36/35: Difference between revisions

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Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
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switched to infobox interval
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m consistent parameter order in Template:Infobox Interval
Line 2: Line 2:
| Icon =  
| Icon =  
| Ratio = 36/35
| Ratio = 36/35
| Monzo = 2 2 -1 -1
| Cents = 48.77038
| Cents = 48.77038
| Monzo = 2 2 -1 -1
| Name = septimal quarter tone
| Name = septimal quarter tone
| Sound = ji-36-35-csound-foscil-220hz.mp3
| Sound = ji-36-35-csound-foscil-220hz.mp3

Revision as of 14:40, 11 October 2018

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
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

[sound info]
Open this interval in xen-calc

The septimal quarter tone (ratio: 36/35, size: 48.77038 cents) 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.

Links

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