12/11: Difference between revisions
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{{Wikipedia|Neutral second}} | {{Wikipedia|Neutral second}} | ||
'''12/11''', the | '''12/11''', conventionally the '''(lesser) undecimal neutral second''', is an 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. | ||
In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second''', which contrasts [[88/81]], the other undecimal neutral second. | |||
The name ''lesser undecimal neutral second'' is said as opposed to [[11/10]], the larger undecimal neutral second or undecimal submajor second (~165 cents), from which it differs by [[121/120]] (~14.4 cents). [[Regular temperament|Temperaments]] which conflate the two (thus [[tempering out]] 121/120) include [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], and their [[support]]ing [[edo]]s: [[15edo]], [[22edo]], [[31edo]], etc. | |||
Many Western listeners might describe 12/11 as sounding "exotic". | |||
== Approximation == | |||
One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the [[octave]] by the comma [[undecimal octatonic 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. | |||
{{Interval edo approximation|12/11}} | |||
== See also == | == See also == | ||
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[[Category:Second]] | [[Category:Second]] | ||
[[Category:Neutral second]] | [[Category:Neutral second]] | ||
[[Category:Over-11]] | [[Category:Over-11 intervals]] | ||
Latest revision as of 11:45, 20 July 2026
| Interval information |
Alpharabian tendoneutral second
reduced
[sound info]
12/11, conventionally the (lesser) undecimal neutral second, is an 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.
In Alpharabian tuning it is known as the Alpharabian tendoneutral second, which contrasts 88/81, the other undecimal neutral second.
The name lesser undecimal neutral second is said as opposed to 11/10, the larger undecimal neutral second or undecimal submajor second (~165 cents), from which it differs by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include orwell, porcupine, mohajira, valentine, and their supporting edos: 15edo, 22edo, 31edo, etc.
Many Western listeners might describe 12/11 as sounding "exotic".
Approximation
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.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 8 | 1\8 | 150.00 | -0.64 | -0.42 |
| 16 | 2\16 | 150.00 | -0.64 | -0.85 |
| 24 | 3\24 | 150.00 | -0.64 | -1.27 |
| 32 | 4\32 | 150.00 | -0.64 | -1.70 |
| 40 | 5\40 | 150.00 | -0.64 | -2.12 |
| 48 | 6\48 | 150.00 | -0.64 | -2.55 |
| 55 | 7\55 | 152.73 | +2.09 | +9.58 |
| 56 | 7\56 | 150.00 | -0.64 | -2.97 |
| 63 | 8\63 | 152.38 | +1.74 | +9.16 |
| 64 | 8\64 | 150.00 | -0.64 | -3.40 |
| 71 | 9\71 | 152.11 | +1.48 | +8.73 |
| 72 | 9\72 | 150.00 | -0.64 | -3.82 |
| 79 | 10\79 | 151.90 | +1.26 | +8.31 |
| 80 | 10\80 | 150.00 | -0.64 | -4.25 |