27/26

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Interval information
Ratio 27/26
Factorization 2-1 × 33 × 13-1
Monzo [-1 3 0 0 0 -1
Size in cents 65.337341¢
Name small tridecimal third tone
Color name 3u1, thu unison
FJS name [math]\text{A1}_{13}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 9.45533
Weil height (log2 max(n, d)) 9.50978
Wilson height (sopfr (nd)) 24
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.36933 bits
Comma size medium

[sound info]
open this interval in xen-calc

In 13-limit just intonation, 27/26, the small tridecimal third tone, appears as the interval between the Pythagorean major sixth (27/16) and the octave-reduced thirteenth harmonic (13/8). It measures about 65.3 ¢. It is close in size to another 13-limit microtone – 26/25. These intervals differ by the superparticular ratio 676/675, about 2.6 ¢, the island comma; tempering it out produces temperaments associated with The Archipelago.

Temperaments

27/26 is tempered out in the patent vals for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35.

Notation

27/26 is significant in Helmholtz-Ellis notation as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to 64/63 and 33/32 for septimal and undecimal, respectively. However, in the Functional Just System, that role is taken by 1053/1024.

Sagittal notation

In the Sagittal system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal ⁠ ⁠ and is called the 13 large diesis, or 13L for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in C-A⁠ ⁠⁠ ⁠. The primary role of ⁠ ⁠ is 8192/8505 (35L down). The upward version is called 1/13L or 13L up and is represented (in a secondary role) by ⁠ ⁠.

See also