61/32: Difference between revisions

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'''61/32'''
{{Infobox Interval
| Name = octave-reduced 61st harmonic
| Color name = 61o7, siwo seventh
| Sound = Ji-61-32-csound-foscil-220hz.mp3
}}
'''61/32''', the [[Octave reduction|octave-reduced]] 61st [[harmonic]]. It is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[244/243]]. Being the octave complement of the harry minor semitone [[64/61]], it can also be used as a generator for [[harry]] and [[tritikleismic]].


= 2<span style="font-size: 80%; vertical-align: super;">-5</span> * 61
In addition, the convergent chain of edos of representing it is {{EDOs| 14, 29, 101, 130, 231 }}, with notable non-convergent edos representing it closely including {{Edos|72 and 159}}, as well as supersets of convergents including {{Edos|58, 87, and 202}}. These are notable tuning systems in their own way, and they can be used to introduce 61-limit harmony into lower-limit music.


1116.8848 cents
== See also ==
* [[64/61]] – its [[octave complement]]
* [[:File:jid_61_32_pluck_adu_dr220.mp3]] - another sound example
* [[Gallery of just intervals]]


[[File:jid_61_32_pluck_adu_dr220.mp3]] [[:File:jid_61_32_pluck_adu_dr220.mp3|sound sample]]
[[Category:Seventh]]
 
[[Category:Major seventh]]
61/32, the octave reduction of the 61st harmonic, is the octave complement of the harry minor semitone [[64/61|64/61]], and so can also be used as a generator for [[Harry|harry]] and [[Tritikleismic|tritikleismic]].

Latest revision as of 04:55, 5 October 2025

Interval information
Ratio 61/32
Subgroup monzo 2.61 [-5 1⟩
Size in cents 1116.885¢
Name octave-reduced 61st harmonic
Color name 61o7, siwo seventh
FJS name [math]\displaystyle{ \text{M7}^{61} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 10.9307
Weil norm (log2 max(n, d)) 11.8615
Wilson norm (sopfr(nd)) 71

[sound info]
Open this interval in xen-calc

61/32, the octave-reduced 61st harmonic. It is sharp of the Pythagorean major seventh (243/128) by 244/243. Being the octave complement of the harry minor semitone 64/61, it can also be used as a generator for harry and tritikleismic.

In addition, the convergent chain of edos of representing it is 14, 29, 101, 130, 231, with notable non-convergent edos representing it closely including 72 and 159, as well as supersets of convergents including 58, 87, and 202. These are notable tuning systems in their own way, and they can be used to introduce 61-limit harmony into lower-limit music.

See also

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