20/17: Difference between revisions
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In [[17-limit]] [[just intonation]], '''20/17''' is the '''diatismic minor third''', measuring about 281.4{{cent}}. It falls short of the [[32/27|Pythagorean minor third (32/27)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[7/6]] and [[13/11]], as it is (7 + 13)/(6 + 11). It is found in the [[harmonic series]] between the 17th and 20th [[harmonic]]s. | In [[17-limit]] [[just intonation]], '''20/17''' is the '''diatismic minor third''', measuring about 281.4{{cent}}. It falls short of the [[32/27|Pythagorean minor third (32/27)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[7/6]] and [[13/11]], as it is (7 + 13)/(6 + 11). It is found in the [[harmonic series]] between the 17th and 20th [[harmonic]]s. | ||
== Approximation == | == Approximation == | ||
{{Interval edo approximation|20/17}} | |||
== See also == | == See also == | ||
* [[17/10]] – its [[octave complement]] | * [[17/10]] – its [[octave complement]] | ||
Latest revision as of 13:11, 3 November 2025
| Interval information |
[sound info]
In 17-limit just intonation, 20/17 is the diatismic minor third, measuring about 281.4 ¢. It falls short of the Pythagorean minor third (32/27) by a diatisma (136/135), hence the name. It is the mediant of 7/6 and 13/11, as it is (7 + 13)/(6 + 11). It is found in the harmonic series between the 17th and 20th harmonics.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 1\4 | 300.00 | +18.64 | +6.21 |
| 13 | 3\13 | 276.92 | -4.44 | -4.80 |
| 17 | 4\17 | 282.35 | +0.99 | +1.41 |
| 21 | 5\21 | 285.71 | +4.36 | +7.62 |
| 26 | 6\26 | 276.92 | -4.44 | -9.61 |
| 30 | 7\30 | 280.00 | -1.36 | -3.40 |
| 34 | 8\34 | 282.35 | +0.99 | +2.82 |
| 38 | 9\38 | 284.21 | +2.85 | +9.03 |
| 43 | 10\43 | 279.07 | -2.29 | -8.20 |
| 47 | 11\47 | 280.85 | -0.51 | -1.99 |
| 51 | 12\51 | 282.35 | +0.99 | +4.23 |
| 60 | 14\60 | 280.00 | -1.36 | -6.79 |
| 64 | 15\64 | 281.25 | -0.11 | -0.58 |
| 68 | 16\68 | 282.35 | +0.99 | +5.64 |
| 77 | 18\77 | 280.52 | -0.84 | -5.38 |
See also
- 17/10 – its octave complement
- 51/40 – its fifth complement
- 17/15 – its fourth complement
- 4\17 (282.353 cents)
- Gallery of just intervals