1053/1024
| Ratio | 1053/1024 |
| Factorization | 2-10 × 34 × 13 |
| Monzo | [-10 4 0 0 0 1⟩ |
| Size in cents | 48.347665¢ |
| Names | tridecimal quartertone, superflat comma |
| Color name | L3o1, latho 1sn, Latho comma |
| FJS name | [math]\text{P1}^{13}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 20.0403 |
| Weil height (log2 max(n, d)) | 20.0806 |
| Wilson height (sopfr(nd)) | 45 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.48189 bits |
| 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.