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 out this comma 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]].

== Approximation ==

== Sagittal notation ==

== 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 ~~ratio~~ it notates is 8~~:13~~, as for example in C:A{{sagittal | (!/ }}. The primary role of {{ sagittal | (!/ }} is [[8505/8192#Sagittal notation | 8192/8505]] (35L down).

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]]. It is worth noting that [[13/8]] is closer to minor than it is to major (some might argue 13/8 to be [[supraminor]] instead of neutral), so [[1053/1024]] is significantly smaller.

=== 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| (|\ }}.

== Temperaments ==

If treated as a [[comma]] to be [[tempering out|tempered out]], it leads to the [[ultraflat]] temperament of the [[2.3.13 subgroup]]. It is tempered out in the [[patent val]]s for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35.

== See also ==

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[[Category:Chroma]]

[[Category:Third tone]]

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

@@ Line 5: / Line 5: @@
 | Comma = yes
 }}
-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 out this comma produces temperaments associated with [[The Archipelago]].
-/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]].
+== Approximation ==
+{{Interval edo approximation}}
-== Sagittal notation ==
+== 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 ratio it notates is 8:13, as for example in C:A{{sagittal | (!/ }}. The primary role of {{ sagittal | (!/ }} is [[8505/8192#Sagittal notation | 8192/8505]] (35L down).
+/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]]. It is worth noting that [[13/8]] is closer to minor than it is to major (some might argue 13/8 to be [[supraminor]] instead of neutral), so [[1053/1024]] is significantly smaller.
+=== 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| (|\ }}.
+== Temperaments ==
+If treated as a [[comma]] to be [[tempering out|tempered out]], it leads to the [[ultraflat]] temperament of the [[2.3.13 subgroup]]. It is tempered out in the [[patent val]]s for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35.
 == See also ==
@@ Line 21: / Line 28: @@
 [[Category:Chroma]]
 [[Category:Third tone]]
+[[Category:Commas named after their interval size]]

27/26: Difference between revisions

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