729/512: Difference between revisions

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Yourmusic Productions (talk | contribs)
m Surely this should have Plato's awesome name for this interval listed as well as the drier technical ones.
m +FJS name; +links
Line 4: Line 4:
| Monzo = -9 6
| Monzo = -9 6
| 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, large wa 4th
| FJS name = A4
| Sound = Ji-729-512-csound-foscil-220hz.mp3
| Sound = Ji-729-512-csound-foscil-220hz.mp3
}}
}}


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 schisma, [[32805/32768]] (less than 2 cents).
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.


== See also ==
== See also ==
* [[1024/729]] - its [[inversion]]
* [[1024/729]] its [[octave complement]]
* [[256/243]] – its [[fifth complement]]
* [[Pythagorean tuning]]
* [[Pythagorean tuning]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]

Revision as of 04:59, 30 December 2020

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

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 schisma (32805/32768), less than 2 cents.

See also