105/64: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Awelotta (talk | contribs)
No edit summary
m +FJS name; +links; +categories
Line 1: Line 1:
{{Infobox Interval|Ratio=105/64|Monzo=-6 1 1 1|Cents=857.094621|Name=septimal neutral sixth}}
{{Infobox Interval
| Ratio = 105/64
| Monzo = -6 1 1 1
| Cents = 857.094621
| Name = septimal neutral sixth
| FJS name = M6<sup>35</sup>
}}


'''105/64''' is a 7 [[Prime limit|prime-limit]] neutral sixth and is 857.095¢ wide. It might be called a septimal neutral sixth.
'''105/64''' is a 7-[[Prime limit|prime-limit]] neutral sixth and is 857.095¢ wide. It might be called a septimal neutral sixth.


When used as a generator, it approximates [[7edo]] as the 6th note of the scale; the difference between 5\7 and 105/64 is 0.048236¢. When we also consider that 105/64 can be thought of as the octave reduced greatest common factor of 3, 5, and 7, 105/64 and its octave equivalents might be used to tune 7edo on a stringed instrument via [[Harmonic|harmonics]], though so far this idea has not been tested.
When used as a generator, it approximates [[7edo]] as the 6th note of the scale; the difference between 5\7 and 105/64 is 0.048236¢. When we also consider that 105/64 can be thought of as the octave reduced greatest common factor of 3, 5, and 7, 105/64 and its octave equivalents might be used to tune 7edo on a stringed instrument via [[harmonic]]s, though so far this idea has not been tested.  
 
== See also ==
* [[Gallery of just intervals]]


[[Category:Just interval]]
[[Category:7-limit]]
[[Category:7-limit]]
[[Category:Interval]]
[[Category:Sixth]]
[[Category:Neutral sixth]]
[[Category:Overtone]]

Revision as of 11:44, 18 March 2021

Interval information
Ratio 105/64
Factorization 2-6 × 3 × 5 × 7
Monzo [-6 1 1 1
Size in cents 857.0946¢
Name septimal neutral sixth
FJS name [math]\displaystyle{ \text{M6}^{35} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 12.7142
Weil norm (log2 max(n, d)) 13.4285
Wilson norm (sopfr(nd)) 27
Open this interval in xen-calc

105/64 is a 7-prime-limit neutral sixth and is 857.095¢ wide. It might be called a septimal neutral sixth.

When used as a generator, it approximates 7edo as the 6th note of the scale; the difference between 5\7 and 105/64 is 0.048236¢. When we also consider that 105/64 can be thought of as the octave reduced greatest common factor of 3, 5, and 7, 105/64 and its octave equivalents might be used to tune 7edo on a stringed instrument via harmonics, though so far this idea has not been tested.

See also