28/27: Difference between revisions

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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]].

== 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.

== Approximation ==

This interval 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.

== Temperaments ==

@@ Line 8: / Line 8: @@
 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]].
+== 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.
 == Approximation ==
 This interval 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.
 == Temperaments ==