128/81: Difference between revisions

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'''128/81'''
{{Infobox Interval
|7 -4>
| Name = Pythagorean minor sixth
| Color name = sw6, sawa 6th
| Sound = jid_128_81_pluck_adu_dr220.mp3
}}


792.1800 cents
'''128/81''' is the '''Pythagorean minor sixth''', created by stacking four instances of [[4/3]] and [[Octave reduction|octave-reducing]]. In contrast to the more typical [[8/5]]—with which it is conflated in [[meantone]]—this interval has a [[harmonic entropy]] level roughly on par with that of [[12/11]]. Thus, some would argue that it is functionally an imperfect dissonance.


[[File:jid_128_81_pluck_adu_dr220.mp3]] [[:File:jid_128_81_pluck_adu_dr220.mp3|sound sample]]
It differs from [[11/7]] by the [[pentacircle comma]].


128/81 is the Pythagorean minor sixth, at -4 steps on the chain of fifths.  Its inversion is [[81/64|81/64]].
== See also ==
[[Category:todo:expand]]
* [[81/64]] – Its [[octave complement]]
* [[Gallery of just intervals]]
* [[Pythagorean tuning]]
 
[[Category:Sixth]]
[[Category:Minor sixth]]

Latest revision as of 14:06, 5 October 2025

Interval information
Ratio 128/81
Factorization 27 × 3-4
Monzo [7 -4
Size in cents 792.18¢
Name Pythagorean minor sixth
Color name sw6, sawa 6th
FJS name [math]\displaystyle{ \text{m6} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 13.3399
Weil norm (log2 max(n, d)) 14
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

128/81 is the Pythagorean minor sixth, created by stacking four instances of 4/3 and octave-reducing. In contrast to the more typical 8/5—with which it is conflated in meantone—this interval has a harmonic entropy level roughly on par with that of 12/11. Thus, some would argue that it is functionally an imperfect dissonance.

It differs from 11/7 by the pentacircle comma.

See also