20/13: Difference between revisions
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{{Infobox Interval | |||
| Name = Barbados sixth, tridecimal semitenth | |||
| Color name = 3uy5, thuyo 5th | |||
| Sound = jid_20_13_pluck_adu_dr220.mp3 | |||
}} | |||
'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 745.8 [[cent]]s. It falls in an ambiguous zone between a narrow minor sixth such as [[14/9]] and a sharp fifth such as [[32/21]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. | |||
In many notation systems based on the [[5L 2s|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 20/13 is a fifth, as it is a [[3/2|perfect fifth (3/2)]] plus an instance of [[40/39]], which is a [[2187/2048|Pythagorean apotome]] minus a stack consisting of an [[81/80|syntonic comma (81/80)]] and a [[1053/1024|tridecimal quartertone (1053/1024)]], none of which changes the [[scale|scale degree]]. It functions as such in voicings of the harmonic thirteenth chord, [[4:5:6:7:9:11:13]]. | |||
|2 | |||
However, 20/13 also appears in voicings of the relatively simple [[10:13:15]] triad, which consists of [[13/10]] and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 20/13 function as an inframinor sixth (if the chord is not taken as a suspension). | |||
[[ | |||
20/13 is the targeted as the wolf fifth in [[Gene Ward Smith]]'s [[Ratwolf]] scale. | |||
== Approximation == | |||
{{Interval edo approximation|20/13}} | |||
== See also == | |||
* [[13/10]] – its [[octave complement]] | |||
* [[Gallery of just intervals]] | |||
[[Category:Interseptimal intervals]] | |||
[[Category:Cocytic]] | |||
[[Category:Sixth]] | |||
[[Category:Subminor sixth]] | |||
[[Category:Fifth]] | |||
[[Category:Superfifth]] | |||
Latest revision as of 16:29, 22 January 2026
| Interval information |
tridecimal semitenth
[sound info]
20/13, the tridecimal semitenth, is a 13-limit interseptimal interval measuring about 745.8 cents. It falls in an ambiguous zone between a narrow minor sixth such as 14/9 and a sharp fifth such as 32/21. The descriptor "interseptimal" comes from Margo Schulter, and indicates its position between those two septimal (7-based) extremes.
In many notation systems based on the diatonic chain-of-fifths notation with commatic alterations (e.g. FJS, HEJI), 20/13 is a fifth, as it is a perfect fifth (3/2) plus an instance of 40/39, which is a Pythagorean apotome minus a stack consisting of an syntonic comma (81/80) and a tridecimal quartertone (1053/1024), none of which changes the scale degree. It functions as such in voicings of the harmonic thirteenth chord, 4:5:6:7:9:11:13.
However, 20/13 also appears in voicings of the relatively simple 10:13:15 triad, which consists of 13/10 and 15/13 that stack to make a 3/2 perfect fifth. This makes 20/13 function as an inframinor sixth (if the chord is not taken as a suspension).
20/13 is the targeted as the wolf fifth in Gene Ward Smith's Ratwolf scale.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 8 | 5\8 | 750.00 | +4.21 | +2.81 |
| 13 | 8\13 | 738.46 | -7.32 | -7.93 |
| 16 | 10\16 | 750.00 | +4.21 | +5.62 |
| 21 | 13\21 | 742.86 | -2.93 | -5.13 |
| 24 | 15\24 | 750.00 | +4.21 | +8.43 |
| 29 | 18\29 | 744.83 | -0.96 | -2.32 |
| 37 | 23\37 | 745.95 | +0.16 | +0.49 |
| 45 | 28\45 | 746.67 | +0.88 | +3.30 |
| 50 | 31\50 | 744.00 | -1.79 | -7.44 |
| 53 | 33\53 | 747.17 | +1.38 | +6.11 |
| 58 | 36\58 | 744.83 | -0.96 | -4.63 |
| 61 | 38\61 | 747.54 | +1.75 | +8.92 |
| 66 | 41\66 | 745.45 | -0.33 | -1.82 |
| 74 | 46\74 | 745.95 | +0.16 | +0.99 |
| 79 | 49\79 | 744.30 | -1.48 | -9.76 |