32768/19683: Difference between revisions

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Created page with "{{Infobox Interval | Name = Pythagorean diminished seventh | Color name = sw2, sawa 7th }} The '''Pythagorean diminished seventh''', '''32768/19683''', may be reached by stac..."
 
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The '''Pythagorean diminished seventh''', '''32768/19683''', may be reached by stacking 9 4/3's and octave reducing. It differs from the classic major sixth, [[5/3]], by the [[schisma]], and, as a result, the Pythagorean diminished seventh is useful in creating rather consonant diminished seventh chords.
The '''Pythagorean diminished seventh''', '''32768/19683''', may be reached by stacking nine [[4/3]]'s and octave reducing. It differs from the classic major sixth, [[5/3]], by the [[schisma]], and, as a result, the Pythagorean diminished seventh is useful in creating rather consonant diminished seventh chords.


== See also ==
== See also ==
* [[19683/16384]] – its [[octave complement]]
* [[19683/16384]] – its [[octave complement]]
* [[59049/32768]] – its [[twelfth complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[Pythagorean tuning]]
* [[Pythagorean tuning]]

Revision as of 07:26, 23 July 2024

Interval information
Ratio 32768/19683
Factorization 215 × 3-9
Monzo [15 -9
Size in cents 882.405¢
Name Pythagorean diminished seventh
Color name sw2, sawa 7th
FJS name [math]\displaystyle{ \text{d7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 29.2647
Weil height (log2 max(n, d)) 30
Wilson height (sopfr(nd)) 57
Open this interval in xen-calc

The Pythagorean diminished seventh, 32768/19683, may be reached by stacking nine 4/3's and octave reducing. It differs from the classic major sixth, 5/3, by the schisma, and, as a result, the Pythagorean diminished seventh is useful in creating rather consonant diminished seventh chords.

See also