6561/4096: Difference between revisions

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"81/64 is a dissonance" is not a universal view
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The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]], and, as a result, despite 81/64 being a dissonance, the Pythagorean augmented fifth is in fact rather consonant.
The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]].
 
== See also ==
== See also ==
* [[8192/6561]] – its [[octave complement]]
* [[8192/6561]] – its [[octave complement]]

Revision as of 23:58, 23 June 2024

Interval information
Ratio 6561/4096
Factorization 2-12 × 38
Monzo [-12 8
Size in cents 815.64¢
Names Pythagorean augmented fifth,
tetratone
Color name Lw5, lawa 5th
FJS name [math]\displaystyle{ \text{A5} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 24.6797
Weil height (log2 max(n, d)) 25.3594
Wilson height (sopfr(nd)) 48
Open this interval in xen-calc

The Pythagorean augmented fifth, 6561/4096, may be reached by stacking two 81/64 intervals. The Medieval music theorist Jacques de Liège referred to it as the tetratone (akin to the ditone and tritone), as it may be reached by stacking four (Pythagorean whole) tones (9/8). It differs from 8/5 by the schisma.

See also