1024/729: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = Pythagorean narrow tritone, Pythagorean diminished fifth
| Ratio = 1024/729
| Color name = sw5, sawa 5th
| Monzo = 10 -6
| Sound = Ji-1024-729-csound-foscil-220hz.mp3
| Cents = 588.26999
| Name = Pythagorean narrow tritone <br>Pythagorean diminished fifth
| Color name = sw5, small wa 5th  
| Sound = jid_1024_729_pluck_adu_dr220.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).
'''1024/729''', the '''Pythagorean diminished fifth''', is the [[octave complement]] of the Pythagorean augmented fourth ([[729/512]]). It 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]] (less than 2 cents).


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


[[Category:3-limit]]
[[Category:Interval ratio]]
[[Category:Tritone]]
[[Category:Tritone]]
[[Category:Pythagorean]]

Latest revision as of 23:23, 11 June 2025

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, sawa 5th
FJS name [math]\displaystyle{ \text{d5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 19.5098
Weil height (log2 max(n, d)) 20
Wilson height (sopfr(nd)) 38

[sound info]
Open this interval in xen-calc

1024/729, the Pythagorean diminished fifth, is the octave complement of the Pythagorean augmented fourth (729/512). It 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 (less than 2 cents).

See also