32/21: Difference between revisions

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m Misc. edits, categories
Clarify the context where it works as a diminished sixth
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| Monzo = 5 -1 0 -1
| Monzo = 5 -1 0 -1
| Cents = 729.21909
| Cents = 729.21909
| Name = septimal superfifth, <br> wide fifth, <br> diminished sixth, <br> octave-reduced 21st subharmonic
| Name = septimal superfifth, <br>wide fifth, <br>octave-reduced 21st subharmonic
| Color name = r5, ru 5th
| Color name = r5, ru 5th
| Sound = jid_32_21_pluck_adu_dr220.mp3
| Sound = jid_32_21_pluck_adu_dr220.mp3
}}
}}


'''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.
'''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 ==
== See also ==

Revision as of 20:11, 17 December 2021

Interval information
Ratio 32/21
Factorization 25 × 3-1 × 7-1
Monzo [5 -1 0 -1
Size in cents 729.2191¢
Names septimal superfifth,
wide fifth,
octave-reduced 21st subharmonic
Color name r5, ru 5th
FJS name [math]\displaystyle{ \text{P5}_{7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 9.39232
Weil norm (log2 max(n, d)) 10
Wilson norm (sopfr(nd)) 20

[sound info]
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