27/26

Interval information

Ratio	27/26
Factorization	2-1 × 33 × 13-1
Monzo	[-1 3 0 0 0 -1⟩
Size in cents	65.33734¢
Name	small tridecimal third tone
Color name	3u1, thu unison
FJS name	[math]\displaystyle{ \text{A1}_{13} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	9.45533
Weil norm (log2 max(n, d))	9.50978
Wilson norm (sopfr(nd))	24
[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 of 27/16 and the thirteenth harmonic of 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 Functional Just System, that role is taken by 1053/1024.

See also

• 52/27 – its octave complement
• 13/9 – its fifth complement
• Gallery of just intervals
• List of superparticular intervals