32/21

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Interval information

Ratio

32/21

Factorization

2⁵ × 3^-1 × 7^-1

[5 -1 0 -1⟩

Size in cents

729.2191¢

Names

septimal superfifth,
wide fifth,
octave-reduced 21st subharmonic

r5, ru 5th

[math]\displaystyle{ \text{P5}_{7} }[/math]

Special properties

reduced,
reduced subharmonic

Tenney height (log₂ nd)

9.39232

Weil height (log₂ max(n, d))

10

Wilson height (sopfr(nd))

20

Harmonic entropy
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])

~4.30841 bits

Open this interval in xen-calc

32/21, the septimal superfifth, is the interval between 9/8 and 12/7. It is 64/63 sharp of 3/2, and so is equated to 3/2 in temperaments such as pajara, superpyth or augene which tempers out 64/63.

In septimal meantone, this interval is represented by the diminished sixth.

See also

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