 ===== | ||
| Line 504: | Line 516: | ||
[-19, 12, 0⟩ (531441:524288) | [-19, 12, 0⟩ (531441:524288) | ||
===== Intercom ===== | ===== Intercom ===== | ||
| Line 555: | Line 568: | ||
[-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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===...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 == | ||
*[[Dual-fifth temperaments]] | Scales that make use of substitute harmonics: | ||
*[[List of octave-reduced harmonics]] | * [[Ed255/128]] and [[Ed257/128]] | ||
*[[Naughty and nice harmonics | * [[Intercom scales]] | ||
Other related concepts: | |||
* [[Shadow]] | |||
* [[Subgroup temperaments]] | |||
** [[Equalizer subgroup]]s | |||
** [[Dual-fifth temperaments]] | |||
** [[Half-prime subgroup]]s | |||
* [[List of octave-reduced harmonics]] | |||
* [[User:MasonGreen1/Naughty and nice harmonics]] | |||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||