85/64: Difference between revisions

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I now realize that 85/64 is not a perfect substitute for 4/3. That said, it does have its uses, and I will eventually describe some of them.
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'''85/64''', the '''septendecimal fourth''', is a [[17-limit]] interval that closely approximates [[4/3]], from which it differs by [[256/255]].  Because it differs from [[15/8]] by [[24/17]], this interval is an easy, relatively low-prime substitute for 4/3 in scales where one desires to simultaneously maintain [[Rothenberg propriety]] and ensure that all notes in the scale suggest the Tonic when played simultaneously.
'''85/64''', the '''septendecimal fourth''', is a [[17-limit]] interval that comes quite close to [[4/3]], from which it differs by [[256/255]].


== See also ==
== See also ==

Revision as of 14:26, 5 September 2021

Interval information
Ratio 85/64
Factorization 2-6 × 5 × 17
Monzo [-6 0 1 0 0 0 1
Size in cents 491.2691¢
Name septendecimal fourth
FJS name [math]\displaystyle{ \text{P4}^{5,17} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 12.4094
Weil height (log2 max(n, d)) 12.8188
Wilson height (sopfr(nd)) 34
Open this interval in xen-calc

85/64, the septendecimal fourth, is a 17-limit interval that comes quite close to 4/3, from which it differs by 256/255.

See also