12/11: Difference between revisions
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|" |
Move approximation info to the corresponding section |
||
| Line 6: | Line 6: | ||
{{Wikipedia|Neutral second}} | {{Wikipedia|Neutral second}} | ||
'''12/11''', the '''undecimal neutral second''' or '''(lesser) 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. | '''12/11''', the '''undecimal neutral second''' or '''(lesser) 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'''. | ||
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. | ||
Many Western listeners might describe 12/11 as sounding "exotic". | Many Western listeners might describe 12/11 as sounding "exotic". | ||
== Approximation == | == 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}} | {{Interval edo approximation|12/11}} | ||
== See also == | == See also == | ||
* [[11/6]] – its [[octave complement]] | * [[11/6]] – its [[octave complement]] | ||
Revision as of 11:35, 20 July 2026
| Interval information |
Alpharabian tendoneutral second
reduced
[sound info]
12/11, the undecimal neutral second or (lesser) 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.
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.
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 |