36/35

Interval information

Ratio	36/35
Factorization	22 × 32 × 5-1 × 7-1
Monzo	[2 2 -1 -1⟩
Size in cents	48.77038¢
Names	septimal quartertone, mint comma
Color name	rg1, rugu unison
FJS name	[math]\displaystyle{ \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
Comma size	medium
S-expressions	S6, S8 × S9
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Septimal quarter tone

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". 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