1024/729: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 1024/729
| Ratio = 1024/729
| Monzo = 10 -6
| Monzo = 10 -6
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}}
}}


'''1024/729''', the '''Pythagorean diminished fifth''', is the [[octave complement]] of the “classic” [[729/512]] [[tritone]]. It may be reached by stacking six perfect fourths ([[4/3]]), and reducing by two octaves, it's is separated from the 5-limit interval of [[45/32]] by the [[schisma]] (less than 2 cents).
'''1024/729''', the '''Pythagorean diminished fifth''', is the [[octave complement]] of the Pythagorean [[tritone]] ([[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 ==
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[[Category:3-limit]]
[[Category:3-limit]]
[[Category:Interval ratio]]
[[Category:Tritone]]
[[Category:Tritone]]
[[Category:Pythagorean]]
[[Category:Listen]]
[[Category:Pages with internal sound examples]]
[[Category:Pages with internal sound examples]]

Revision as of 21:28, 16 February 2022

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 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

1024/729, the Pythagorean diminished fifth, is the octave complement of the Pythagorean tritone (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