28/27: Difference between revisions
m Normalising usage of Infobox Interval |
m +link to diatonic semitone; +todo |
||
| Line 12: | Line 12: | ||
== Terminology == | == 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. | 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. | ||
== Temperaments == | == Temperaments == | ||
| Line 24: | Line 24: | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Trienstonic clan]], where it is tempered out | * [[Trienstonic clan]], where it is tempered out | ||
* [[Trienstonisma]], the difference by which a stack of five 28/ | * [[Trienstonisma]], the difference by which a stack of five 28/27's falls short of [[6/5]] | ||
[[Category:Second]] | [[Category:Second]] | ||
| Line 31: | Line 31: | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Trienstonic]] | [[Category:Trienstonic]] | ||
{{Todo| improve synopsis }} | |||
Revision as of 08:33, 25 May 2023
| Interval information |
small septimal chroma,
subminor second,
septimal minor second,
trienstonic comma
reduced
S4 / S6
[sound info]
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.
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 Pythagorean minor second (256/243) altered by the 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.
Temperaments
Tempering out 28/27 leads to the trienstonic clan of temperaments.
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
- Trienstonic clan, where it is tempered out
- Trienstonisma, the difference by which a stack of five 28/27's falls short of 6/5