Relative cent: Difference between revisions

Line 5:

An existing example is the [[turkish cent]], which is the relative cent of [[106edo]]. The iota, the relative cent for [[17edo]], has been proposed by [[George Secor]] and [[Margo Schulter]] for use with 17edo, and [[Tútim_Dennsuul_Wafiil|Tútim Dennsuul]] has advocated the [[purdal]], which divides the octave into 9900 parts (being relative cents of [[99edo]]). The [[millioctave]] is another such measure, as it can be viewed as the relative cent measure for [[10edo]].

Measuring the error of an approximation of an interval in an EDO in terms of relative cents gives the [[relative error]], which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.

== Relative Error ==

''Main article: [[Relative error]]''

Measuring the error of an approximation of an interval in an EDO in terms of relative cents gives the '''relative error''', which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.

== Application for quantifying approximation ==

@@ Line 5: / Line 5: @@
 An existing example is the [[turkish cent]], which is the relative cent of [[106edo]]. The iota, the relative cent for [[17edo]], has been proposed by [[George Secor]] and [[Margo Schulter]] for use with 17edo, and [[Tútim_Dennsuul_Wafiil|Tútim Dennsuul]] has advocated the [[purdal]], which divides the octave into 9900 parts (being relative cents of [[99edo]]). The [[millioctave]] is another such measure, as it can be viewed as the relative cent measure for [[10edo]].
-Measuring the error of an approximation of an interval in an EDO in terms of relative cents gives the [[relative error]], which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.
+== Relative Error ==
+''Main article: [[Relative error]]''
+Measuring the error of an approximation of an interval in an EDO in terms of relative cents gives the '''relative error''', which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.
 == Application for quantifying approximation ==