81/64: Difference between revisions

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m Undo revision 211128 by M1k1 H2tsun2 (talk)
Tag: Undo
Overthink (talk | contribs)
m See also: "a chord where it is the first step" isn't notable enough; there are many
 
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* [[128/81]] – its [[octave complement]]
* [[128/81]] – its [[octave complement]]
* [[32/27]] – its [[fifth complement]]
* [[32/27]] – its [[fifth complement]]
* [[64:81:96:108]] – a chord where it is the first step
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[Pythagorean tuning]]
* [[Pythagorean tuning]]

Latest revision as of 10:56, 27 December 2025

Interval information
Ratio 81/64
Factorization 2-6 × 34
Monzo [-6 4
Size in cents 407.82¢
Names Pythagorean major third,
ditone
Color name Lw3, lawa 3rd
FJS name [math]\displaystyle{ \text{M3} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 12.3399
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

The Pythagorean major third, 81/64 may be reached by stacking four perfect fifths (3/2), and reducing by two octaves. It is also known as the ditone, as it may be reached by stacking two (Pythagorean whole) tones (9/8). In contrast to the more typical 5/4—with which it is conflated in meantone—this interval is a bit more discordant on its own, with a harmonic entropy level somewhere between that of 9/8 and that of 8/7. Thus, some would argue that it is functionally an imperfect dissonance.

See also