1053/1024: Difference between revisions

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{{Infobox Interval

| Name = tridecimal quartertone, ~~tridecimal~~ comma

| Name = tridecimal quartertone, superflat comma

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

| Comma = yes

}}

'''1053/1024''', the '''tridecimal quartertone''', '''tridecimal 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''', 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]].

== ~~Sagittal notation~~ ==

== Temperaments ==

~~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 ratio it notates is 8:13, as for example in A:F{{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up).

[[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'''.

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

== Notation ==

1053/1024 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. However, in [[Helmholtz-Ellis notation]], that role is taken by [[27/26]].

=== 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 ==

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[[Category:Quartertone]]

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

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = tridecimal quartertone, tridecimal comma
+| Name = tridecimal quartertone, superflat comma
 | Color name = L3o1, latho 1sn,<br>Latho comma
 | Comma = yes
 }}
-'''1053/1024''', the '''tridecimal quartertone''', '''tridecimal 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''', 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]].
-== Sagittal notation ==
+== Temperaments ==
-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 ratio it notates is 8:13, as for example in A:F{{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up).
+[[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'''.
-== Functional Just System and Helmholtz-Ellis notation ==
+== Notation ==
-/1024 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. However, in [[Helmholtz-Ellis notation]], that role is taken by [[27/26]].
+=== 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 ==
@@ Line 18: / Line 22: @@
 [[Category:Quartertone]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named after their interval size]]