TOP tuning: Difference between revisions

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Given a tuning T and a rational number q in the domain of T, the ''signed error'' of T on q is defined as Err(q) = T(q) - cents(q). The ''absolute error'' Arr(q) = |Err(q)| is the absolute value of the signed error.

The ''proportional error'' and ''absolute proportional error'' take into account the [[Benedetti_height|Benedetti height]] or [[Tenney_Height|Tenney height]] of q. If q is expressed as a fraction n/d in lowest terms, then Benedetti height is nd and the Tenney height is log₂(nd).

The ''proportional error'' and ''absolute proportional error'' take into account the [[Benedetti_height|Benedetti height]] or [[Tenney_Height|Tenney height]] of q. If q is expressed as a fraction n/d in lowest terms, then Benedetti height is nd and the Tenney height is log₂(nd). The ''proportional error'' is defined as 0 when q equals 1 and otherwise PE(q) = Err(q)/cents(nd) = Err(q)/1200log₂(nd). The ''absolute proportional error'' is defined as 0 when q equals 1 and otherwise APE(q) = Arr(q)/cents(nd) = Arr(q)/1200log₂(nd)

The ''proportional error'' is defined as 0 when q equals 1 and otherwise PE(q) = Err(q)/cents(nd) = Err(q)/1200log₂(nd).

The ''absolute proportional error'' is defined as 0 when q equals 1 and otherwise APE(q) = Arr(q)/cents(nd) = Arr(q)/1200log₂(nd)

Note that the same logarithmic measure - cents, expressed as 1200log₂ - is used in both numerator and denominator, so a logarithm with any other base would yield the same result. Thus, the definition is not in fact based on cents.

@@ Line 7: / Line 7: @@
 Given a tuning T and a rational number q in the domain of T, the ''signed error'' of T on q is defined as Err(q) = T(q) - cents(q). The ''absolute error'' Arr(q) = |Err(q)| is the absolute value of the signed error.
-The ''proportional error'' and ''absolute proportional error'' take into account the [[Benedetti_height|Benedetti height]] or [[Tenney_Height|Tenney height]] of q. If q is expressed as a fraction n/d in lowest terms, then Benedetti height is nd and the Tenney height is log₂(nd).
+The ''proportional error'' and ''absolute proportional error'' take into account the [[Benedetti_height|Benedetti height]] or [[Tenney_Height|Tenney height]] of q. If q is expressed as a fraction n/d in lowest terms, then Benedetti height is nd and the Tenney height is log₂(nd). The ''proportional error'' is defined as 0 when q equals 1 and otherwise PE(q) = Err(q)/cents(nd) = Err(q)/1200log₂(nd). The ''absolute proportional error'' is defined as 0 when q equals 1 and otherwise APE(q) = Arr(q)/cents(nd) = Arr(q)/1200log₂(nd)
-The ''proportional error'' is defined as 0 when q equals 1 and otherwise PE(q) = Err(q)/cents(nd) = Err(q)/1200log₂(nd).
-The ''absolute proportional error'' is defined as 0 when q equals 1 and otherwise APE(q) = Arr(q)/cents(nd) = Arr(q)/1200log₂(nd)
 Note that the same logarithmic measure - cents, expressed as 1200log₂ - is used in both numerator and denominator, so a logarithm with any other base would yield the same result. Thus, the definition is not in fact based on cents.