32/21: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal superfifth, wide fifth, octave-reduced 21st subharmonic | |||
| Name = septimal superfifth, | |||
| 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:Fifth]] | [[Category:Fifth]] | ||
[[Category:Superfifth]] | [[Category:Superfifth]] | ||
Latest revision as of 13:04, 3 November 2025
| Interval information |
wide fifth,
octave-reduced 21st subharmonic
reduced subharmonic
[sound info]
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 | 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 |