1053/1024

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.

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
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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

• Medium comma
• Gallery of just intervals