From Xenharmonic Wiki
(Redirected from Trienstonic comma)
Jump to navigation Jump to search
Interval information
Ratio 28/27
Factorization 22 × 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,
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

[sound info]
open this interval in xen-calc
English Wikipedia has an article on:

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.


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.


Tempering out 28/27 leads to the trienstonic clan of temperaments.

See also