28/27: Difference between revisions
It need to be pointed out the names differ by contexts (and "septimal third-tone" sounds most neutral so I place it first) |
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The [[superparticular]] interval '''28/27''', '''septimal third-tone | 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 [[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 == | |||
Tempering out 28/27 leads to the [[trienstonic clan]] of temperaments. | |||
== See also == | == See also == | ||
* [[27/14]] – its [[octave complement]] | * [[27/14]] – its [[octave complement]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of | * [[Gallery of just intervals]] | ||
* [[Trienstonic clan]], where it is tempered out | * [[Trienstonic clan]], where it is tempered out | ||
* [[Wikipedia: Septimal third tone]] | * [[Wikipedia: Septimal third tone]] | ||
Revision as of 16:10, 10 April 2021
| Interval information |
small septimal chroma,
subminor second,
septimal minor second,
trienstonic comma
reduced
[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
- List of superparticular intervals
- Gallery of just intervals
- Trienstonic clan, where it is tempered out
- Wikipedia: Septimal third tone