16/15 - Revision history

FloraC: Recategorize

2026-04-05T10:46:12Z

Recategorize

← Older revision		Revision as of 10:46, 5 April 2026
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	[[Category:Semitone]]		[[Category:Semitone]]
	[[Category:Father]]		[[Category:Father]]
	[[Category:Commas named ~~after~~ their ~~interval size~~]]		[[Category:Commas named for the generator of their temperament]]

2026-04-05T10:45:11Z

Update links

← Older revision		Revision as of 10:45, 5 April 2026
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	== Approximation ==		== Approximation ==
	16/15 is very accurately approximated by [[43edo]] (4\43).		16/15 is very accurately approximated by [[43edo]] (4\43).
	{{~~Interval_Edo_Approximation~~\|16/15}}
			{{Interval edo approximation\|16/15}}

	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a [[comma]] to be [[tempering out\|tempered out]], it produces [[father]] temperament, and lends itself the name '''father comma'''. In this [[exotemperament]], 4/3 and 5/4 are equated, and major thirds and fifths become [[octave complement]]s of each other. It is a [[Mersenne comma]].		When this ratio is taken as a [[comma]] to be [[tempering out\|tempered out]], it produces [[father]] temperament, and lends itself the name '''father comma'''. In this [[exotemperament]], 4/3 and 5/4 are equated, and major thirds and fifths become [[octave complement]]s of each other. It is a [[Mersenne comma]].
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	* [[Stockhausenic]]		* [[Stockhausenic]]

	In addition, ~~this~~ [[fractional-octave temperaments]] are generated by a ~16/15:		In addition, the following [[fractional-octave temperaments]] are generated by a ~16/15:
	* [[Quintosec]]		* [[Quintosec]]
	{{~~todo~~\|complete list}}		{{Todo\|complete list}}

	Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic]].		Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic (temperament)\|hendecatonic]].

	== See also ==		== See also ==

2025-11-03T05:57:00Z

← Older revision		Revision as of 05:57, 3 November 2025
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	== Approximation ==		== Approximation ==
	16/15 is very accurately approximated by [[43edo]] (4\43).		16/15 is very accurately approximated by [[43edo]] (4\43).

	{{Interval_Edo_Approximation\|16/15}}		{{Interval_Edo_Approximation\|16/15}}


	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a [[comma]] to be [[tempering out\|tempered out]], it produces [[father]] temperament, and lends itself the name '''father comma'''. In this [[exotemperament]], 4/3 and 5/4 are equated, and major thirds and fifths become [[octave complement]]s of each other. It is a [[Mersenne comma]].		When this ratio is taken as a [[comma]] to be [[tempering out\|tempered out]], it produces [[father]] temperament, and lends itself the name '''father comma'''. In this [[exotemperament]], 4/3 and 5/4 are equated, and major thirds and fifths become [[octave complement]]s of each other. It is a [[Mersenne comma]].

2025-11-03T05:55:41Z

← Older revision		Revision as of 05:55, 3 November 2025
Line 17:		Line 17:
	== Approximation ==		== Approximation ==
	16/15 is very accurately approximated by [[43edo]] (4\43).		16/15 is very accurately approximated by [[43edo]] (4\43).

			{{Interval_Edo_Approximation\|16/15}}


	== Temperaments ==		== Temperaments ==
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	Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic]].		Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic]].

	~~{{Interval_Edo_Approximation\|16/15}}~~

	== See also ==		== See also ==

2025-11-03T05:50:36Z

@@ Line 30: / Line 30: @@
 Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic]].
-{| class="wikitable"
-|+ EDO Approximations for 16/15
+{{Interval_Edo_Approximation|16/15}}
-|-
 == See also ==
 * [[15/8]] – its [[octave complement]]

2025-11-03T04:04:28Z

adding edo approximation tables

@@ Line 30: / Line 30: @@
 Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic]].
+{| class="wikitable"
 == See also ==
 * [[15/8]] – its [[octave complement]]

2025-08-06T02:03:48Z

2025-08-05T19:39:49Z

Temperaments: Remove duplicate entry

← Older revision		Revision as of 19:39, 5 August 2025
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	The following [[linear temperament]]s are [[generate]]d by a [[~]]16/15:		The following [[linear temperament]]s are [[generate]]d by a [[~]]16/15:
	* [[Vavoom]]		* [[Vavoom]]
	* [[Stockhausenic]]
	* [[Stockhausenic]]		* [[Stockhausenic]]

2025-08-05T18:00:19Z

Add more differences in lead section, add approximation section, add temperaments using 16/15 as a generator (merged from 1ed16/15)

@@ Line 6: / Line 6: @@
 }}
 {{Wikipedia|Semitone}}
-The [[5-limit]] [[superparticular]] interval '''16/15''' is the '''just diatonic semitone''', '''classic(al) diatonic semitone''' or '''ptolemaic diatonic semitone'''<ref>For reference, see [[5-limit]]. </ref> – the difference between the major third [[5/4]] and the fourth [[4/3]], and between [[3/2]] and [[8/5]].
+The [[5-limit]] [[superparticular]] interval '''16/15''' is the '''just diatonic semitone''', '''classic(al) diatonic semitone''' or '''ptolemaic diatonic semitone'''<ref>For reference, see [[5-limit]]. </ref>.
 == Temperaments ==
 When this ratio is taken as a [[comma]] to be [[tempering out|tempered out]], it produces [[father]] temperament, and lends itself the name '''father comma'''. In this [[exotemperament]], 4/3 and 5/4 are equated, and major thirds and fifths become [[octave complement]]s of each other. It is a [[Mersenne comma]].
 == See also ==

2024-11-03T06:22:16Z

← Older revision		Revision as of 06:22, 3 November 2024
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	[[Category:Semitone]]		[[Category:Semitone]]
	[[Category:Father]]		[[Category:Father]]
			[[Category:Commas named after their interval size]]

← Older revision		Revision as of 02:03, 6 August 2025
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[16/15 equal-step tuning]] – equal multiplication of this interval

	== Notes ==		== Notes ==