6561/4096: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = Pythagorean augmented fifth, tetratone
| Ratio = 6561/4096
| Color name = Lw5, lawa 5th
| Monzo = -12 8
| Cents = 815.64000
| Name = Pythagorean augmented fifth
| Color name =  
| FJS name =
| Sound =
}}
}}


The '''Pythagorean augmented fifth''', '''6564/4096''', may be reached by stacking two [[81/64]] intervals. 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]] major thirds. The Medieval music theorist {{w|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 [[9/8|(Pythagorean whole) tones (9/8)]], and he considered it highly discordant.<ref>''Pythagorean Tuning and Medieval Polyphony'', Margo Schulter, 10 June 1998</ref> It differs from [[8/5]] by the [[schisma]], and from [[3/2]] by the [[apotome]].


== See also ==
== See also ==
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* [[Pythagorean tuning]]
* [[Pythagorean tuning]]


[[Category:3-limit]]
== Notes ==
[[Category:Interval]]
 
[[Category:Ratio]]
[[Category:Fifth]]
[[Category:Pythagorean]]
[[Category:Augmented fifth]]