1024/729: Difference between revisions

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m schisma linked
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| Monzo = 10 -6
| Monzo = 10 -6
| Cents = 588.26999
| Cents = 588.26999
| Name = Pythagorean narrow tritone <br>Pythagorean diminished fifth
| Name = Pythagorean narrow tritone, <br>Pythagorean diminished fifth
| Color name = sw5, small wa 5th  
| Color name = sw5, small wa 5th
| FJS name = d5
| Sound = Ji-1024-729-csound-foscil-220hz.mp3
| Sound = Ji-1024-729-csound-foscil-220hz.mp3
}}
}}


The '''Pythagorean diminished fifth''', '''1024/729''', may be reached by stacking six perfect fourths ([[4/3]]), and reducing by two octaves. It is separated from the 5-limit interval of 45/32 by the schisma, [[32805/32768]] (less than 2 cents).
The '''Pythagorean diminished fifth''', '''1024/729''', may be reached by stacking six perfect fourths ([[4/3]]), and reducing by two octaves. It is separated from the 5-limit interval of [[45/32]] by the [[32805/32768|schisma (32805/32768)]], less than 2 cents.


== See also ==
== See also ==
* [[729/512]] - its [[inversion]]
* [[729/512]] its [[octave complement]]
* [[2187/2048]] – its [[fifth complement]]
* [[Pythagorean tuning]]
* [[Pythagorean tuning]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]

Revision as of 05:02, 30 December 2020

Interval information
Ratio 1024/729
Factorization 210 × 3-6
Monzo [10 -6
Size in cents 588.27¢
Names Pythagorean narrow tritone,
Pythagorean diminished fifth
Color name sw5, small wa 5th
FJS name [math]\displaystyle{ \text{d5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 19.5098
Weil norm (log2 max(n, d)) 20
Wilson norm (sopfr(nd)) 38

[sound info]
Open this interval in xen-calc

The Pythagorean diminished fifth, 1024/729, may be reached by stacking six perfect fourths (4/3), and reducing by two octaves. It is separated from the 5-limit interval of 45/32 by the schisma (32805/32768), less than 2 cents.

See also