13/8: Difference between revisions
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+FJS name; cleanup; expansion |
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| Monzo = -3 0 0 0 0 1 | | Monzo = -3 0 0 0 0 1 | ||
| Cents = 840.52766 | | Cents = 840.52766 | ||
| Name = tridecimal neutral sixth | | Name = (lesser) tridecimal neutral sixth | ||
| Color name = 3o6, tho 6th | |||
| FJS name = m6<sup>13</sup> | |||
| Sound = jid_13_8_pluck_adu_dr220.mp3 | | Sound = jid_13_8_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''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. | '''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¢. | |||
13/8 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos. | |||
== See also == | == See also == | ||
* [[16/13]] – its [[octave complement]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:13-limit]] | [[Category:13-limit]] | ||
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[[Category:Neutral sixth]] | [[Category:Neutral sixth]] | ||
[[Category:Sixth]] | [[Category:Sixth]] | ||
[[Category:Untwelve]] | [[Category:Untwelve]] | ||
[[Category:Overtone]] | [[Category:Overtone]] | ||
[[Category:Over-2]] | [[Category:Over-2]] | ||
Revision as of 10:14, 20 September 2020
| 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¢.
13/8 is a fraction of a cent away from the neutral third found in the 10n family of edos.