105/64: Difference between revisions

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Expansion
Added color name, misc. edits, categories
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| Cents = 857.094621
| Cents = 857.094621
| Name = septimal neutral sixth
| Name = septimal neutral sixth
| FJS name = M6<sup>35</sup>
| Color name = zoyo 6th, zy6
| FJS name = M6<sup>5,7</sup>
| Sound =
}}
}}


'''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-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¢. In addition, it only differs from the [[64/39|large tridecimal neutral sixth (64/39)]] by a [[4096/4095|schismina (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 [[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 0.048¢. In addition, it only differs from the large tridecimal neutral sixth ([[64/39]]) by a schismina ([[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 [[harmonic]]s, though so far this idea has not been tested.


== See also ==
== See also ==
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[[Category:7-limit]]
[[Category:7-limit]]
[[Category:Interval]]
[[Category:Sixth]]
[[Category:Sixth]]
[[Category:Neutral sixth]]
[[Category:Neutral sixth]]
[[Category:Overtone]]
[[Category:Harmonics]]

Revision as of 04:55, 12 December 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
Color name zoyo 6th, zy6
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¢. In addition, it only differs from the large tridecimal neutral sixth (64/39) by a schismina (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