16/13: Difference between revisions
added the color name |
13/8 is the octave-reduced form of 13/1 Tags: Mobile edit Mobile web edit |
||
| (9 intermediate revisions by 6 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic | |||
| Name = (greater) tridecimal neutral third, | |||
| Color name = 3u3, thu 3rd | | Color name = 3u3, thu 3rd | ||
| Sound = jid_16_13_pluck_adu_dr220.mp3 | | Sound = jid_16_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
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 [[octave reduction|octave-reduced]] 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 harmonic of the [[harmonic series]]. | 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]]. | ||
| Line 15: | Line 11: | ||
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]]. | |||
== Approximation == | |||
{{Interval edo approximation|16/13}} | |||
== See also == | == See also == | ||
* [[13/8]] – its [[octave complement]] | * [[13/8]] – its [[octave complement]] | ||
| Line 20: | Line 20: | ||
* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Neutral third]] | [[Category:Neutral third]] | ||