729/512: Difference between revisions

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put main lemma first, improve sentence about literal meaning of "tritone"
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| Cents = 611.73001
| Cents = 611.73001
| Name = Pythagorean tritone, <br>Pythagorean augmented fourth, <br>The Tyrant
| Name = Pythagorean tritone, <br>Pythagorean augmented fourth, <br>The Tyrant
| Color name = Lw4, large wa 4th
| Color name = Lw4, lawa 4th
| FJS name = A4
| FJS name = A4
| Sound = Ji-729-512-csound-foscil-220hz.mp3
| Sound = Ji-729-512-csound-foscil-220hz.mp3

Revision as of 01:39, 13 July 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, lawa 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