15/13: Difference between revisions
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Semifourth and other things |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = tridecimal semifourth | | Name = tridecimal semifourth | ||
| Color name = 3uy2, thuyo 2nd | | Color name = 3uy2, thuyo 2nd | ||
| Sound = jid_15_13_pluck_adu_dr220.mp3 | | Sound = jid_15_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢, wherein two instances of this fall short of [[4/3]] by [[676/675]]. | |||
In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. | |||
When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second". In extended [[Pythagorean tuning]] it is extremely close to {{Monzo|43 -27}}. | |||
== Approximation == | |||
{{Interval edo approximation|15/13}} | |||
== See also == | == See also == | ||
* [[26/15]] – its [[octave complement]] | * [[26/15]] – its [[octave complement]] | ||
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* [[The Archipelago]] | * [[The Archipelago]] | ||
[[Category:Interseptimal intervals]] | |||
[[Category:Interseptimal]] | |||
[[Category:Semifourth]] | [[Category:Semifourth]] | ||
[[Category:Third]] | [[Category:Third]] | ||
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[[Category:Second]] | [[Category:Second]] | ||
[[Category:Supermajor second]] | [[Category:Supermajor second]] | ||
Latest revision as of 18:59, 10 April 2026
| Interval information |
[sound info]
In 13-limit just intonation, 15/13, the tridecimal semifourth is an interval measuring about 247.7¢, wherein two instances of this fall short of 4/3 by 676/675.
In the language of Margo Schulter, 15/13 is an instance of an interseptimal interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second 8/7 and the small minor third 7/6. (15/13)×(13/10) = 3/2, which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a root-3rd-P5 triad that goes 26:30:39, with a 15/13 inframinor third up from the root.
When being used as type of second, it is given the name ultramajor second as it is even sharper than 8/7 which is often called a "supermajor second". In extended Pythagorean tuning it is extremely close to [43 -27⟩.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 5 | 1\5 | 240.00 | -7.74 | -3.23 |
| 10 | 2\10 | 240.00 | -7.74 | -6.45 |
| 15 | 3\15 | 240.00 | -7.74 | -9.68 |
| 19 | 4\19 | 252.63 | +4.89 | +7.74 |
| 24 | 5\24 | 250.00 | +2.26 | +4.52 |
| 29 | 6\29 | 248.28 | +0.53 | +1.29 |
| 34 | 7\34 | 247.06 | -0.68 | -1.93 |
| 39 | 8\39 | 246.15 | -1.59 | -5.16 |
| 44 | 9\44 | 245.45 | -2.29 | -8.38 |
| 48 | 10\48 | 250.00 | +2.26 | +9.04 |
| 53 | 11\53 | 249.06 | +1.32 | +5.81 |
| 58 | 12\58 | 248.28 | +0.53 | +2.58 |
| 63 | 13\63 | 247.62 | -0.12 | -0.64 |
| 68 | 14\68 | 247.06 | -0.68 | -3.87 |
| 73 | 15\73 | 246.58 | -1.17 | -7.09 |