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 terms ''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 terms ''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). Note that the same logarithmic measure - cents, expressed as 1200log₂ - is being 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, which are used simply for convenience.

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.

These quantities are often collectively referred to as ''Tenney-weighted error''.

These ~~metrics~~ are often collectively referred to as ''Tenney-weighted error''.

=TOP tuning=

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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 terms ''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 terms ''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). Note that the same logarithmic measure - cents, expressed as 1200log₂ - is being 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, which are used simply for convenience.
-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.
+These quantities are often collectively referred to as ''Tenney-weighted error''.
-These metrics are often collectively referred to as ''Tenney-weighted error''.
 =TOP tuning=

TOP tuning: Difference between revisions

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