21/13: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = tridecimal supraminor sixth | | Name = tridecimal supraminor sixth | ||
| Color name = thuzo 6th, 3uz6 | | Color name = thuzo 6th, 3uz6 | ||
| Sound = ji-21-13-csound-foscil-220hz.mp3 | | Sound = ji-21-13-csound-foscil-220hz.mp3 | ||
}} | }} | ||
'''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s in size. It has a very good approximation in [[13edo]]. | '''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s 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{{cent}}. | ||
This interval is a ratio of two consecutive Fibonacci numbers | 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]]. | ||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Sixth]] | [[Category:Sixth]] | ||
[[Category:Supraminor sixth]] | [[Category:Supraminor sixth]] | ||
[[Category:Golden ratio approximations]] | [[Category:Golden ratio approximations]] | ||
Latest revision as of 05:32, 8 August 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.