20/13: Difference between revisions

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| Sound = jid_20_13_pluck_adu_dr220.mp3

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'''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).

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.

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 | 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).
+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.