27/26: Difference between revisions

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{{Infobox Interval

~~| Ratio = 27/26~~

~~| Monzo = -1 3 0 0 0 -1~~

~~| Cents = 65.33734~~

| Name = small tridecimal third tone

| Color name = 3u1, thu unison

~~| FJS name = A1<sub>13</sub>~~

| Sound = jid_27_26_pluck_adu_dr220.mp3

| 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 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]]~~.

== Temperaments ==

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 [[Functional Just System]], that role is taken by [[1053/1024]].

== 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 {{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 ==

* [[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]]

~~[[Category:13-limit]]~~

[[Category:Chroma]]

[[Category:Third tone]]

[[Category:~~Medium comma]]~~

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

~~[[Category:Superparticular]]~~

~~[[Category:Pages with internal sound examples~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 27/26
-| Monzo = -1 3 0 0 0 -1
-| Cents = 65.33734
 | Name = small tridecimal third tone
 | Color name = 3u1, thu unison
-| FJS name = A1<sub>13</sub>
 | Sound = jid_27_26_pluck_adu_dr220.mp3
+| 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 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]].
+== Temperaments ==
+/26 is tempered out in the patent vals for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35.
-/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]].
+== Notation ==
+/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 ==
 * [[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]]
-[[Category:13-limit]]
 [[Category:Chroma]]
 [[Category:Third tone]]
-[[Category:Medium comma]]
+[[Category:Commas named after their interval size]]
-[[Category:Superparticular]]
-[[Category:Pages with internal sound examples]]