28/27
| 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.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 18 | 1\18 | 66.67 | +3.71 | +5.56 |
| 19 | 1\19 | 63.16 | +0.20 | +0.31 |
| 20 | 1\20 | 60.00 | -2.96 | -4.93 |
| 37 | 2\37 | 64.86 | +1.90 | +5.87 |
| 38 | 2\38 | 63.16 | +0.20 | +0.62 |
| 39 | 2\39 | 61.54 | -1.42 | -4.62 |
| 40 | 2\40 | 60.00 | -2.96 | -9.87 |
| 56 | 3\56 | 64.29 | +1.32 | +6.18 |
| 57 | 3\57 | 63.16 | +0.20 | +0.94 |
| 58 | 3\58 | 62.07 | -0.89 | -4.31 |
| 59 | 3\59 | 61.02 | -1.94 | -9.56 |
| 75 | 4\75 | 64.00 | +1.04 | +6.49 |
| 76 | 4\76 | 63.16 | +0.20 | +1.25 |
| 77 | 4\77 | 62.34 | -0.62 | -4.00 |
| 78 | 4\78 | 61.54 | -1.42 | -9.25 |
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
- Trienstonoschisma, the difference by which a stack of five 28/27's falls short of 6/5