105/64: Difference between revisions

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{{Infobox Interval|Ratio=105/64|Monzo=-6 1 1 1|Cents=857.094621|Name=septimal neutral sixth}}
{{Infobox Interval
| Name = septimal neutral sixth
| Color name = zy6, zoyo 6th
}}
'''105/64''' is a [[7-limit]] neutral sixth and is 857.095{{c}} 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 0.048{{c}}, 1/7 of an [[akjaysma]]. In addition, it only differs from the large tridecimal neutral sixth ([[64/39]]) by [[4096/4095]]. When we also consider that 105/64 can be thought of as the [[octave reduction|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.


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.
== See also ==
* [[Gallery of just intervals]]


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

Latest revision as of 10:09, 3 March 2026

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
Color name zy6, zoyo 6th
FJS name [math]\displaystyle{ \text{M6}^{5,7} }[/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-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 0.048 ¢, 1/7 of an akjaysma. In addition, it only differs from the large tridecimal neutral sixth (64/39) by 4096/4095. 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