32/21: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 32/21
| Name = septimal superfifth, wide fifth, octave-reduced 21st subharmonic
| Monzo = 5 -1 0 -1
| Cents = 729.21909
| Name = septimal superfifth, <br> wide fifth, <br> diminished sixth, <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.
== Approximation ==
{{Interval edo approximation|32/21}}
== See also ==
== See also ==
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[21/16]] its [[inverse interval]]
* [[21/16]], its [[inverse interval]]


[[Category:7-limit]]
[[Category:Fifth]]
[[Category:Fifth]]
[[Category:Superfifth]]
[[Category:Superfifth]]
[[Category:Octave-reduced subharmonics]]
[[Category:Pages with internal sound examples]]

Latest revision as of 13:04, 3 November 2025

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.

Approximation

Edo approximations for 32/21 (729.22 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
5 3\5 720.00 -9.22 -3.84
10 6\10 720.00 -9.22 -7.68
18 11\18 733.33 +4.11 +6.17
23 14\23 730.43 +1.22 +2.33
28 17\28 728.57 -0.65 -1.51
33 20\33 727.27 -1.95 -5.35
38 23\38 726.32 -2.90 -9.19
41 25\41 731.71 +2.49 +8.50
46 28\46 730.43 +1.22 +4.66
51 31\51 729.41 +0.19 +0.82
56 34\56 728.57 -0.65 -3.02
61 37\61 727.87 -1.35 -6.86
69 42\69 730.43 +1.22 +6.99
74 45\74 729.73 +0.51 +3.15
79 48\79 729.11 -0.11 -0.69

See also