Microtemperament - Revision history

Inthar at 23:48, 2 June 2026

2026-06-02T23:48:02Z

← Older revision		Revision as of 23:48, 2 June 2026
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	A '''microtemperament''' is a very accurate and usually very complex [[temperament]]. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.		A '''microtemperament''' is a very accurate and usually very complex [[temperament]]. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.

	Notable microtemperaments are [[Schismic]], [[Alphatricot]], and [[Ennealimmal]]. Of these, Schismic is the exception: while Ennealimmal requires a 36-note ~~scale~~ in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note ~~scale~~ if the prime subharmonics are to be included, and an 81-note ~~scale~~ to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving [[53edo]] as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note ~~scale~~ in [[29edo]] or [[41edo]], making it somewhat more tractable.		Notable microtemperaments are [[Schismic]], [[Alphatricot]], and [[Ennealimmal]]. Of these, Schismic is the exception: while Ennealimmal requires a 36-note [[MOS]] in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note MOS if the prime subharmonics are to be included, and an 81-note MOS to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving [[53edo]] as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note MOS in [[29edo]] or [[41edo]], making it somewhat more tractable.

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Inthar at 23:47, 2 June 2026

2026-06-02T23:47:23Z

← Older revision		Revision as of 23:47, 2 June 2026
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	Notable microtemperaments are [[Schismic]], [[Alphatricot]], and [[Ennealimmal]]. Of these, Schismic is the exception: while Ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving [[53edo]] as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in [[29edo]] or [[41edo]], making it somewhat more tractable.		Notable microtemperaments are [[Schismic]], [[Alphatricot]], and [[Ennealimmal]]. Of these, Schismic is the exception: while Ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving [[53edo]] as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in [[29edo]] or [[41edo]], making it somewhat more tractable.

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2026-06-02T21:13:53Z

Add links to various pages

← Older revision		Revision as of 21:13, 2 June 2026
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	A '''microtemperament''' is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.		A '''microtemperament''' is a very accurate and usually very complex [[temperament]]. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.

	Notable microtemperaments are Schismic, Alphatricot, and Ennealimmal. Of these, Schismic is the exception: while Ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewhat more tractable.		Notable microtemperaments are [[Schismic]], [[Alphatricot]], and [[Ennealimmal]]. Of these, Schismic is the exception: while Ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving [[53edo]] as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in [[29edo]] or [[41edo]], making it somewhat more tractable.

Inthar at 20:26, 2 June 2026

2026-06-02T20:26:29Z

← Older revision		Revision as of 20:26, 2 June 2026
Line 1:		Line 1:
	A '''microtemperament''' is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.		A '''microtemperament''' is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.

	Notable microtemperaments are ~~schismic~~, ~~alphatricot~~, and ~~ennealimmal~~. Of these, ~~schismic~~ is the exception: while ~~ennealimmal~~ requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while ~~alphatricot~~ reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, ~~schismic~~ finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewhat more tractable.		Notable microtemperaments are Schismic, Alphatricot, and Ennealimmal. Of these, Schismic is the exception: while Ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while Alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, Schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewhat more tractable.

Inthar at 20:25, 2 June 2026

2026-06-02T20:25:48Z

← Older revision		Revision as of 20:25, 2 June 2026
Line 1:		Line 1:
	A '''microtemperament''' is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.		A '''microtemperament''' is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.

	Notable microtemperaments are schismic, alphatricot, and ennealimmal. Of these, schismic is the exception: while ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it ~~somewh~~		Notable microtemperaments are schismic, alphatricot, and ennealimmal. Of these, schismic is the exception: while ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewhat more tractable.

Inthar at 20:22, 2 June 2026

2026-06-02T20:22:34Z

← Older revision		Revision as of 20:22, 2 June 2026
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	A microtemperament is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.		A '''microtemperament''' is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.

	Notable microtemperaments are schismic, alphatricot, and ennealimmal. Of these, schismic is the exception: while ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewh		Notable microtemperaments are schismic, alphatricot, and ennealimmal. Of these, schismic is the exception: while ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewh

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2026-06-02T19:44:44Z

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A microtemperament is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to [[comma theory]]. Additionally, they usually have extremely narrow tuning ranges.

Notable microtemperaments are schismic, alphatricot, and ennealimmal. Of these, schismic is the exception: while ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewh