13/8: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 13/8 | | Ratio = 13/8 | ||
| Monzo = -3 0 0 0 0 1 | | Monzo = -3 0 0 0 0 1 | ||
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== Approximation == | == Approximation == | ||
13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10). | 13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10). | ||
This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent|¢]] sharp of the golden ratio. | |||
== See also == | == See also == | ||
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[[Category:13-limit]] | [[Category:13-limit]] | ||
[[Category: | [[Category:Sixth]] | ||
[[Category:Neutral sixth]] | [[Category:Neutral sixth]] | ||
[[Category: | [[Category:Golden ratio approximations]] | ||
[[Category:Octave-reduced harmonics]] | |||
[[Category:Over-2]] | |||
[[Category:Untwelve]] | [[Category:Untwelve]] | ||
[[Category:Pages with internal sound examples]] | [[Category:Pages with internal sound examples]] | ||
Revision as of 18:45, 18 December 2021
| Interval information |
reduced harmonic
[sound info]
13/8 is the (lesser) tridecimal neutral sixth, which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In 13-limit just intonation, 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of 3/2 and 7/4, separated from each by the superparticular ratios 13/12 and 14/13, respectively. The word "lesser" is added when necessary to differentiate it from 64/39, another tridecimal neutral sixth.
13/8 differs from the Pythagorean minor sixth 128/81 by 1053/1024, about 48¢, from the classic minor sixth 8/5 by 65/64, about 27¢, from the undecimal neutral sixth 18/11 by 144/143, about 12¢, and from the rastmic neutral sixth 44/27 by 352/351, about 4.9¢.
Approximation
13/8 is a fraction of a cent away from the neutral sixth found in the 10n-edo family (7\10).
This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the golden ratio. In this case, 13/8 is ~7.4 ¢ sharp of the golden ratio.