729/512: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 729/512
| Ratio = 729/512
| Monzo = -9 6
| Monzo = -9 6
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| Sound = Ji-729-512-csound-foscil-220hz.mp3
| Sound = Ji-729-512-csound-foscil-220hz.mp3
}}
}}
 
'''729/512''', the '''Pythagorean augmented fourth''', may be reached by stacking six perfect fifths ([[3/2]]), and [[octave reduction|reducing by three octaves]]. It is separated from the 5-limit interval of [[64/45]] by the schisma ([[32805/32768]]), less than 2{{cent}}.
'''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.


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>.
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>.
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[[Category:3-limit]]
[[Category:3-limit]]
[[Category:Interval ratio]]
[[Category:Tritone]]
[[Category:Tritone]]

Revision as of 16:03, 23 March 2022

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, lawa 4th
FJS name [math]\displaystyle{ \text{A4} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 18.5098
Weil norm (log2 max(n, d)) 19.0196
Wilson norm (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 ¢.

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