1053/1024: Difference between revisions

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{{Infobox Interval
{{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''' or '''Hunt minor submediant 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]]
* [[Gallery of just intervals]]


[[Category:13-limit]]
[[Category:Medium comma]]
[[Category:Ratio]]
[[Category:Quartertone]]
[[Category:Quartertone]]
[[Category:Overtone]]
[[Category:Commas named for their regular temperament properties]]
[[Category:Commas named after their interval size]]

Latest revision as of 05:21, 24 December 2024

Interval information
Ratio 1053/1024
Factorization 2-10 × 34 × 13
Monzo [-10 4 0 0 0 1
Size in cents 48.34767¢
Names tridecimal quartertone,
superflat comma
Color name L3o1, latho 1sn,
Latho comma
FJS name [math]\displaystyle{ \text{P1}^{13} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 20.0403
Weil norm (log2 max(n, d)) 20.0806
Wilson norm (sopfr(nd)) 45
Comma size medium
Open this interval in xen-calc

1053/1024, the tridecimal quartertone, tridecimal formal comma, or Hunt minor submediant comma, is a 13-limit interval of about 48.3 cents. 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.

Temperaments

Tempering out this comma in the 2.3.13 subgroup results in the superflat temperament, giving rise to the name superflat comma.

Notation

Sagittal notation

In the Sagittal system, this comma (possibly tempered) is represented (in a secondary role) by the 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 ⁠. The primary role of is 36/35 (35M up). The downward version is called 1/13M or 13M down and is represented (in a secondary role) by .

Functional Just System and Helmholtz-Ellis 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.

See also