729/512: Difference between revisions

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The '''Pythagorean augmented fourth''', '''729/512''', may be reached by stacking six perfect fifths ([[3/2]]), and reducing by three octaves. It is separated from the 5-limit interval of [[64/45]] by the [[32805/32768|schisma (32805/32768)]], less than 2 cents.
'''729/512''', the '''Pythagorean augmented fourth''', may be reached by stacking six perfect fifths ([[3/2]]), and reducing by three octaves. It is separated from the 5-limit interval of [[64/45]] by the [[32805/32768|schisma (32805/32768)]], less than 2 cents.


In addition, it can be interpreted as a literal tritone, since it can be made by stacking three whole tones, [[9/8]].
From a literal point of view, this interval is the only one that rightly bears the name ''[[tritone]]'', because it is created by combining three [[tone]]s: <code>([[9/8]])<sup>3</sup></code>.


== See also ==
== See also ==

Revision as of 15:33, 3 June 2021

Interval information
Ratio 729/512
Factorization 2-9 × 36
Monzo [-9 6
Size in cents 611.73¢
Names Pythagorean tritone,
Pythagorean augmented fourth,
The Tyrant
Color name Lw4, large wa 4th
FJS name [math]\displaystyle{ \text{A4} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 18.5098
Weil height (log2 max(n, d)) 19.0196
Wilson height (sopfr(nd)) 36

[sound info]
Open this interval in xen-calc

729/512, the Pythagorean augmented fourth, may be reached by stacking six perfect fifths (3/2), and reducing by three octaves. It is separated from the 5-limit interval of 64/45 by the schisma (32805/32768), less than 2 cents.

From a literal point of view, this interval is the only one that rightly bears the name tritone, because it is created by combining three tones: (9/8)3.

See also