13/8: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

| Name = (lesser) tridecimal neutral sixth

~~| Ratio = 13/8~~

| Color name = 3o6, tho 6th

~~| Monzo = -3 0 0 0 0 1~~

~~| Cents = 840.52766~~

| Name = tridecimal neutral sixth

| Sound = jid_13_8_pluck_adu_dr220.mp3

~~| Color name = 3o6, tho 6th~~

}}

'''13/8''' is the '''tridecimal neutral sixth''' ~~measuring~~ about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[~~Just~~ intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. It differs from the [[~~11-limit~~]] neutral sixth [[18/11]] by [[144/143]], about 12.1¢.

'''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of [[5/4]] and [[13/10]].

13/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢.

== Approximation ==

13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10).

This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent|¢]] sharp of the golden ratio.

== See also ==

* [[16/13]] – its [[octave complement]]

* [[64/39]] – the greater tridecimal neutral sixth

* [[Gallery of just intervals]]

* [[16/13]] its octave complement

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

[[Category:Sixth]]

~~[[Category:Interval ratio]]~~

~~[[Category:Just interval]]~~

~~[[Category:Listen~~]]

[[Category:Neutral sixth]]

[[Category:~~Sixth]]~~

[[Category:Golden ratio approximations]]

~~[[Category:Tridecimal]]~~

~~[[Category:Untwelve]]~~

~~[[Category:Overtone]]~~

~~[[Category:Over-2~~]]

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 {{Infobox Interval
-| JI glyph =
+| Name = (lesser) tridecimal neutral sixth
-| Ratio = 13/8
+| Color name = 3o6, tho 6th
-| Monzo = -3 0 0 0 0 1
-| Cents = 840.52766
-| Name = tridecimal neutral sixth
 | Sound = jid_13_8_pluck_adu_dr220.mp3
-| Color name = 3o6, tho 6th
 }}
-'''13/8''' is the '''tridecimal neutral sixth''' measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[Just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. It differs from the [[11-limit]] neutral sixth [[18/11]] by [[144/143]], about 12.1¢.
+'''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of [[5/4]] and [[13/10]].
+/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢.
+== Approximation ==
+/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10).
+This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent|¢]] sharp of the golden ratio.
 == See also ==
+* [[16/13]] – its [[octave complement]]
+* [[64/39]] – the greater tridecimal neutral sixth
 * [[Gallery of just intervals]]
-* [[16/13]] its octave complement
-[[Category:13-limit]]
+[[Category:Sixth]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
-[[Category:Listen]]
 [[Category:Neutral sixth]]
-[[Category:Sixth]]
+[[Category:Golden ratio approximations]]
-[[Category:Tridecimal]]
-[[Category:Untwelve]]
-[[Category:Overtone]]
-[[Category:Over-2]]