18/17 - Revision history

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

2025-11-03T13:06:18Z

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

← Older revision		Revision as of 13:06, 3 November 2025
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	In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).		In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 25/24}}		{{Interval edo approximation\|25/24}}
	== Terminology and notation ==		== Terminology and notation ==
	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.		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.

Pailiaq at 06:39, 3 November 2025

2025-11-03T06:39:33Z

← Older revision		Revision as of 06:39, 3 November 2025
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	In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).		In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).
			== Approximation ==
			{{Interval_Edo_Approximation \| 25/24}}
	== Terminology and notation ==		== Terminology and notation ==
	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.		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.

Lériendil at 07:22, 17 August 2025

2025-08-17T07:22:05Z

← Older revision		Revision as of 07:22, 17 August 2025
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	* [[Schismatic_family#Quintilischis_(2.3.5.17)\|Quintilischis]].		* [[Schismatic_family#Quintilischis_(2.3.5.17)\|Quintilischis]].
	{{todo\|complete list}}		{{todo\|complete list}}
	Note that all of these reach [[4/3]] as a stack of five 18/17 intervals.		Note that all of these reach [[4/3]] as a stack of five 18/17 intervals (tempering out the [[quinticular comma]]).

	Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.		Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.

Lériendil at 07:21, 17 August 2025

2025-08-17T07:21:16Z

← Older revision		Revision as of 07:21, 17 August 2025
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	* [[Quintaleap]]		* [[Quintaleap]]
	* [[Quindromeda]]		* [[Quindromeda]]
	* [[Schismatic_family#Quintilischis_(2.3.5.17)\|Quintilischis]]		* [[Schismatic_family#Quintilischis_(2.3.5.17)\|Quintilischis]].
	{{todo\|complete list}}		{{todo\|complete list}}
			Note that all of these reach [[4/3]] as a stack of five 18/17 intervals.

	Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.		Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.

Fredg999: Remove link to deleted page

2025-08-07T19:09:58Z

Remove link to deleted page

← Older revision		Revision as of 19:09, 7 August 2025
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[1ed18/17]] – equal multiplication of this interval

	== References ==		== References ==

Fredg999: Merge from 1ed18/17 before deletion

2025-08-07T16:18:04Z

Merge from 1ed18/17 before deletion

← Older revision		Revision as of 16:18, 7 August 2025
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	}}		}}

	In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about ~~99¢~~. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).		In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).

	== Terminology and notation ==		== Terminology and notation ==
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	The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.		The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.

			== Temperaments ==
			{{w\|Vincenzo Galilei}} (1520-1591) proposed a tuning based on eleven 18/17 semitones and one larger semitone of about 111.5{{cent}} (the [[octave complement]])<ref>Barbour, J. Murray. ''[https://archive.org/details/tuningtemperamen00barb/page/n7/mode/2up Tuning and temperament: a historical survey]'', p. 57.</ref>. This [[well temperament]] provides seven wide perfect fifths of about 705.2{{cent}} and five narrow perfect fifths of about 692.7{{cent}}, whose distribution is [[maximally even]] instead of grouping together the wide and the narrow fifths along the [[circle of fifths]], as is often the case in other well temperaments.

			The following [[linear temperament]]s are [[generate]]d by a [[~]]18/17 in the 2.3.5.17 and 2.3.5.17.19 [[subgroup]]s:
			* [[Quintaleap]]
			* [[Quindromeda]]
			* [[Schismatic_family#Quintilischis_(2.3.5.17)\|Quintilischis]]
			{{todo\|complete list}}

			Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.

	== See also ==		== See also ==
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[1ed18/17]] – equal multiplication of this interval		* [[1ed18/17]] – equal multiplication of this interval

			== References ==
			<references/>

	[[Category:Second]]		[[Category:Second]]

BudjarnLambeth at 07:09, 3 November 2024

2024-11-03T07:09:52Z

← Older revision		Revision as of 07:09, 3 November 2024
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	[[Category:Chroma]]		[[Category:Chroma]]
	[[Category:Semitone]]		[[Category:Semitone]]
			[[Category:Commas named after their interval size]]

BudjarnLambeth: | Comma = yes

2024-10-14T04:59:23Z

| Comma = yes

← Older revision		Revision as of 04:59, 14 October 2024
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	\| Color name = 17u1, su unison		\| Color name = 17u1, su unison
	\| Sound = jid_18_17_pluck_adu_dr220.mp3		\| Sound = jid_18_17_pluck_adu_dr220.mp3
			\| Comma = yes
	}}		}}

Lériendil at 07:08, 13 September 2024

2024-09-13T07:08:18Z

← Older revision		Revision as of 07:08, 13 September 2024
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	* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243\|Pythagorean minor second (256/243)]].		* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243\|Pythagorean minor second (256/243)]].

	The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17.		The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.

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

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

2024-01-04T08:17:57Z

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

← Older revision		Revision as of 08:17, 4 January 2024
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	== Terminology and notation ==		== Terminology and notation ==
	~~There exists a disagreement in different conceptualization~~ systems on whether 18/17 should be a [[diatonic semitone]] or a [[chromatic semitone~~]]. In the [[Functional Just System~~]], ~~it is~~ a ~~chromatic semitone, separated by~~ [[~~4131/4096~~]] ~~from [[2187/2048]], the Pythagorean chromatic semitone~~. In [[~~Helmholtz~~-~~Ellis notation~~]]~~, it is~~ a diatonic semitone, separated by [[2187/2176]] from [[256/243]], the Pythagorean diatonic semitone. The term "small septendecimal semitone" omits the diatonic/chromatic part 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 18/17 specifically:
			* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048\|Pythagorean augmented unison (2187/2048)]].
			* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243\|Pythagorean minor second (256/243)]].

			The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17.

	== See also ==		== See also ==
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[18/17 ~~equal-step tuning~~]] – equal multiplication of this interval		* [[1ed18/17]] – equal multiplication of this interval

	[[Category:Second]]		[[Category:Second]]
	[[Category:Chroma]]		[[Category:Chroma]]
	[[Category:Semitone]]		[[Category:Semitone]]