13/12: Difference between revisions
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{{Infobox Interval | |||
| | | Name = (lesser) tridecimal neutral second | ||
| Color name = 3o2, tho 2nd | |||
| Sound = jid_13_12_pluck_adu_dr220.mp3 | |||
}} | |||
138. | In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢). | ||
[[ | == Approximation == | ||
It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]]. | |||
{{Interval edo approximation|{{PAGENAME}}}} | |||
== Temperaments == | |||
13/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators. | |||
A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu. | |||
See | == See also == | ||
[[ | * [[24/13]] – its [[octave complement]] | ||
[[ | * [[18/13]] – its [[fifth complement]] | ||
[[ | * [[Gallery of just intervals]] | ||
[[Category: | * [[List of superparticular intervals]] | ||
[[Category:second]] | |||
[[Category:Second]] | |||
[[Category:Neutral second]] | |||
Latest revision as of 05:30, 27 January 2026
| Interval information |
reduced
[sound info]
In 13-limit just intonation, 13/12 is the (lesser) tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).
Approximation
It is approximated to within about 0.11 cents by the 3-step interval of 26edo.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 8 | 1\8 | 150.00 | +11.43 | +7.62 |
| 9 | 1\9 | 133.33 | -5.24 | -3.93 |
| 17 | 2\17 | 141.18 | +2.60 | +3.69 |
| 18 | 2\18 | 133.33 | -5.24 | -7.86 |
| 26 | 3\26 | 138.46 | -0.11 | -0.24 |
| 34 | 4\34 | 141.18 | +2.60 | +7.38 |
| 35 | 4\35 | 137.14 | -1.43 | -4.17 |
| 43 | 5\43 | 139.53 | +0.96 | +3.45 |
| 44 | 5\44 | 136.36 | -2.21 | -8.10 |
| 52 | 6\52 | 138.46 | -0.11 | -0.48 |
| 60 | 7\60 | 140.00 | +1.43 | +7.14 |
| 61 | 7\61 | 137.70 | -0.87 | -4.41 |
| 69 | 8\69 | 139.13 | +0.56 | +3.21 |
| 70 | 8\70 | 137.14 | -1.43 | -8.34 |
| 78 | 9\78 | 138.46 | -0.11 | -0.72 |
Temperaments
13/12 can be used to generate bleu temperament in the 2.3.7.11.13 subgroup, mapping 3/2 to +5 generators, 7/4 to +7 generators, 11/8 to +4 generators, and 13/8 to +6 generators.
A slightly sharp 13/12 generates glacier temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu.