27/22: Difference between revisions
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Hotcrystal0 (talk | contribs) mention its closeness to 13\44 |
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'''27/22''', conventionally called the '''rastmic neutral third''', is [[243/242]] (7.1{{cent}}) sharp of [[11/9]], and together with 11/9 makes [[3/2]], so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between [[10/9]] and [[15/11]], and 11/9 and [[3/2]] and their inversions. As this is the larger of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian tendoneutral third''' in [[Alpharabian tuning]]. | '''27/22''', conventionally called the '''rastmic neutral third''', is [[243/242]] (7.1{{cent}}) sharp of [[11/9]], and together with 11/9 makes [[3/2]], so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between [[10/9]] and [[15/11]], and 11/9 and [[3/2]] and their inversions. As this is the larger of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian tendoneutral third''' in [[Alpharabian tuning]]. It is extremely close to [[44edo]]'s 13\44 neutral third, however the first multiple of 44edo to map it consistently is [[176edo]]. | ||
== Approximation == | == Approximation == | ||
{{Interval edo approximation|27/22}} | {{Interval edo approximation|27/22}} | ||
Latest revision as of 16:45, 11 March 2026
| Interval information |
Alpharabian tendoneutral third
[sound info]
27/22, conventionally called the rastmic neutral third, is 243/242 (7.1 ¢) sharp of 11/9, and together with 11/9 makes 3/2, so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between 10/9 and 15/11, and 11/9 and 3/2 and their inversions. As this is the larger of two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian tendoneutral third in Alpharabian tuning. It is extremely close to 44edo's 13\44 neutral third, however the first multiple of 44edo to map it consistently is 176edo.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 7 | 2\7 | 342.86 | -11.69 | -6.82 |
| 10 | 3\10 | 360.00 | +5.45 | +4.54 |
| 17 | 5\17 | 352.94 | -1.61 | -2.28 |
| 20 | 6\20 | 360.00 | +5.45 | +9.09 |
| 24 | 7\24 | 350.00 | -4.55 | -9.09 |
| 27 | 8\27 | 355.56 | +1.01 | +2.27 |
| 34 | 10\34 | 352.94 | -1.61 | -4.55 |
| 37 | 11\37 | 356.76 | +2.21 | +6.81 |
| 44 | 13\44 | 354.55 | -0.00 | -0.01 |
| 51 | 15\51 | 352.94 | -1.61 | -6.83 |
| 54 | 16\54 | 355.56 | +1.01 | +4.54 |
| 61 | 18\61 | 354.10 | -0.45 | -2.28 |
| 64 | 19\64 | 356.25 | +1.70 | +9.08 |
| 68 | 20\68 | 352.94 | -1.61 | -9.10 |
| 71 | 21\71 | 354.93 | +0.38 | +2.26 |
| 78 | 23\78 | 353.85 | -0.70 | -4.56 |