17/12 - Revision history

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:04:14Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:04, 3 November 2025
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	The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.		The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 17/12}}		{{Interval edo approximation\|17/12}}
	== See also ==		== See also ==
	* [[24/17]] – its [[octave complement]]		* [[24/17]] – its [[octave complement]]

Pailiaq at 07:27, 3 November 2025

2025-11-03T07:27:47Z

← Older revision		Revision as of 07:27, 3 November 2025
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	The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.		The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.
			== Approximation ==
			{{Interval_Edo_Approximation \| 17/12}}
	== See also ==		== See also ==
	* [[24/17]] – its [[octave complement]]		* [[24/17]] – its [[octave complement]]

FloraC: Simplify the "terminology and notation" section since it's addressed in the 17-limit page

2024-01-04T08:24:40Z

Simplify the "terminology and notation" section since it's addressed in the 17-limit page

← Older revision		Revision as of 08:24, 4 January 2024
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	}}		}}

	In [[17-limit]] [[just intonation]], '''17/12''' is the '''~~larger~~ septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.		In [[17-limit]] [[just intonation]], '''17/12''' is the '''large septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.

	17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].		17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].

	== Terminology and notation ==		== Terminology and notation ==
	~~There exists a disagreement in different conceptualization~~ systems on whether 17/12 should be ~~an augmented fourth or~~ a ~~diminished fifth. In~~ [[~~Functional Just System~~]]~~, it is~~ a ~~diminished fifth, separated by~~ [[~~4131/4096]] from [[1024/729~~]], the ~~Pythagorean diminished fifth In~~ [[~~Helmholtz-Ellis notation~~]]~~, it is an augmented fourth, separated by~~ [[~~2187/2176~~]] ~~from [[729/512]], the Pythagorean augmented fourth. The term "large septendecimal tritone" omits the distinction and only describes its melodic property i.e. the size~~.		Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class\|HC17]]. See [[17-limit]] for a detailed discussion.

	In ~~practice~~, ~~the interval category may~~, ~~arguably, vary~~ by ~~context~~. ~~One solution for the JI user who uses expanded~~ [[~~circle~~-~~of-fifths~~ notation]] is ~~to prepare a~~ [[Pythagorean ~~comma~~]] ~~accidental so that~~ the ~~interval can be notated~~ in ~~either category~~.		For 17/12 specifically:
			* In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from the [[1024/729\|Pythagorean diminished fifth (1024/729)]].
			* In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from the [[729/512\|Pythagorean augmented fourth (729/512)]].

			The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.

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

FloraC: +terminology and notation

2023-01-14T09:17:18Z

+terminology and notation

← Older revision		Revision as of 09:17, 14 January 2023
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	}}		}}

	In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[~~EDO~~]] system contains a close approximation to these intervals.		In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.

	17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].		17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].

			== Terminology and notation ==
			There exists a disagreement in different conceptualization systems on whether 17/12 should be an augmented fourth or a diminished fifth. In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from [[1024/729]], the Pythagorean diminished fifth In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from [[729/512]], the Pythagorean augmented fourth. The term "large septendecimal tritone" omits the distinction and only describes its melodic property i.e. the size.

			In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category.

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

Plumtree: Normalising usage of Infobox Interval

2022-10-25T12:07:06Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 12:07, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 17/12~~
	~~\| Monzo = -2 -1 0 0 0 0 1~~
	~~\| Cents = 603.00041~~
	\| Name = larger septendecimal tritone		\| Name = larger septendecimal tritone
	\| Color name = 17o5, iso 5th		\| Color name = 17o5, iso 5th
	~~\| FJS name = d5<sup>17</sup>~~
	\| Sound = jid_17_12_pluck_adu_dr220.mp3		\| Sound = jid_17_12_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:17-limit]]~~
	[[Category:Tritone]]		[[Category:Tritone]]

Fredg999 category edits: Removing from Category:Pages with internal sound examples using Cat-a-lot

2022-02-22T23:46:42Z

Removing from Category:Pages with internal sound examples using Cat-a-lot

← Older revision		Revision as of 23:46, 22 February 2022
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	[[Category:17-limit]]		[[Category:17-limit]]
	[[Category:Tritone]]		[[Category:Tritone]]
	~~[[Category:Pages with internal sound examples]]~~

TallKite: added the color name

2022-02-13T05:08:56Z

added the color name

← Older revision		Revision as of 05:08, 13 February 2022
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	\| Cents = 603.00041		\| Cents = 603.00041
	\| Name = larger septendecimal tritone		\| Name = larger septendecimal tritone
	\| Color name =		\| Color name = 17o5, iso 5th
	\| FJS name = d5<sup>17</sup>		\| FJS name = d5<sup>17</sup>
	\| Sound = jid_17_12_pluck_adu_dr220.mp3		\| Sound = jid_17_12_pluck_adu_dr220.mp3

Fredg999: Misc. edits, categories

2021-12-12T21:00:49Z

Misc. edits, categories

← Older revision		Revision as of 21:00, 12 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 17/12		\| Ratio = 17/12
	\| Monzo = -2 -1 0 0 0 0 1		\| Monzo = -2 -1 0 0 0 0 1
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	}}		}}

	In [[17-limit]] [[just intonation]], '''17/12''' is the "larger septendecimal tritone", measuring very nearly 603¢. Its inversion is the ~~"first~~ septendecimal tritone," [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.		In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.

	17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].		17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].
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	[[Category:17-limit]]		[[Category:17-limit]]
	~~[[Category:Interval]]~~
	~~[[Category:Ratio]]~~
	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]

Userminusone at 18:46, 27 March 2021

2021-03-27T18:46:08Z

← Older revision		Revision as of 18:46, 27 March 2021
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	[[Category:Ratio]]		[[Category:Ratio]]
	[[Category:Tritone]]		[[Category:Tritone]]
			[[Category:Pages with internal sound examples]]

FloraC: +FJS name

2020-10-19T12:28:26Z

+FJS name

← Older revision		Revision as of 12:28, 19 October 2020
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	\| Name = larger septendecimal tritone		\| Name = larger septendecimal tritone
	\| Color name =		\| Color name =
			\| FJS name = d5<sup>17</sup>
	\| Sound = jid_17_12_pluck_adu_dr220.mp3		\| Sound = jid_17_12_pluck_adu_dr220.mp3
	}}		}}
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	17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].		17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].

	''See also: [[Gallery of just intervals]]''		== See also ==
			* [[24/17]] – its [[octave complement]]
			* [[18/17]] – its [[fifth complement]]
			* [[Gallery of just intervals]]

	[[Category:17-limit]]		[[Category:17-limit]]
			[[Category:Interval]]
			[[Category:Ratio]]
	[[Category:Tritone]]		[[Category:Tritone]]
	~~[[Category:Interval]]~~