35/32: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal neutral second | | Name = septimal neutral second | ||
| Color name = | | Color name = zy2, zoyo 2nd | ||
| Sound = jid_35_32_pluck_adu_dr220.mp3 | | Sound = jid_35_32_pluck_adu_dr220.mp3 | ||
| Comma = no | |||
}} | }} | ||
'''35/32''', the '''septimal neutral second''', is approximately half of a [[6/5]] just minor third; (6/5)/(35/32)<sup>2</sup> = [[6144/6125]], the porwell comma. It is the interval between [[8/7]] and [[5/4]]. It is 385/384 sharp of [[12/11]], and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to [[keenanismic chords]], interpreting [[48/35]] as [[11/8]]. It is also [[176/175]] flat of [[11/10]], and tempering that out instead leads to [[valinorsmic chords]] and interprets 48/35 as [[15/11]]. | '''35/32''', the '''septimal neutral second''', is approximately half of a [[6/5]] just minor third; (6/5)/(35/32)<sup>2</sup> = [[6144/6125]], the porwell comma. It is the interval between [[8/7]] and [[5/4]]. It is 385/384 sharp of [[12/11]], and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to [[keenanismic chords]], interpreting [[48/35]] as [[11/8]]. It is also [[176/175]] flat of [[11/10]], and tempering that out instead leads to [[valinorsmic chords]] and interprets 48/35 as [[15/11]]. | ||
It is very closely approximated by [[31edo|4\31]], being just 0.3 [[cents]] sharp of that interval. | |||
== Approximation == | |||
{{Interval edo approximation|35/32}} | |||
== See also == | == See also == | ||
* [[64/35]] its [[ | * [[64/35]] – its [[octave complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Neutral second]] | [[Category:Neutral second]] | ||
[[Category: | [[Category:Mint]] | ||
Latest revision as of 13:12, 3 November 2025
| Interval information |
reduced harmonic
[sound info]
35/32, the septimal neutral second, is approximately half of a 6/5 just minor third; (6/5)/(35/32)2 = 6144/6125, the porwell comma. It is the interval between 8/7 and 5/4. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to keenanismic chords, interpreting 48/35 as 11/8. It is also 176/175 flat of 11/10, and tempering that out instead leads to valinorsmic chords and interprets 48/35 as 15/11.
It is very closely approximated by 4\31, being just 0.3 cents sharp of that interval.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 7 | 1\7 | 171.43 | +16.29 | +9.50 |
| 8 | 1\8 | 150.00 | -5.14 | -3.43 |
| 15 | 2\15 | 160.00 | +4.86 | +6.08 |
| 16 | 2\16 | 150.00 | -5.14 | -6.85 |
| 23 | 3\23 | 156.52 | +1.38 | +2.65 |
| 31 | 4\31 | 154.84 | -0.30 | -0.78 |
| 38 | 5\38 | 157.89 | +2.76 | +8.72 |
| 39 | 5\39 | 153.85 | -1.29 | -4.20 |
| 46 | 6\46 | 156.52 | +1.38 | +5.30 |
| 47 | 6\47 | 153.19 | -1.95 | -7.63 |
| 54 | 7\54 | 155.56 | +0.42 | +1.87 |
| 62 | 8\62 | 154.84 | -0.30 | -1.55 |
| 69 | 9\69 | 156.52 | +1.38 | +7.95 |
| 70 | 9\70 | 154.29 | -0.85 | -4.98 |
| 77 | 10\77 | 155.84 | +0.70 | +4.52 |
| 78 | 10\78 | 153.85 | -1.29 | -8.41 |