28/27

Interval information

Ratio	28/27
Factorization	22 × 3-3 × 7
Monzo	[2 -3 0 1⟩
Size in cents	62.9609¢
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 (log2 nd)	9.56224
Weil height (log2 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
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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 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