13/8: Difference between revisions

(16 intermediate revisions by 9 users not shown)

Line 1:

~~'''13/8'''~~

{{Infobox Interval

|~~-3 0 0 0 0 1>~~

| Name = (lesser) tridecimal neutral sixth

| Color name = 3o6, tho 6th

| Sound = jid_13_8_pluck_adu_dr220.mp3

}}

840.~~52766 cents~~

'''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]].

[[~~File:jid_13_8_pluck_adu_dr220.mp3~~]] [[~~:File:jid_13_8_pluck_adu_dr220.mp3|sound sample~~]]

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¢.

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¢.

== Approximation ==

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

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

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.

[[~~Category:interval~~]]

[[~~Category:just_interval~~]]

== See also ==

[[~~Category:listen~~]]

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

[[~~Category:neutral_sixth~~]]

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

[[Category:~~ratio~~]]

* [[Gallery of just intervals]]

[[Category:sixth]]

[[Category:~~tridecimal]]~~

[[Category:Sixth]]

~~[[Category:untwelve~~]]

[[Category:Neutral sixth]]

[[Category:Golden ratio approximations]]

@@ Line 1: / Line 1: @@
-'''13/8'''
+{{Infobox Interval
-|-3 0 0 0 0 1&gt;
+| Name = (lesser) tridecimal neutral sixth
+| Color name = 3o6, tho 6th
+| Sound = jid_13_8_pluck_adu_dr220.mp3
+}}
-.52766 cents
+'''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]].
-[[File:jid_13_8_pluck_adu_dr220.mp3]] [[:File:jid_13_8_pluck_adu_dr220.mp3|sound sample]]
+/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¢.
-/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¢.
+== Approximation ==
+/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10).
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+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.
-[[Category:interval]]
-[[Category:just_interval]]
+== See also ==
-[[Category:listen]]
+* [[16/13]] – its [[octave complement]]
-[[Category:neutral_sixth]]
+* [[64/39]] – the greater tridecimal neutral sixth
-[[Category:ratio]]
+* [[Gallery of just intervals]]
-[[Category:sixth]]
-[[Category:tridecimal]]
+[[Category:Sixth]]
-[[Category:untwelve]]
+[[Category:Neutral sixth]]
+[[Category:Golden ratio approximations]]