28/27: Difference between revisions

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The [[superparticular]] interval '''28/27''' (also '''small 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]].

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.

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).

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

== See also ==

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 The [[superparticular]] interval '''28/27''' (also '''small 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]].
-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.
+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).
+It is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
 == See also ==