13/10: Difference between revisions

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| Sound = jid_13_10_pluck_adu_dr220.mp3

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In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2 [[cent]]s. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. 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]]), 13/10 is a fourth, as it is a [[4/3|perfect fourth (4/3)]] minus 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 the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].

However, 13/10 also appears in 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 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.

However, 13/10 also appears in 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 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.

== Interval chain ==

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 | Sound = jid_13_10_pluck_adu_dr220.mp3
 }}
 In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2 [[cent]]s. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. 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]]), 13/10 is a fourth, as it is a [[4/3|perfect fourth (4/3)]] minus 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 the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].
-However, 13/10 also appears in 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 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.
+However, 13/10 also appears in 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 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.
 == Interval chain ==