36/35: Difference between revisions
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'''36/35''', the '''septimal quarter tone''' (~48.8 [[cent|¢]]) 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]]. | '''36/35''', the '''septimal quarter tone''' (~48.8 [[cent|¢]]) 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 "<span style="display: inline-block; transform: rotate(180deg)">7</span>" (an turned 7), and the reciprocal 35/36 with an ordinary 7. | |||
== See also == | == See also == | ||
Revision as of 03:38, 10 January 2023
| Interval information |
reduced
S8 × S9
[sound info]
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.
Ben Johnston's notation denotes this interval with "7" (an turned 7), and the reciprocal 35/36 with an ordinary 7.
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