21/13: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 21/13~~

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

~~| Cents = 830.25325~~

| Name = tridecimal supraminor sixth

| Color name = thuzo 6th, 3uz6

~~| FJS name = M6<sup>7</sup><sub>13</sub>~~

| Sound = ji-21-13-csound-foscil-220hz.mp3

}}

'''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s in size. It has a very good approximation in [[13edo]].

'''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s in size. It has a very good approximation in [[13edo]], and notably, 5 of these intervals differ from [[11/1]] by 4084223/4084101, a comma of a mere 0.052{{cent}}.

This interval is a ratio of two consecutive {{w|Fibonacci numbers}} and thus a convergent to [[acoustic phi]] (the interval of a [[golden ratio]]). In this case, 21/13 is ~2.8{{cent}} flat of acoustic phi. It differs from [[13/8]], the previous such convergent, by [[169/168]], and from the following convergent [[34/21]] by [[442/441]].

== See also ==

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* [[Gallery of just intervals]]

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

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

[[Category:Sixth]]

[[Category:Supraminor sixth]]

[[Category:~~Pages with internal sound examples~~]]

[[Category:Golden ratio approximations]]

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 {{Infobox Interval
-| Icon =
-| Ratio = 21/13
-| Monzo = 0 1 0 1 0 -1
-| Cents = 830.25325
 | Name = tridecimal supraminor sixth
 | Color name = thuzo 6th, 3uz6
-| FJS name = M6<sup>7</sup><sub>13</sub>
 | Sound = ji-21-13-csound-foscil-220hz.mp3
 }}
-'''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s in size. It has a very good approximation in [[13edo]].
+'''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s in size. It has a very good approximation in [[13edo]], and notably, 5 of these intervals differ from [[11/1]] by 4084223/4084101, a comma of a mere 0.052{{cent}}.
+This interval is a ratio of two consecutive {{w|Fibonacci numbers}} and thus a convergent to [[acoustic phi]] (the interval of a [[golden ratio]]). In this case, 21/13 is ~2.8{{cent}} flat of acoustic phi. It differs from [[13/8]], the previous such convergent, by [[169/168]], and from the following convergent [[34/21]] by [[442/441]].
 == See also ==
@@ Line 16: / Line 13: @@
 * [[Gallery of just intervals]]
-[[Category:13-limit]]
-[[Category:Interval ratio]]
 [[Category:Sixth]]
 [[Category:Supraminor sixth]]
-[[Category:Pages with internal sound examples]]
+[[Category:Golden ratio approximations]]