28/27: Difference between revisions

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{{Infobox Interval

| Name = septimal third-tone, small septimal chroma, subminor second, septimal minor second, trienstonic comma

| Name = septimal third-tone, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma

| Color name = z2, zo 2nd

| Sound = jid_28_27_pluck_adu_dr220.mp3

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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]].

It 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.

== ~~Terminology~~ ==

== Approximation ==

~~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 '''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~~.

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

== Temperaments ==

~~Tempering~~ out 28/27 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.

== 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 (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 ==

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* [[List of superparticular 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/~~27s~~ falls short of [[6/5]]

[[Category:Second]]

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[[Category:Chroma]]

[[Category:Trienstonic]]

[[Category:Commas named for the intervals they stack]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septimal third-tone, small septimal chroma, subminor second, septimal minor second, trienstonic comma
+| Name = septimal third-tone, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma
 | Color name = z2, zo 2nd
 | Sound = jid_28_27_pluck_adu_dr220.mp3
@@ Line 9: / Line 9: @@
 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.
+== Terminology ==
+/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.
-== Terminology ==
+== Approximation ==
-/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 '''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.
+This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
 == Temperaments ==
-Tempering out 28/27 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.
+== 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 (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 ==
@@ Line 23: / Line 28: @@
 * [[List of superparticular 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 28/27s falls short of [[6/5]]
 [[Category:Second]]
@@ Line 31: / Line 35: @@
 [[Category:Chroma]]
 [[Category:Trienstonic]]
+[[Category:Commas named for the intervals they stack]]
+{{Todo| improve synopsis }}