Radian: Difference between revisions

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-Radian, radial major second, or radial whole tone is an interval of 1200/2pi cents.
+{{Infobox Interval|Ratio=2^(1/(2pi))|Monzo=undefined|Cents=190.98593|Name=radian, radial major second, radial whole tone}}
+'''Radian''', '''radial major second''', or a '''radial whole tone''' is an interval of <math>\frac{1200}/{2\pi}</math cents.
+The interval has an interpretation that relates to all [[EDO|EDOs]]. Since pitch classes in all equal divisions of the octave form in the shape of a circle, radian interval therefore occurs as the radius of this perceptional circle.
-{{Infobox Interval|Ratio=2^(1/(2pi))|Monzo=undefined|Cents=190.98593|Name=radian, radial major second, radial whole tone}}
+Radian is 13 cents below just [[9/8]] and 9 cents below [[12edo]] major second of exactly 1/6 of a circle, or 200 cents.
+== Approximations ==
+Closest equal temperament approximations of the radian can be derived from the continued fraction of 1/2pi: 4\[[25edo|25]], 7\[[44edo|44]], 53\333, and 113\710. 7\44 and 113\710 are complementary to the historically notable 22/7 and 355/113 approximations of pi.
+Other approximations include 5\[[31edo|31]], which is also for the meantone, 11\69, the local meantone as well, and 13\82. Starting with 88edo, difference between the radian (14 steps out of 88) and 9/8 (15 steps out of 88) is visible.