28/27 - Revision history

FloraC: Rewrite; simplify essentially duplicate names; - "small septimal chroma", not attested anywhere

2026-08-01T11:30:46Z

Rewrite; simplify essentially duplicate names; - "small septimal chroma", not attested anywhere

← Older revision		Revision as of 11:30, 1 August 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = septimal third-tone~~, small septimal chroma, subminor second~~, septimal minor second, ~~septimal~~ subminor second, trienstonic comma		\| Name = septimal third-tone, septimal minor second, subminor second, trienstonic comma
	\| Color name = z2, zo 2nd		\| Color name = z2, zo 2nd
	\| Sound = jid_28_27_pluck_adu_dr220.mp3		\| Sound = jid_28_27_pluck_adu_dr220.mp3
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	{{Wikipedia\| Septimal third tone }}		{{Wikipedia\| Septimal third tone }}

	~~The~~ [[~~superparticular~~]] ~~interval~~ '''28/27''', '''septimal third-tone''' ~~has the seventh [[triangular number]]~~ as ~~a numerator and is~~ the difference between [[15/14]] and [[10/9]], [[9/8]] and [[7/6]], [[9/7]] and [[4/3]], [[3/2]] and [[14/9]], [[12/7]] and [[16/9]], and [[9/5]] and [[28/15]].		In [[7-limit]] [[just intonation]], '''28/27''', measuring about 63.0 [[cent]]s, is conventionally known as the '''septimal third-tone'''. It arises as the difference between [[15/14]] and [[10/9]], between [[9/8]] and [[7/6]], between [[9/7]] and [[4/3]], between [[3/2]] and [[14/9]], between [[12/7]] and [[16/9]], and between [[9/5]] and [[28/15]]. Since it is flat of the [[Pythagorean limma]] by a [[64/63\|septimal comma (64/63)]], it may be called the '''septimal (sub)minor second''' if treated as an interval in its own right, analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

	~~== Terminology ==~~		Finally, since it is a [[superparticular ratio]] which has the seventh [[triangular number]] as a numerator, it a [[triangle-particular]] ratio with factorization ([[49/48]])⋅(64/63).
	~~28/27~~ is ~~traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like~~ [[~~septimal meantone~~]]~~) with~~ the ~~classic chroma,~~ [[~~25/24~~]]~~. However~~, it is a ''[[~~diatonic semitone~~]]~~'' in just intonation notation systems such as~~ [[~~Sagittal notation]], [[Helmholtz–Ellis notation~~]]~~, and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243~~)~~]] altered by the [[64/63\|septimal comma~~ (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

	== Approximation ==		== Approximation ==
	This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.		This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.

	{{Interval edo approximation\|28/27}}		{{Interval edo approximation\|28/27}}

	== Temperaments ==		== Temperaments ==
	If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic ~~temperaments~~'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.		If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic''' temperament.

			See [[Trienstonic clan]] for the rank-2 [[clan]] of temperaments where it is tempered out.

	== Notation ==		== Notation ==
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	[[Category:Trienstonic]]		[[Category:Trienstonic]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]

	~~{{Todo\| improve synopsis }}~~

Overthink: /* See also */ new name

2025-12-15T02:56:02Z

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

2025-11-03T13:01:32Z

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

← Older revision		Revision as of 13:01, 3 November 2025
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	== Approximation ==		== Approximation ==
	This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.		This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
	{{~~Interval_Edo_Approximation~~ \| 28/27}}		{{Interval edo approximation\|28/27}}
	== Temperaments ==		== Temperaments ==
	If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.		If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.

Pailiaq at 06:03, 3 November 2025

2025-11-03T06:03:09Z

← Older revision		Revision as of 06:03, 3 November 2025
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	== Approximation ==		== Approximation ==
	This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.		This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
			{{Interval_Edo_Approximation \| 28/27}}
	== Temperaments ==		== Temperaments ==
	If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.		If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.

FloraC: Move the approximation section down

2025-01-06T13:31:35Z

Move the approximation section down

← Older revision		Revision as of 13:31, 6 January 2025
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	The [[superparticular]] interval '''28/27''', '''septimal third-tone''' has the seventh [[triangular number]] as a numerator and is the difference between [[15/14]] and [[10/9]], [[9/8]] and [[7/6]], [[9/7]] and [[4/3]], [[3/2]] and [[14/9]], [[12/7]] and [[16/9]], and [[9/5]] and [[28/15]].		The [[superparticular]] interval '''28/27''', '''septimal third-tone''' has the seventh [[triangular number]] as a numerator and is the difference between [[15/14]] and [[10/9]], [[9/8]] and [[7/6]], [[9/7]] and [[4/3]], [[3/2]] and [[14/9]], [[12/7]] and [[16/9]], and [[9/5]] and [[28/15]].

			== Terminology ==
			28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

	== Approximation ==		== Approximation ==
	This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.		This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.

	~~== Terminology ==~~
	28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

	== Temperaments ==		== Temperaments ==

FloraC: Sectioning and misc. cleanup and fixes

2025-01-06T13:30:58Z

Sectioning and misc. cleanup and fixes

← Older revision		Revision as of 13:30, 6 January 2025
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	The [[superparticular]] interval '''28/27''', '''septimal third-tone''' has the seventh [[triangular number]] as a numerator and is the difference between [[15/14]] and [[10/9]], [[9/8]] and [[7/6]], [[9/7]] and [[4/3]], [[3/2]] and [[14/9]], [[12/7]] and [[16/9]], and [[9/5]] and [[28/15]].		The [[superparticular]] interval '''28/27''', '''septimal third-tone''' has the seventh [[triangular number]] as a numerator and is the difference between [[15/14]] and [[10/9]], [[9/8]] and [[7/6]], [[9/7]] and [[4/3]], [[3/2]] and [[14/9]], [[12/7]] and [[16/9]], and [[9/5]] and [[28/15]].

