27/26: Difference between revisions

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 reduction|octave-reduced]] thirteenth [[harmonic]] ([[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 tempered out in the patent vals for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35.  

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]].

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{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{{nbhsp}}{{sagittal | (!/ }}. The primary role of {{ sagittal | (!/ }} is [[8505/8192#Sagittal notation | 8192/8505]] (35L down). The upward version is called '''1/13L''' or '''13L up''' and is represented (in a secondary role) by {{sagittal| (|\ }}.

== See also ==

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

 

[[Category:Commas named after their interval size]]