28/27: Difference between revisions

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~~'''28/27'''~~

{{Infobox Interval

|2 -~~3 0 1>~~

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

| Color name = z2, zo 2nd

| Sound = jid_28_27_pluck_adu_dr220.mp3

| Comma = yes

}}

62.~~9609 cents~~

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.

[[~~File:jid_28_27_pluck_adu_dr220.mp3~~]] [[~~:File:jid_28_27_pluck_adu_dr220.mp3|sound sample~~]]

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).

~~The septimal chroma or septimal third-tone~~ is ~~the~~ [[~~superparticular|superparticular~~]] ~~interval 28/27~~, ~~which has the seventh triangular number as a numerator~~ and ~~which 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 28/25~~.

== Approximation ==

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

[~~http:/~~/en.~~wikipedia~~.~~org~~/~~wiki~~/~~Septimal_third-tone http:~~//en.~~wikipedia~~.~~org~~/~~wiki~~/~~Septimal_third-~~tone]

== Temperaments ==

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 ==

=== 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 ==

* [[27/14]] – its [[octave complement]]

* [[81/56]] – its [[fifth complement]]

* [[9/7]] – its [[fourth complement]]

* [[List of superparticular intervals]]

* [[Gallery of just intervals]]

* [[Trienstonoschisma]], the difference by which a stack of five 28/27's falls short of [[6/5]]

[[Category:Second]]

[[Category:Semitone]]

[[Category:Third tone]]

[[Category:Chroma]]

[[Category:Trienstonic]]

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

@@ Line 1: / Line 1: @@
-'''28/27'''
+{{Infobox Interval
-|2 -3 0 1&gt;
+| Name = septimal third-tone, septimal minor second, subminor second, trienstonic comma
+| Color name = z2, zo 2nd
+| Sound = jid_28_27_pluck_adu_dr220.mp3
+| Comma = yes
+}}
+{{Wikipedia| Septimal third tone }}
-.9609 cents
+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.
-[[File:jid_28_27_pluck_adu_dr220.mp3]] [[:File:jid_28_27_pluck_adu_dr220.mp3|sound sample]]
+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).
-The septimal chroma or septimal third-tone is the [[superparticular|superparticular]] interval 28/27, which has the seventh triangular number as a numerator and which 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 28/25.
+== Approximation ==
+This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
-[http://en.wikipedia.org/wiki/Septimal_third-tone http://en.wikipedia.org/wiki/Septimal_third-tone]
+{{Interval edo approximation|28/27}}
+== Temperaments ==
+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 ==
+=== 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 ==
+* [[27/14]] – its [[octave complement]]
+* [[81/56]] – its [[fifth complement]]
+* [[9/7]] – its [[fourth complement]]
+* [[List of superparticular intervals]]
+* [[Gallery of just intervals]]
+* [[Trienstonoschisma]], the difference by which a stack of five 28/27's falls short of [[6/5]]
+[[Category:Second]]
+[[Category:Semitone]]
+[[Category:Third tone]]
+[[Category:Chroma]]
+[[Category:Trienstonic]]
+[[Category:Commas named for the intervals they stack]]