262144/177147 - Revision history

FloraC: Note that it's inconsistently mapped in 23edo and note how to consistently approximate it. +categories

2025-02-07T12:33:35Z

Note that it's inconsistently mapped in 23edo and note how to consistently approximate it. +categories

← Older revision		Revision as of 12:33, 7 February 2025
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	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is often called a "wolf fifth" due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]]. It is very closely approximated by [[23edo]]'s flat fifth of 13\23.		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is often called a "wolf fifth" due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].

			== Approximation ==
			Like any 3-limit intervals, this interval is well approximated by any equal tuning with accurate octaves and fifths. It is very closely, though inconsistently approximated by [[23edo]]'s flat fifth of 13\23. The first superset of 23edo that consistently approximates it is {{nowrap\| 23 × 11 {{=}} [[253edo]] }}.

	== Temperaments ==		== Temperaments ==
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	[[Category:Fifth]]		[[Category:Fifth]]
			[[Category:Subfifth]]
			[[Category:Sixth]]
			[[Category:Diminished sixth]]

Lériendil at 13:37, 6 February 2025

2025-02-06T13:37:07Z

← Older revision		Revision as of 13:37, 6 February 2025
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	}}		}}

	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is often called a "wolf fifth" due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is often called a "wolf fifth" due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]]. It is very closely approximated by [[23edo]]'s flat fifth of 13\23.

	== Temperaments ==		== Temperaments ==

ArrowHead294 at 19:36, 15 January 2025

2025-01-15T19:36:24Z

← Older revision		Revision as of 19:36, 15 January 2025
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	}}		}}

	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is often called a "wolf fifth" due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].

	== Temperaments ==		== Temperaments ==
	In [[compton]] temperament, this interval and [[3/2]] are tempered together, because the ~~pythagorean~~ comma [[531441/524288]] is tempered out.		In [[compton]] temperament, this interval and [[3/2]] are tempered together, because the Pythagorean comma ([[531441/524288]]) is tempered out.

	If this interval itself is taken as a comma to be tempered out, it leads to the [[malicious]] temperament, and the interval can be called the ''malicious comma'' (the origin of the "''malicious com''pliance" pun from that page).		If this interval itself is taken as a comma to be tempered out, it leads to the [[malicious]] temperament, and the interval can be called the ''malicious comma'' (the origin of the "''malicious com''pliance" pun from that page).

FloraC: Vertical spacing

2024-07-16T10:57:09Z

Vertical spacing

← Older revision		Revision as of 10:57, 16 July 2024
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	In [[compton]] temperament, this interval and [[3/2]] are tempered together, because the pythagorean comma [[531441/524288]] is tempered out.		In [[compton]] temperament, this interval and [[3/2]] are tempered together, because the pythagorean comma [[531441/524288]] is tempered out.

			If this interval itself is taken as a comma to be tempered out, it leads to the [[malicious]] temperament, and the interval can be called the ''malicious comma'' (the origin of the "''malicious com''pliance" pun from that page).
	If this interval itself is taken as a comma to be tempered out, it leads to the [[malicious]] temperament, and the interval can be called the '''malicious comma''' (the origin of the ''''malicious com'''pliance' pun from that page).

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

VectorGraphics: added mal temperament

2024-07-16T09:20:36Z

added mal temperament

← Older revision		Revision as of 09:20, 16 July 2024
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	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].

			== Temperaments ==
			In [[compton]] temperament, this interval and [[3/2]] are tempered together, because the pythagorean comma [[531441/524288]] is tempered out.


			If this interval itself is taken as a comma to be tempered out, it leads to the [[malicious]] temperament, and the interval can be called the '''malicious comma''' (the origin of the ''''malicious com'''pliance' pun from that page).

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

Eliora: Undo revision 129456 by Eliora (talk) oops that is [29 -18] not [18 -11]

2023-12-20T16:54:05Z

Undo revision 129456 by Eliora (talk) oops that is [29 -18] not [18 -11]

← Older revision		Revision as of 16:54, 20 December 2023
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	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].

	~~== Temperaments ==~~
	~~[[18edo]] has such a large error on 3/2 that it treats this interval as a comma, this interval being a difference between 11 perfect fifths of [[3/2]] and 7 octaves.~~

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

Eliora at 16:53, 20 December 2023

2023-12-20T16:53:25Z

← Older revision		Revision as of 16:53, 20 December 2023
Line 5:		Line 5:

	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].

			== Temperaments ==
			[[18edo]] has such a large error on 3/2 that it treats this interval as a comma, this interval being a difference between 11 perfect fifths of [[3/2]] and 7 octaves.

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

Yourmusic Productions: More relationships.

2023-12-19T18:02:56Z

More relationships.

← Older revision		Revision as of 18:02, 19 December 2023
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	}}		}}

	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning.		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth [[40/27]] by a [[schisma]].

			== See also ==
			* [[177147/131072]] – its [[octave complement]]
			* [[Gallery of just intervals]]

	[[Category:Fifth]]		[[Category:Fifth]]

VectorGraphics: e

2023-12-19T17:34:00Z

← Older revision		Revision as of 17:34, 19 December 2023
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	}}		}}

	'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval.		'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning.

	[[Category:Fifth]]		[[Category:Fifth]]

Secretcoffee: Created page with "{{Infobox Interval | Name = Pythagorean diminished sixth | Color name = sasawa 6th, ssw6 }} '''262144/177147''', the '''Pythagorean diminished sixth''', is a 3-limit inte..."

2023-07-12T20:21:23Z

Created page with "{{Infobox Interval | Name = Pythagorean diminished sixth | Color name = sasawa 6th, ssw6 }} '''262144/177147''', the '''Pythagorean diminished sixth''', is a 3-limit inte..."

New page

{{Infobox Interval
| Name = Pythagorean diminished sixth
| Color name = sasawa 6th, ssw6
}}

'''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval.

[[Category:Fifth]]