13/8: Difference between revisions

(15 intermediate revisions by 8 users not shown)

Line 1:

{{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 a neutral sixth ~~measuring~~ about 840.5¢, falling between the categories of minor sixth and major sixth. In [[~~13-limit|~~13-limit]] [[~~Just_intonation|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|~~3/2]] and [[~~7/4|~~7/4]], separated from each by the [[~~superparticular|~~superparticular]] ratios [[~~13/12|~~13/12]] and [[14/13~~|14~~/13]], ~~respectively~~. It differs from the [[~~11-limit|11-limit~~]] neutral sixth [[~~18/11|~~18/11]] by [[144/143~~|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]]

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~ [[Category:~~13-limit~~]]

[[Category:Sixth]]

[[Category:~~interval]]~~

[[Category:Neutral sixth]]

~~[[Category:just_interval]]~~

[[Category:Golden ratio approximations]]

~~[[Category:listen]]~~

~~[[Category:neutral_sixth~~]]

[[Category:ratio]]

~~[[Category:sixth]]~~

~~[[Category:tridecimal]]~~

~~[[Category:untwelve~~]]

@@ Line 1: / Line 1: @@
 {{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
 }}
-/8 is a neutral sixth measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit|13-limit]] [[Just_intonation|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|3/2]] and [[7/4|7/4]], separated from each by the [[superparticular|superparticular]] ratios [[13/12|13/12]] and [[14/13|14/13]], respectively. It differs from the [[11-limit|11-limit]] neutral sixth [[18/11|18/11]] by [[144/143|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]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+[[Category:Sixth]]
-[[Category:interval]]
+[[Category:Neutral sixth]]
-[[Category:just_interval]]
+[[Category:Golden ratio approximations]]
-[[Category:listen]]
-[[Category:neutral_sixth]]
-[[Category:ratio]]
-[[Category:sixth]]
-[[Category:tridecimal]]
-[[Category:untwelve]]