28/27: Difference between revisions
Changed "septimal minor second" to "septimal subminor second" in order to distinguish from 15/14 |
m Move the approximation section down |
||
| (27 intermediate revisions by 9 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal third-tone, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma | |||
| Name = | |||
| Color name = z2, zo 2nd | | Color name = z2, zo 2nd | ||
| Sound = jid_28_27_pluck_adu_dr220.mp3 | | Sound = jid_28_27_pluck_adu_dr220.mp3 | ||
| Comma = yes | |||
}} | }} | ||
{{Wikipedia| Septimal third tone }} | |||
The [[superparticular]] interval '''28/27''' | 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. | |||
== Temperaments == | |||
If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out. | |||
== 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 (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]] | ||
* [[ | * [[81/56]] – its [[fifth complement]] | ||
* [ | * [[9/7]] – its [[fourth complement]] | ||
* [[List of superparticular intervals]] | |||
* [[Gallery of just intervals]] | |||
* [[Trienstonisma]], the difference by which a stack of five 28/27's falls short of [[6/5]] | |||
[[Category: | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Third tone]] | [[Category:Third tone]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Trienstonic]] | |||
[[Category:Commas named for the intervals they stack]] | |||
{{Todo| improve synopsis }} | |||
Latest revision as of 13:31, 6 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.
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.
Approximation
This interval is very accurately approximated by 19edo (1\19), and hence the enneadecal temperament.
Temperaments
If treated as a comma to be tempered out, 28/27 may be called the trienstonic comma, which leads to the trienstonic temperaments. See Trienstonic clan for the rank-2 clan of temperaments where it is tempered out.
Notation
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
- Trienstonisma, the difference by which a stack of five 28/27's falls short of 6/5