1053/1024: Difference between revisions

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'''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 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 ==
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).
== 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]].  
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]].  



Revision as of 05:18, 9 October 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,
tridecimal 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 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.

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 ratio it notates is 8:13, as for example in A:F. The primary role of is 36/35 (35M up).

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