Microtemperament - Revision history

Overthink: add this sentence

2026-06-22T05:16:15Z

add this sentence

← Older revision		Revision as of 05:16, 22 June 2026
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	A '''microtemperament''' is a [[regular temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just.		A '''microtemperament''' is a [[regular temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively [[just]].

	There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments {{EDOs\|118, 171, 270 …}} are [[5-limit]] microtemperaments; that {{EDOs\|171, 270, 441, 612, 643 …}} are [[7-limit]] microtemperaments; {{EDOs\|764, 836, 1084, 1106 …}} are [[11-limit]] microtemperaments, and that {{EDOs\|1171, 1178, 1186 …}} are [[13-limit]] microtemperaments.		There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments {{EDOs\|118, 171, 270 …}} are [[5-limit]] microtemperaments; that {{EDOs\|171, 270, 441, 612, 643 …}} are [[7-limit]] microtemperaments; {{EDOs\|764, 836, 1084, 1106 …}} are [[11-limit]] microtemperaments, and that {{EDOs\|1171, 1178, 1186 …}} are [[13-limit]] microtemperaments.

	Putting 118 and 171 together, we see that the 5-limit [[schismatic]] temperament, which tempers out the [[schisma]] (32805/32768), is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[ennealimmal]] temperament, which tempers out the [[breedsma]] (2401/2400) and the [[ragisma]] (4375/4374), is also a microtemperament. A list of microtemperaments can be found at [[:Category: Microtemperaments]].		Higher-rank microtemperaments are also useful as simplifications of just intonation. Putting 118 and 171 together, we see that the 5-limit [[schismatic]] temperament, which tempers out the [[schisma]] (32805/32768), is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[ennealimmal]] temperament, which tempers out the [[breedsma]] (2401/2400) and the [[ragisma]] (4375/4374), is also a microtemperament. A list of microtemperaments can be found at [[:Category: Microtemperaments]].

	The opposite of a microtemperament is an [[exotemperament]], which is very inaccurate and tempers out large and/or high-damage commas, such as [[16/15]], [[25/24]], or [[28/27]].		The opposite of a microtemperament is an [[exotemperament]], which is very inaccurate and tempers out large and/or high-damage commas, such as [[16/15]], [[25/24]], or [[28/27]].

Overthink: link category; explain exotemperaments

2026-06-22T04:52:16Z

link category; explain exotemperaments

← Older revision		Revision as of 04:52, 22 June 2026
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	There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments {{EDOs\|118, 171, 270 …}} are [[5-limit]] microtemperaments; that {{EDOs\|171, 270, 441, 612, 643 …}} are [[7-limit]] microtemperaments; {{EDOs\|764, 836, 1084, 1106 …}} are [[11-limit]] microtemperaments, and that {{EDOs\|1171, 1178, 1186 …}} are [[13-limit]] microtemperaments.		There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments {{EDOs\|118, 171, 270 …}} are [[5-limit]] microtemperaments; that {{EDOs\|171, 270, 441, 612, 643 …}} are [[7-limit]] microtemperaments; {{EDOs\|764, 836, 1084, 1106 …}} are [[11-limit]] microtemperaments, and that {{EDOs\|1171, 1178, 1186 …}} are [[13-limit]] microtemperaments.

	Putting 118 and 171 together, we see that the 5-limit [[schismatic]] temperament, which tempers out the [[schisma]] (32805/32768), is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[ennealimmal]] temperament, which tempers out the [[breedsma]] (2401/2400) and the [[ragisma]] (4375/4374), is also a microtemperament.		Putting 118 and 171 together, we see that the 5-limit [[schismatic]] temperament, which tempers out the [[schisma]] (32805/32768), is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[ennealimmal]] temperament, which tempers out the [[breedsma]] (2401/2400) and the [[ragisma]] (4375/4374), is also a microtemperament. A list of microtemperaments can be found at [[:Category: Microtemperaments]].

	The opposite of a microtemperament is an [[exotemperament]].		The opposite of a microtemperament is an [[exotemperament]], which is very inaccurate and tempers out large and/or high-damage commas, such as [[16/15]], [[25/24]], or [[28/27]].

	== Practical notes ==		== Practical notes ==

FloraC: - category (set category)

2026-04-23T07:12:02Z

- category (set category)

← Older revision		Revision as of 07:12, 23 April 2026
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	* [[Very high accuracy temperaments]]		* [[Very high accuracy temperaments]]

	~~[[Category:Microtemperaments\| ]] <!-- main article -->~~
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

ArrowHead294 at 18:50, 22 December 2024

2024-12-22T18:50:17Z

← Older revision		Revision as of 18:50, 22 December 2024
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	== See also ==		== See also ==
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
			* [[Very high accuracy temperaments]]

	[[Category:Microtemperaments\| ]] <!-- main article -->		[[Category:Microtemperaments\| ]] <!-- main article -->
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

Fredg999: Improve lead section, split last paragraph into "practical notes" section, misc. edits

2024-08-23T04:36:19Z

Improve lead section, split last paragraph into "practical notes" section, misc. edits

← Older revision		Revision as of 04:36, 23 August 2024
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	~~Any system of~~ [[temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.		A '''microtemperament''' is a [[regular temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just.

