12/11: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 12/11 | | Ratio = 12/11 | ||
| Monzo = 2 1 0 0 -1 | | Monzo = 2 1 0 0 -1 | ||
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| Sound = jid_12_11_pluck_adu_dr220.mp3 | | Sound = jid_12_11_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Neutral second}} | |||
'''12/11''', the '''undecimal neutral second''' or '''(lesser) neutral second''', is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In | '''12/11''', the '''undecimal neutral second''' or '''(lesser) neutral second''', is a strangely exotic interval found between the 11th and 12th partials of the [[harmonic series]]. In [[just intonation]] it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)<sup>8</sup>/2 = {{Monzo|15 8 0 0 -8}}. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well. | ||
12/11 differs from the larger undecimal neutral second [[11/10]] (~165 cents) by [[121/120]] (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], etc. | 12/11 differs from the larger undecimal neutral second [[11/10]] (~165 cents) by [[121/120]] (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], etc. | ||
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[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category: | [[Category:Second]] | ||
[[Category:Neutral second]] | [[Category:Neutral second]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Over-11]] | [[Category:Over-11]] | ||
Revision as of 17:06, 11 March 2022
| Interval information |
reduced
[sound info]
12/11, the undecimal neutral second or (lesser) neutral second, is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In just intonation it is represented by the superparticular ratio 12/11, and is about 150.6 cents large. One step of 8edo is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)8/2 = [15 8 0 0 -8⟩. It follows that EDOs which are multiples of 8, such as 16edo and 24edo, will also represent this interval well.
12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include 15edo, 22edo, 31edo, orwell, porcupine, mohajira, valentine, etc.