36/35
| Ratio | 36/35 |
| Factorization | 22 × 32 × 5-1 × 7-1 |
| Monzo | [2 2 -1 -1⟩ |
| Size in cents | 48.770381¢ |
| Names | septimal quartertone, mint comma |
| Color name | rg1, rugu unison |
| FJS name | [math]\text{P1}_{5,7}[/math] |
| Special properties | square superparticular, reduced |
| Tenney height (log2 nd) | 10.2992 |
| Weil height (log2 max(n, d)) | 10.3399 |
| Wilson height (sopfr (nd)) | 22 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.78662 bits |
| Comma size | medium |
| S-expressions | S6, S8 × S9 |
[sound info] | |
| open this interval in xen-calc | |
36/35, the septimal quartertone (~48.8 ¢) is the difference between 10/9 and 8/7, 7/6 and 6/5, 5/4 and 9/7, 14/9 and 8/5, 5/3 and 12/7, and 7/4 and 9/5. It has a numerator which is both the sixth square number and the eighth triangular number, leading to it being the product of two superparticular commas both as 64/63 × 81/80 and as 66/65 × 78/77; it is also 45/44 × 176/175, 51/50 × 120/119, 128/125 × 225/224, 50/49 × 126/125 and 56/55 × 99/98.
Ben Johnston's notation denotes this interval with "7" (a turned 7), and the reciprocal 35/36 with an ordinary 7.
Temperaments
When treated as a comma to be tempered out, it is known as the mint comma, and tempering it out leads to the mint temperament. See mint family, the family of rank-3 temperaments where it is tempered out, and mint temperaments, the collection of rank-2 temperaments where it is tempered out.
Etymology
The name mint comma was given by Mike Battaglia in 2012, for minor third because "it mixes 7/6 and 6/5 together into one minty interval"[1]. Before that, it had been known as the quartonic comma, which refers to another comma today.
See also
- 35/18 – its octave complement
- 35/24 – its fifth complement
- Gallery of just intervals
- List of superparticular intervals