28/27: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

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

~~| Ratio = 28/27~~

~~| Monzo = 2 -3 0 1~~

~~| Cents = 62.9609~~

| Name = ~~septimal chroma,~~ septimal third-tone

| Color name = z2, zo 2nd

| Sound = jid_28_27_pluck_adu_dr220.mp3

| Comma = yes

}}

~~The~~ [[~~superparticular~~]] ~~interval~~ '''28/27''' ~~(also '''septimal chroma''' or~~ '''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.

~~If treated as an interval in its own right~~, it ~~may be described~~ as ~~the septimal minor second~~, ~~since~~ it ~~differs from the Pythagorean minor second~~ [[~~256/243~~]] by [[64/63]], and ~~from~~ [[16/15]] by [[~~36/35~~]]~~. This is analogous to~~ the ~~septimal major second~~ [[~~8/7~~]]~~, which has~~ the ~~same relationship with~~ [[~~9/8~~]] and [[10/9]]~~, respectively~~. ~~Such classification suggests the function of~~ a ~~strong leading tone added to the traditional harmony~~.

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).

== Approximation ==

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

== 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 ==

* [[~~Gallery of Just Intervals~~]]

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

* [[27/14]] - its [[~~inverse interval~~]]

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

* [~~https:~~//~~en.wikipedia.org~~/~~wiki/Septimal_third_tone Septimal third tone - Wikipedia~~]

* [[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:~~7-limit]]~~

[[Category:Second]]

~~[[Category:Interval]]~~

~~[[Category:Superparticular~~]]

[[Category:Semitone]]

[[Category:Third tone]]

[[Category:Chroma]]

[[Category:Trienstonic]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = septimal third-tone, septimal minor second, subminor second, trienstonic comma
-| Ratio = 28/27
-| Monzo = 2 -3 0 1
-| Cents = 62.9609
-| Name = septimal chroma, septimal third-tone
 | Color name = z2, zo 2nd
 | Sound = jid_28_27_pluck_adu_dr220.mp3
+| Comma = yes
 }}
+{{Wikipedia| Septimal third tone }}
-The [[superparticular]] interval '''28/27''' (also '''septimal chroma''' or '''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.
-If treated as an interval in its own right, it may be described as the septimal minor second, since it differs from the Pythagorean minor second [[256/243]] by [[64/63]], and from [[16/15]] by [[36/35]]. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]] and [[10/9]], respectively. Such classification suggests the function of a strong leading tone added to the traditional harmony.
+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).
+== Approximation ==
+This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
+{{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 ==
-* [[Gallery of Just Intervals]]
+* [[27/14]] – its [[octave complement]]
-* [[27/14]] - its [[inverse interval]]
+* [[81/56]] – its [[fifth complement]]
-* [https://en.wikipedia.org/wiki/Septimal_third_tone Septimal third tone &#45; Wikipedia]
+* [[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:7-limit]]
+[[Category:Second]]
-[[Category:Interval]]
-[[Category:Superparticular]]
 [[Category:Semitone]]
 [[Category:Third tone]]
 [[Category:Chroma]]
+[[Category:Trienstonic]]
+[[Category:Commas named for the intervals they stack]]