1053/1024: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

| Name = tridecimal quartertone, superflat comma

~~| Ratio = 1053/1024~~

| Color name = L3o1, latho 1sn,<br>Latho comma

~~| Monzo = -10 4 0 0 0 1~~

| Comma = yes

~~| Cents = 48.34767~~

| Name = tridecimal comma

| Color name = L3o1, latho ~~comma~~

~~| FJS name = P1~~<~~sup>13</sup~~>

| ~~Sound~~ =

}}

'''1053/1024''', the '''tridecimal comma''', is a [[~~ratio~~]] of about 48.3 [[cent~~|cents~~]]. It is ~~significant in~~ [[~~Functional Just System~~]] 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. For example, it is the interval between the Pythagorean major third~~ [[81/64]] ~~and the tridecimal neutral third~~ [[16/13]].

'''1053/1024''', the '''tridecimal quartertone''', '''tridecimal formal comma''', or '''Hunt minor submediant comma''', is a [[13-limit]] interval of about 48.3 [[cent]]s. It is the interval between the Pythagorean major third of [[81/64]] and the tridecimal neutral third of [[16/13]]. It can be considered a type of [[quartertone]]. It is [[4096/4095]] smaller than [[36/35]], and [[352/351]] smaller than [[33/32]].

~~1053/1024 can be considered a type of quarter tone. It is~~ [[~~4096/4095~~]] ~~smaller than~~ [[~~36/35~~]]~~, and~~ [[~~352/351]] smaller than [[33/32~~]].

== Temperaments ==

[[Tempering out]] this comma in the 2.3.13 [[subgroup]] results in the [[No-fives subgroup temperaments #Superflat|superflat]] temperament, giving rise to the name '''superflat comma'''.

== See ~~Also~~ ==

== Notation ==

=== Sagittal notation ===

In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | /|) }} and is called the '''13 medium diesis''', or '''13M''' for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in A-F{{nbhsp}}{{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up). The downward version is called '''1/13M''' or '''13M down''' and is represented (in a secondary role) by {{sagittal| \!) }}.

=== Functional Just System and Helmholtz-Ellis notation ===

1053/1024 is significant in [[Functional Just System]] as the [[13-limit|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 [[Helmholtz-Ellis notation]], that role is taken by [[27/26]].

== See also ==

* [[Medium comma]]

* [[Gallery of just intervals]]

[[Category:Quartertone]]

[[Category:Commas named for their regular temperament properties]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
+| Name = tridecimal quartertone, superflat comma
-| Ratio = 1053/1024
+| Color name = L3o1, latho 1sn,<br>Latho comma
-| Monzo = -10 4 0 0 0 1
+| Comma = yes
-| Cents = 48.34767
-| Name = tridecimal comma
-| Color name = L3o1, latho comma
-| FJS name = P1<sup>13</sup>
-| Sound =
 }}
-'''1053/1024''', the '''tridecimal comma''', is a [[ratio]] of about 48.3 [[cent|cents]]. It is significant in [[Functional Just System]] 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. For example, it is the interval between the Pythagorean major third [[81/64]] and the tridecimal neutral third [[16/13]].
+'''1053/1024''', the '''tridecimal quartertone''', '''tridecimal formal comma''', or '''Hunt minor submediant comma''', is a [[13-limit]] interval of about 48.3 [[cent]]s. It is the interval between the Pythagorean major third of [[81/64]] and the tridecimal neutral third of [[16/13]]. It can be considered a type of [[quartertone]]. It is [[4096/4095]] smaller than [[36/35]], and [[352/351]] smaller than [[33/32]].
-/1024 can be considered a type of quarter tone. It is [[4096/4095]] smaller than [[36/35]], and [[352/351]] smaller than [[33/32]].
+== Temperaments ==
+[[Tempering out]] this comma in the 2.3.13 [[subgroup]] results in the [[No-fives subgroup temperaments #Superflat|superflat]] temperament, giving rise to the name '''superflat comma'''.
-== See Also ==
+== Notation ==
+=== Sagittal notation ===
+In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | /|) }} and is called the '''13 medium diesis''', or '''13M''' for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in A-F{{nbhsp}}{{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up). The downward version is called '''1/13M''' or '''13M down''' and is represented (in a secondary role) by {{sagittal| \!) }}.
+=== Functional Just System and Helmholtz-Ellis notation ===
+/1024 is significant in [[Functional Just System]] as the [[13-limit|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 [[Helmholtz-Ellis notation]], that role is taken by [[27/26]].
+== See also ==
+* [[Medium comma]]
 * [[Gallery of just intervals]]
+[[Category:Quartertone]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named after their interval size]]