27/26
Jump to navigation
Jump to search
| 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{n\cdot d}[/math]) |
~4.74374 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.
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.
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