16/13: Difference between revisions
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reworked |
Add the info about the difference from 81/64 and 27/22 |
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| Cents = 359.47234 | | Cents = 359.47234 | ||
| Name = neutral tridecimal third | | Name = neutral tridecimal third | ||
| | | FJS name = M3<sub>13</sub> | ||
| Sound = jid_16_13_pluck_adu_dr220.mp3 | | Sound = jid_16_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[13-limit]] [[just intonation]], '''16/13''' is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. It differs from [[5/4]] by [[65/64]], about | In [[13-limit]] [[just intonation]], '''16/13''' is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. It differs from [[81/64]] by [[1053/1024]], about 48¢, from [[5/4]] by [[65/64]], about 27¢, from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢, and from the rastmic neutral third [[27/22]] by [[352/351]], about 4.9¢. A [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is [[512/507]], about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the [[harmonic series]]. | ||
See | == See also == | ||
* [[13/8]] - its [[octave complement]] | |||
* [[39/32]] - its fifth complement | |||
* [[Gallery of Just Intervals]] | |||
[[Category:13-limit]] | [[Category:13-limit]] | ||
Revision as of 07:49, 30 August 2020
| Interval information |
reduced subharmonic
[sound info]
In 13-limit just intonation, 16/13 is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of 13/8, the 13th harmonic. It differs from 81/64 by 1053/1024, about 48¢, from 5/4 by 65/64, about 27¢, from the undecimal neutral third 11/9 by 144/143, about 12¢, and from the rastmic neutral third 27/22 by 352/351, about 4.9¢. A root-3rd-P5 triad featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, 39/32, which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the harmonic series.
See also
- 13/8 - its octave complement
- 39/32 - its fifth complement
- Gallery of Just Intervals