27/26: Difference between revisions
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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{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, 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]]. | |||
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 == | == See also == | ||
* [[52/27]] – its [[octave complement]] | * [[52/27]] – its [[octave complement]] | ||
* [[13/9]] – its [[fifth complement]] | * [[13/9]] – its [[fifth complement]] | ||
* [[26/25]] - the large tridecimal third tone | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Revision as of 13:55, 22 March 2022
| Interval information |
reduced
[sound info]
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 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