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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 the absolute value of the proportional error. 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 1200log₂(nd) may be regarded as the shortest possible distance traversed in harmonic space while realising the interval q as a sequence of elementary steps of the form 1:p, where the p are prime factors of q. Each such step traverses 1200log₂(p). Therefore, the rate at which error accumulates during this traversal is the total error divided by the total distance. The units of measure vanish.

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

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 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 the absolute value of the proportional error. 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 1200log₂(nd) may be regarded as the shortest possible distance traversed in harmonic space while realising the interval q as a sequence of elementary steps of the form 1:p, where the p are prime factors of q. Each such step traverses 1200log₂(p). Therefore, the rate at which error accumulates during this traversal is the total error divided by the total distance. The units of measure vanish.
 These quantities are often collectively referred to as ''Tenney-weighted error''.