16/13: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic | |||
| Color name = 3u3, thu 3rd | |||
| Name = (greater) tridecimal neutral third, | |||
| | |||
| Sound = jid_16_13_pluck_adu_dr220.mp3 | | Sound = jid_16_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
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In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. | In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. | ||
16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[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 | 16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[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 harmonic of the [[harmonic series]]. | ||
16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos. | 16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos. | ||
16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]]. | |||
== See also == | == See also == | ||
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* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
[[Category: | [[Category:Third]] | ||
[[Category:Neutral third]] | [[Category:Neutral third]] | ||
Latest revision as of 09:05, 15 May 2025
| Interval information |
octave-reduced 13th subharmonic
reduced subharmonic
[sound info]
In 13-limit just intonation, 16/13, the (greater) tridecimal neutral third, is a 13-limit-based interval measuring about 359.5¢. It is the inversion of 13/8, the 13th harmonic.
16/13 differs from the Pythagorean major third 81/64 by 1053/1024, about 48¢, from the classic major third 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 harmonic of the harmonic series.
16/13 is a fraction of a cent away from the neutral third found in the 10n family of edos.
16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like 5/4.