81/64: Difference between revisions

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m Normalising usage of Infobox Interval
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{{Infobox Interval
{{Infobox Interval
| Ratio = 81/64
| Monzo = -6 4
| Cents = 407.82000
| Name = Pythagorean major third
| Name = Pythagorean major third
| Color name = Lw3, lawa 3rd
| Color name = Lw3, lawa 3rd
| FJS name = M3
| Sound = jid_81_64_pluck_adu_dr220.mp3
| Sound = jid_81_64_pluck_adu_dr220.mp3
}}
}}
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* [[Pythagorean tuning]]
* [[Pythagorean tuning]]


[[Category:3-limit]]
[[Category:Third]]
[[Category:Third]]
[[Category:Major third]]
[[Category:Major third]]
{{todo|expand}}
{{todo|expand}}

Revision as of 17:03, 25 October 2022

Interval information
Ratio 81/64
Factorization 2-6 × 34
Monzo [-6 4
Size in cents 407.82¢
Name Pythagorean major third
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

The Pythagorean major third, 81/64, may be reached by stacking four perfect fifths (3/2), and reducing by two octaves. In contrast to the more typical 5/4- with which it is conflated in meantone- this interval is a bit more dissonant when not bridged by a stack of 3/2 intervals within in a chord, 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