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 ([[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]]. | 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]]. | ||
== 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]]. | 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 {{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 == | == See also == | ||
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[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Third tone]] | [[Category:Third tone]] | ||
[[Category:Commas named after their interval size]] | |||
Latest revision as of 07:21, 3 November 2024
| 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 (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