28/27
Ratio | 28/27 |
Factorization | 2^{2} × 3^{-3} × 7 |
Monzo | [2 -3 0 1⟩ |
Size in cents | 62.960904¢ |
Names | septimal third-tone, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma |
Color name | z2, zo 2nd |
FJS name | [math]\text{m2}^{7}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 9.56224 |
Weil height (log_{2} max(n, d)) | 9.61471 |
Wilson height (sopfr (nd)) | 20 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.37861 bits |
Comma size | medium |
S-expressions | S7 × S8, S4 / S6 |
[sound info] | |
open this interval in xen-calc |
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 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 (equiv. 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