28/27: Difference between revisions
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{{Wikipedia| Septimal third tone }} | {{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]]. | 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. | It is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament. | ||
Revision as of 22:11, 19 January 2022
| 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
- 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 28/27s falls short of 6/5