161/128: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
+categories
Plumtree (talk | contribs)
m Normalising usage of Infobox Interval
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Ratio = 161/128
| Name = just/Pythagorean major third meantone, octave-reduced 161th harmonic
| Monzo = -7 0 0 1 0 0 0 0 1
| Cents = 397.10025
| Name = just/Pythagorean major third meantone, <br>octave-reduced 161th harmonic
| FJS name = M3<sup>7,23</sup>
| Color name = 23oz4
| Color name = 23oz4
}}
}}
Line 14: Line 10:
It can also be calculated from the [[81/80|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.  
It can also be calculated from the [[81/80|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.  


[[Category:23-limit]]
[[Category:Third]]
[[Category:Third]]
[[Category:Major third]]
[[Category:Major third]]

Revision as of 14:16, 25 October 2022

Interval information
Ratio 161/128
Subgroup monzo 2.7.23 [-7 1 1
Size in cents 397.1003¢
Names just/Pythagorean major third meantone,
octave-reduced 161th harmonic
Color name 23oz4
FJS name [math]\displaystyle{ \text{M3}^{7,23} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 14.3309
Weil height (log2 max(n, d)) 14.6618
Wilson height (sopfr(nd)) 44
Open this interval in xen-calc

In just intonation, 161/128 is the frequency ratio between the 161th and the 128th harmonic.

It is the mean between the just major third and the Pythagorean major third: (5/4 + 81/64)/2 = 161/128.

It can also be calculated from the syntonic comma: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.