28/27: Difference between revisions
Wikispaces>genewardsmith **Imported revision 244888913 - Original comment: ** |
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{{Infobox Interval | |||
| Name = septimal third-tone, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma | |||
| Color name = z2, zo 2nd | |||
| Sound = jid_28_27_pluck_adu_dr220.mp3 | |||
| Comma = yes | |||
}} | |||
{{Wikipedia| 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]]. | |||
== 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 == | |||
* [[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:Second]] | |||
[[Category:Semitone]] | |||
[[Category:Third tone]] | |||
[[Category:Chroma]] | |||
[[Category:Trienstonic]] | |||
[[Category:Commas named for the intervals they stack]] | |||
{{Todo| improve synopsis }} | |||