20/13: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = Barbados sixth, tridecimal semitenth

~~| Ratio = 20/13~~

~~| Monzo = 2 0 1 0 0 -1~~

~~| Cents = 745.78605~~

| Name = Barbados sixth, ~~<br/> ratwolf wolf fifth, <br/> tridecimal semi-augmented fifth, <br/>~~ tridecimal ~~ultraminor sixth~~

| 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]].

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 ==

== See also ==

* [[13/10]] – its [[octave complement]]

* [[Gallery of just intervals]]

* [[13/10]] - its [[inverse interval]]

[[Category:~~13-limit~~]]

[[Category:Interseptimal intervals]]

[[Category:~~Interval~~]]

[[Category:Cocytic]]

[[Category:Sixth]]

[[Category:Subminor sixth]]

[[Category:Fifth]]

[[Category:Superfifth]]

[[Category:~~todo:expand~~]]

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 {{Infobox Interval
-| Icon =
+| Name = Barbados sixth, tridecimal semitenth
-| Ratio = 20/13
-| Monzo = 2 0 1 0 0 -1
-| Cents = 745.78605
-| Name = Barbados sixth, <br/> ratwolf wolf fifth, <br/> tridecimal semi-augmented fifth, <br/> tridecimal ultraminor sixth
 | 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]].
+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).
+/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]]
-* [[13/10]] - its [[inverse interval]]
-[[Category:13-limit]]
+[[Category:Interseptimal intervals]]
-[[Category:Interval]]
+[[Category:Cocytic]]
 [[Category:Sixth]]
+[[Category:Subminor sixth]]
 [[Category:Fifth]]
+[[Category:Superfifth]]
-[[Category:todo:expand]]