21/13: Difference between revisions
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This interval is a ratio of two consecutive {{w|Fibonacci numbers}} and thus a convergent to [[acoustic phi]] (the interval of a [[golden ratio]]). In this case, 21/13 is ~2.8{{cent}} flat of acoustic phi. It differs from [[13/8]], the previous such convergent, by [[169/168]], and from the following convergent [[34/21]] by [[442/441]]. | This interval is a ratio of two consecutive {{w|Fibonacci numbers}} and thus a convergent to [[acoustic phi]] (the interval of a [[golden ratio]]). In this case, 21/13 is ~2.8{{cent}} flat of acoustic phi. It differs from [[13/8]], the previous such convergent, by [[169/168]], and from the following convergent [[34/21]] by [[442/441]]. | ||
== Approximation == | |||
{{Interval edo approximation|21/13}} | |||
== See also == | == See also == | ||
* [[26/21]] – its [[octave complement]] | * [[26/21]] – its [[octave complement]] | ||
Latest revision as of 13:04, 3 November 2025
| Interval information |
[sound info]
21/13, the tridecimal supraminor sixth, is ca. 830 cents in size. It has a very good approximation in 13edo, and notably, 5 of these intervals differ from 11/1 by 4084223/4084101, a comma of a mere 0.052 ¢.
This interval is a ratio of two consecutive Fibonacci numbers and thus a convergent to acoustic phi (the interval of a golden ratio). In this case, 21/13 is ~2.8 ¢ flat of acoustic phi. It differs from 13/8, the previous such convergent, by 169/168, and from the following convergent 34/21 by 442/441.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | -30.25 | -7.56 |
| 10 | 7\10 | 840.00 | +9.75 | +8.12 |
| 13 | 9\13 | 830.77 | +0.52 | +0.56 |
| 16 | 11\16 | 825.00 | -5.25 | -7.00 |
| 23 | 16\23 | 834.78 | +4.53 | +8.68 |
| 26 | 18\26 | 830.77 | +0.52 | +1.12 |
| 29 | 20\29 | 827.59 | -2.67 | -6.45 |
| 36 | 25\36 | 833.33 | +3.08 | +9.24 |
| 39 | 27\39 | 830.77 | +0.52 | +1.68 |
| 42 | 29\42 | 828.57 | -1.68 | -5.89 |
| 49 | 34\49 | 832.65 | +2.40 | +9.80 |
| 52 | 36\52 | 830.77 | +0.52 | +2.24 |
| 55 | 38\55 | 829.09 | -1.16 | -5.33 |
| 65 | 45\65 | 830.77 | +0.52 | +2.79 |
| 68 | 47\68 | 829.41 | -0.84 | -4.77 |
| 78 | 54\78 | 830.77 | +0.52 | +3.35 |