	It is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.		== Approximation ==
			This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.

	== Terminology ==		== Terminology ==
	28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[~~Helmholtz–Ellis~~ notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.		28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

	== Temperaments ==		== Temperaments ==
	~~On the other hand~~, 28/27 may be called the '''trienstonic comma''' ~~if it is treated as a [[comma]] to be tempered out~~, which leads to the [[~~trienstonic~~ clan]] of temperaments.		If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.

	== Sagittal notation ==		== Notation ==
	In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (\|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 (equivalently, 7/4), as for example in ~~C–A~~{{nbhsp}}{{sagittal \| (\|\ }}. The primary role of {{ sagittal \| (\|\ }} is [[8505/8192#Sagittal notation \| 8505/8192]] (35L). The downward version is called '''1/7L''' or '''7L down''' and is represented (in a secondary role) by {{sagittal\| (!/ }}.		=== Sagittal notation ===
			In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal\| (\|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 (equivalently, 7/4), as for example in C–A{{nbhsp}}{{sagittal \| (\|\ }}. The primary role of {{sagittal\| (\|\ }} is [[8505/8192 #Sagittal notation\|8505/8192]] (35L). The downward version is called '''1/7L''' or '''7L down''' and is represented (in a secondary role) by {{sagittal\| (!/ }}.

	== See also ==		== See also ==
	* [[27/14]] – its [[octave complement]		* [[27/14]] – its [[octave complement]]
	* [[81/56]] – its [[fifth complement]]		* [[81/56]] – its [[fifth complement]]
	* [[9/7]] – its [[fourth complement]]		* [[9/7]] – its [[fourth complement]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Trienstonic clan]], where it is tempered out
	* [[Trienstonisma]], the difference by which a stack of five 28/27's falls short of [[6/5]]		* [[Trienstonisma]], the difference by which a stack of five 28/27's falls short of [[6/5]]

ArrowHead294 at 21:27, 3 January 2025

2025-01-03T21:27:31Z

← Older revision		Revision as of 21:27, 3 January 2025
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	== Terminology ==		== Terminology ==
	28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.		28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

	~~On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]] to be tempered out.~~

	== Temperaments ==		== Temperaments ==
	~~Tempering out~~ 28/27 leads to the [[trienstonic clan]] of temperaments.		On the other hand, 28/27 may be called the '''trienstonic comma''' if it is treated as a [[comma]] to be tempered out, which leads to the [[trienstonic clan]] of temperaments.

	== Sagittal notation ==		== Sagittal notation ==

ArrowHead294 at 21:26, 3 January 2025

2025-01-03T21:26:35Z

← Older revision		Revision as of 21:26, 3 January 2025
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	== Terminology ==		== Terminology ==
	28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]], and [[Functional Just System]], viewed as the [[256/243\|Pythagorean ~~minor second~~ (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony. On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]] to be tempered out.		28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243\|Pythagorean limma (256/243)]] altered by the [[64/63\|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.

			On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]] to be tempered out.

	== Temperaments ==		== Temperaments ==
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (\|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 (~~equiv.~~ 7/4), as for example in C-A{{nbhsp}}{{sagittal \| (\|\ }}. The primary role of {{ sagittal \| (\|\ }} is [[8505/8192#Sagittal notation \| 8505/8192]] (35L). The downward version is called '''1/7L''' or '''7L down''' and is represented (in a secondary role) by {{sagittal\| (!/ }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (\|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 (equivalently, 7/4), as for example in C–A{{nbhsp}}{{sagittal \| (\|\ }}. The primary role of {{ sagittal \| (\|\ }} is [[8505/8192#Sagittal notation \| 8505/8192]] (35L). The downward version is called '''1/7L''' or '''7L down''' and is represented (in a secondary role) by {{sagittal\| (!/ }}.

	== See also ==		== See also ==
	* [[27/14]] – its [[octave complement]]		* [[27/14]] – its [[octave complement]
	* [[81/56]] – its [[fifth complement]]		* [[81/56]] – its [[fifth complement]]
	* [[9/7]] – its [[fourth complement]]		* [[9/7]] – its [[fourth complement]]

BudjarnLambeth at 00:11, 4 November 2024

2024-11-04T00:11:11Z

← Older revision		Revision as of 00:11, 4 November 2024
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	[[Category:Chroma]]		[[Category:Chroma]]
	[[Category:Trienstonic]]		[[Category:Trienstonic]]
	~~[[Category:Commas named for their regular temperament properties]]~~
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]

	{{Todo\| improve synopsis }}		{{Todo\| improve synopsis }}

BudjarnLambeth at 00:10, 4 November 2024

2024-11-04T00:10:09Z

← Older revision		Revision as of 00:10, 4 November 2024
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	[[Category:Trienstonic]]		[[Category:Trienstonic]]
	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]
			[[Category:Commas named for the intervals they stack]]

	{{Todo\| improve synopsis }}		{{Todo\| improve synopsis }}

← Older revision		Revision as of 02:56, 15 December 2025
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[~~Trienstonisma~~]], the difference by which a stack of five 28/27's falls short of [[6/5]]		* [[Trienstonoschisma]], the difference by which a stack of five 28/27's falls short of [[6/5]]

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