	Putting 118 and 171 together, we see that the 5-limit [[~~Schismatic\|~~schismatic ~~temperament~~]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[~~Ennealimmal\|~~ennealimmal ~~temperament~~]], which tempers out the [[~~2401/2400\|~~breedsma]] 2401/2400 and [[~~4375/4374\|~~ragisma]] 4375/4374, is also a microtemperament.		There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments {{EDOs\|118, 171, 270 …}} are [[5-limit]] microtemperaments; that {{EDOs\|171, 270, 441, 612, 643 …}} are [[7-limit]] microtemperaments; {{EDOs\|764, 836, 1084, 1106 …}} are [[11-limit]] microtemperaments, and that {{EDOs\|1171, 1178, 1186 …}} are [[13-limit]] microtemperaments.

			Putting 118 and 171 together, we see that the 5-limit [[schismatic]] temperament, which tempers out the [[schisma]] (32805/32768), is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[ennealimmal]] temperament, which tempers out the [[breedsma]] (2401/2400) and the [[ragisma]] (4375/4374), is also a microtemperament.

	The opposite of a microtemperament is an [[exotemperament]].		The opposite of a microtemperament is an [[exotemperament]].

			== Practical notes ==
	Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].		Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].

	[[Category:Microtemperaments\| ]]		== See also ==
	<!-- main article -->		* [[Unnoticeable comma]]

			[[Category:Microtemperaments\| ]] <!-- main article -->
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

Fredg999 category edits: Moving from Category:Microtemperament to Category:Microtemperaments using Cat-a-lot

2022-02-28T20:14:06Z

Moving from Category:Microtemperament to Category:Microtemperaments using Cat-a-lot

← Older revision		Revision as of 20:14, 28 February 2022
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	Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].		Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].

	[[Category:~~Microtemperament~~\| ]] <!-- main article -->		[[Category:Microtemperaments\| ]]
			<!-- main article -->
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

FloraC: Expand on how to tune microtemperaments

2021-10-31T16:26:36Z

Expand on how to tune microtemperaments

← Older revision		Revision as of 16:26, 31 October 2021
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	Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.		Any system of [[temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.

	Putting 118 and 171 together, we see that the 5-limit [[Schismatic\|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal\|ennealimmal temperament]], which tempers out the [[2401/2400\|breedsma]] 2401/2400 and [[4375/4374\|ragisma]] 4375/4374, is also a microtemperament.		Putting 118 and 171 together, we see that the 5-limit [[Schismatic\|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal\|ennealimmal temperament]], which tempers out the [[2401/2400\|breedsma]] 2401/2400 and [[4375/4374\|ragisma]] 4375/4374, is also a microtemperament.

	The opposite of a microtemperament is an [[exotemperament]].		The opposite of a microtemperament is an [[exotemperament]].

			Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].

	[[Category:Microtemperament\| ]] <!-- main article -->		[[Category:Microtemperament\| ]] <!-- main article -->
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

Cmloegcmluin: add link to opposite

2021-05-12T18:54:51Z

add link to opposite

← Older revision		Revision as of 18:54, 12 May 2021
Line 2:		Line 2:

	Putting 118 and 171 together, we see that the 5-limit [[Schismatic\|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal\|ennealimmal temperament]], which tempers out the [[2401/2400\|breedsma]] 2401/2400 and [[4375/4374\|ragisma]] 4375/4374, is also a microtemperament.		Putting 118 and 171 together, we see that the 5-limit [[Schismatic\|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal\|ennealimmal temperament]], which tempers out the [[2401/2400\|breedsma]] 2401/2400 and [[4375/4374\|ragisma]] 4375/4374, is also a microtemperament.

			The opposite of a microtemperament is an [[exotemperament]].

	[[Category:Microtemperament\| ]] <!-- main article -->		[[Category:Microtemperament\| ]] <!-- main article -->
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

FloraC: Improve categories

2021-04-03T09:23:26Z

Improve categories

← Older revision		Revision as of 09:23, 3 April 2021
Line 4:		Line 4:

	[[Category:Microtemperament\| ]] <!-- main article -->		[[Category:Microtemperament\| ]] <!-- main article -->
	[[Category:~~Theory~~]]		[[Category:Regular temperament theory]]
	[[Category:Method]]		[[Category:Method]]

FloraC: Cleanup

2020-10-13T05:42:41Z

Cleanup

← Older revision		Revision as of 05:42, 13 October 2020
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	Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171~~, 236~~, 270 ~~...~~ are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 ~~...~~ are 7-limit microtemperaments; 764, 836, 1084, 1106 ~~...~~ are 11-limit microtemperaments, and that 1171, 1178, 1186 ~~...~~ are 13-limit microtemperaments.		Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.

	Putting 118 and 171 together, we see that the 5-limit [~~http://en.wikipedia.org/wiki/Schismatic_temperament~~ schismatic temperament], which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[~~Breedsmic_temperaments~~\|ennealimmal temperament]], which tempers out the [~~http:~~/~~/en.wikipedia.org/wiki/Breedsma~~ breedsma] 2401/2400 and ~~the~~ [~~http:~~/~~/en.wikipedia.org/wiki/Ragisma~~ ragisma] 4375/4374 is also a microtemperament.		Putting 118 and 171 together, we see that the 5-limit [[Schismatic\|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal\|ennealimmal temperament]], which tempers out the [[2401/2400\|breedsma]] 2401/2400 and [[4375/4374\|ragisma]] 4375/4374, is also a microtemperament.

	[[Category:Microtemperament\| ]] <!-- main article -->		[[Category:Microtemperament\| ]] <!-- main article -->
	[[Category:Theory]]		[[Category:Theory]]
	[[Category:Method]]		[[Category:Method]]