16/13: Difference between revisions
About its proximity to 10edo |
13/8 is the octave-reduced form of 13/1 Tags: Mobile edit Mobile web edit |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic | |||
| Color name = 3u3, thu 3rd | |||
| Name = neutral | |||
| | |||
| 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 | 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 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]] | * [[13/8]] – its [[octave complement]] | ||
* [[39/32]] | * [[39/32]] – its [[fifth complement]] | ||
* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
[[Category: | [[Category:Third]] | ||
[[Category:Neutral third]] | [[Category:Neutral third]] | ||
Latest revision as of 17:11, 30 May 2026
| 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 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 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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 7 | 2\7 | 342.86 | -16.62 | -9.69 |
| 10 | 3\10 | 360.00 | +0.53 | +0.44 |
| 17 | 5\17 | 352.94 | -6.53 | -9.25 |
| 20 | 6\20 | 360.00 | +0.53 | +0.88 |
| 27 | 8\27 | 355.56 | -3.92 | -8.81 |
| 30 | 9\30 | 360.00 | +0.53 | +1.32 |
| 37 | 11\37 | 356.76 | -2.72 | -8.37 |
| 40 | 12\40 | 360.00 | +0.53 | +1.76 |
| 47 | 14\47 | 357.45 | -2.03 | -7.93 |
| 50 | 15\50 | 360.00 | +0.53 | +2.20 |
| 57 | 17\57 | 357.89 | -1.58 | -7.49 |
| 60 | 18\60 | 360.00 | +0.53 | +2.64 |
| 67 | 20\67 | 358.21 | -1.26 | -7.05 |
| 70 | 21\70 | 360.00 | +0.53 | +3.08 |
| 77 | 23\77 | 358.44 | -1.03 | -6.61 |
| 80 | 24\80 | 360.00 | +0.53 | +3.52 |