27/26
Ratio | 27/26 |
Factorization | 2^{-1} × 3^{3} × 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 (log_{2} nd) | 9.45533 |
Weil height (log_{2} 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
- 52/27 – its octave complement
- 13/9 – its fifth complement
- 26/25 - the large tridecimal third tone
- Gallery of just intervals
- List of superparticular intervals