36/35

Interval information

Ratio	36/35
Factorization	22 × 32 × 5-1 × 7-1
Monzo	[2 2 -1 -1⟩
Size in cents	48.77038¢
Name	septimal quarter tone
Color name	rg1, rugu unison
FJS name	[math]\displaystyle{ \text{P1}_{35} }[/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
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36/35, the septimal quarter tone (~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.

English Wikipedia has an article on:

Septimal quarter tone

See also

• 35/18 – its octave complement
• 35/24 – its fifth complement
• Gallery of just intervals
• List of superparticular intervals
• Mint family, the family of rank-3 temperaments where it is tempered out
• Mint temperaments, the collection of rank-2 temperaments where it is tempered out