28/27: Difference between revisions

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The [[superparticular]] interval '''28/27''', '''septimal third-tone~~''' or '''small septimal chroma~~''' 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]].

~~Although called a ''chroma'' for its proximity (and conflation in systems like~~ [[~~septimal meantone~~]]) ~~with the classic chroma [[25/24]]~~, ~~28/27 is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]]~~ and [[Functional Just System]] because it is [[64/63]] smaller than the Pythagorean minor second [[256/243]]. 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~~.

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

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 [[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.

~~On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]]~~ to ~~be tempered out, and in fact~~ the [[trienstonic clan]] ~~does exactly that~~.

== Temperaments ==

Tempering out 28/27 leads to the [[trienstonic clan]] of temperaments.

== See also ==

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

* [[List of superparticular intervals]]

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

* [[Gallery of just intervals]]

* [[Trienstonic clan]], where it is tempered out

* [[Wikipedia: Septimal third tone]]

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-The [[superparticular]] interval '''28/27''', '''septimal third-tone''' or '''small septimal chroma''' 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]].
-Although called a ''chroma'' for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma [[25/24]], 28/27 is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is [[64/63]] smaller than the Pythagorean minor second [[256/243]]. 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.
+It is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
-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 [[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.
-On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]] to be tempered out, and in fact the [[trienstonic clan]] does exactly that.
+== Temperaments ==
+Tempering out 28/27 leads to the [[trienstonic clan]] of temperaments.
 == See also ==
 * [[27/14]] – its [[octave complement]]
 * [[List of superparticular intervals]]
-* [[Gallery of Just Intervals]]
+* [[Gallery of just intervals]]
 * [[Trienstonic clan]], where it is tempered out
 * [[Wikipedia: Septimal third tone]]