24/17 - Revision history

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

2025-11-03T13:15:58Z

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

← Older revision		Revision as of 13:15, 3 November 2025
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	The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].		The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 24/17}}		{{Interval edo approximation\|24/17}}
	== See also ==		== See also ==
	* [[17/12]] – its [[octave complement]]		* [[17/12]] – its [[octave complement]]

Pailiaq at 07:25, 3 November 2025

2025-11-03T07:25:16Z

← Older revision		Revision as of 07:25, 3 November 2025
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	The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].		The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].
			== Approximation ==
			{{Interval_Edo_Approximation \| 24/17}}
	== See also ==		== See also ==
	* [[17/12]] – its [[octave complement]]		* [[17/12]] – its [[octave complement]]

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

2024-01-04T08:22:01Z

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

← Older revision		Revision as of 08:22, 4 January 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~smaller~~ septendecimal tritone		\| Name = small septendecimal tritone
	\| Color name = 17u4, su 4th		\| Color name = 17u4, su 4th
	\| Sound = jid_24_17_pluck_adu_dr220.mp3		\| Sound = jid_24_17_pluck_adu_dr220.mp3
	}}		}}

	In [[17-limit]] [[just intonation]], '''24/17''' is the '''~~smaller~~ septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way.		In [[17-limit]] [[just intonation]], '''24/17''' is the '''small septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way.

	== Terminology and notation ==		== Terminology and notation ==
	~~There exists a disagreement in different conceptualization~~ systems on whether 24/17 should be ~~an augmented fourth or~~ a ~~diminished fifth. In~~ [[~~Functional Just System~~]]~~, it is an augmented fourth, separated by~~ [[~~4131/4096~~]] ~~from~~ [[~~729/512~~]]~~, the Pythagorean augmented fourth~~. In [[~~Helmholtz~~-~~Ellis notation~~]]~~, it is~~ a diminished fifth, separated by [[2187/2176]] from [[1024/729]], the Pythagorean diminished fifth. The term "small 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 24/17 specifically:
			* In [[Functional Just System]], it is an augmented fourth, separated by [[4131/4096]] from the [[729/512\|Pythagorean augmented fourth (729/512)]].
			* In [[Helmholtz-Ellis notation]], it is a diminished fifth, separated by [[2187/2176]] from the [[1024/729\|Pythagorean diminished fifth (1024/729)]].

			The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].

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

FloraC: Style

2023-01-14T09:20:44Z

Style

← Older revision		Revision as of 09:20, 14 January 2023
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	}}		}}

	In [[17-limit]] [[just intonation]], '''24/17''' is the '''smaller septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[~~EDO~~]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good ~~EDO~~ system for using the half-octave in this way.		In [[17-limit]] [[just intonation]], '''24/17''' is the '''smaller septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way.

	== Terminology and notation ==		== Terminology and notation ==

FloraC: +terminology and notation

2023-01-14T09:19:31Z

+terminology and notation

← Older revision		Revision as of 09:19, 14 January 2023
Line 6:		Line 6:

	In [[17-limit]] [[just intonation]], '''24/17''' is the '''smaller septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[EDO]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good EDO system for using the half-octave in this way.		In [[17-limit]] [[just intonation]], '''24/17''' is the '''smaller septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[EDO]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good EDO system for using the half-octave in this way.

			== Terminology and notation ==
			There exists a disagreement in different conceptualization systems on whether 24/17 should be an augmented fourth or a diminished fifth. In [[Functional Just System]], it is an augmented fourth, separated by [[4131/4096]] from [[729/512]], the Pythagorean augmented fourth. In [[Helmholtz-Ellis notation]], it is a diminished fifth, separated by [[2187/2176]] from [[1024/729]], the Pythagorean diminished fifth. The term "small 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 ==

TallKite: added color name

2022-12-04T01:08:05Z

added color name

← Older revision		Revision as of 01:08, 4 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = smaller septendecimal tritone		\| Name = smaller septendecimal tritone
			\| Color name = 17u4, su 4th
	\| Sound = jid_24_17_pluck_adu_dr220.mp3		\| Sound = jid_24_17_pluck_adu_dr220.mp3
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T14:27:12Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 14:27, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 24/17~~
	~~\| Monzo = 3 1 0 0 0 0 -1~~
	~~\| Cents = 596.99959~~
	\| Name = smaller septendecimal tritone		\| Name = smaller septendecimal tritone
	~~\| Color name =~~
	~~\| FJS name = A4<sub>17</sub>~~
	\| Sound = jid_24_17_pluck_adu_dr220.mp3		\| Sound = jid_24_17_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

2022-02-22T23:46:44Z

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]]~~

Fredg999: Misc. edits, categories

2021-12-15T19:07:14Z

Misc. edits, categories

← Older revision		Revision as of 19:07, 15 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 24/17		\| Ratio = 24/17
	\| Monzo = 3 1 0 0 0 0 -1		\| Monzo = 3 1 0 0 0 0 -1
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	[[Category:17-limit]]		[[Category:17-limit]]
	~~[[Category:Interval]]~~
	~~[[Category:Ratio]]~~
	[[Category:Tritone]]		[[Category:Tritone]]
			[[Category:Pages with internal sound examples]]

FloraC: +FJS name

2020-10-19T12:28:19Z

+FJS name

← Older revision		Revision as of 12:28, 19 October 2020
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	\| Name = smaller septendecimal tritone		\| Name = smaller septendecimal tritone
	\| Color name =		\| Color name =
			\| FJS name = A4<sub>17</sub>
	\| Sound = jid_24_17_pluck_adu_dr220.mp3		\| Sound = jid_24_17_pluck_adu_dr220.mp3
	}}		}}

	In [[17-limit]] [[just intonation]], '''24/17''' is the "smaller septendecimal tritone", measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone." The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[EDO]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good EDO system for using the half-octave in this way.		In [[17-limit]] [[just intonation]], '''24/17''' is the '''smaller septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[EDO]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good EDO system for using the half-octave in this way.

	''See also: [[Gallery of just intervals]]''		== See also ==
			* [[17/12]] – its [[octave complement]]
			* [[17/16]] – its [[fifth complement]]
			* [[Gallery of just intervals]]

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