28/27: Difference between revisions
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== 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 | 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. | ||
On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]] to be tempered out. | |||
== Temperaments == | == Temperaments == | ||
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== Sagittal notation == | == Sagittal notation == | ||
In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | (|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 ( | In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | (|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 (equivalently, 7/4), as for example in C–A{{nbhsp}}{{sagittal | (|\ }}. The primary role of {{ sagittal | (|\ }} is [[8505/8192#Sagittal notation | 8505/8192]] (35L). The downward version is called '''1/7L''' or '''7L down''' and is represented (in a secondary role) by {{sagittal| (!/ }}. | ||
== See also == | == See also == | ||
* [[27/14]] – its [[octave complement | * [[27/14]] – its [[octave complement] | ||
* [[81/56]] – its [[fifth complement]] | * [[81/56]] – its [[fifth complement]] | ||
* [[9/7]] – its [[fourth complement]] | * [[9/7]] – its [[fourth complement]] | ||
Revision as of 21:26, 3 January 2025
| Interval information |
small septimal chroma,
subminor second,
septimal minor second,
septimal subminor 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 the Functional Just System, viewed as the Pythagorean limma (256/243) altered by the 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.
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.
Sagittal notation
In the Sagittal system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal and is called the 7 large diesis, or 7L for short, because the simplest interval it notates is 7/1 (equivalently, 7/4), as for example in C–A . The primary role of is 8505/8192 (35L). The downward version is called 1/7L or 7L down and is represented (in a secondary role) by .
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