TOP tuning: Difference between revisions
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For example, if M is |-4 4 -1> then q = 81/80 (a [[syntonic comma]]). If T is <1200 1900 2800| (a multiple of [[12edo]]) then <T|M> = -4800 + 7600 - 2800 = 0. Thus, while cents(q) = 21.506290, T(q) = 0 (i.e., the tuning tempers away the syntonic comma). | For example, if M is |-4 4 -1> then q = 81/80 (a [[syntonic comma]]). If T is <1200 1900 2800| (a multiple of [[12edo]]) then <T|M> = -4800 + 7600 - 2800 = 0. Thus, while cents(q) = 21.506290, T(q) = 0 (i.e., the tuning tempers away the syntonic comma). | ||
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 | 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'' is defined as 0 when q equals 1 and otherwise PE(q) = Err(q)/cents(nd) = Err(q)/1200log₂(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 ''absolute proportional error'' is defined as 0 when q equals 1 and otherwise APE(q) = Arr(q)/cents(nd) = Arr(q)/1200log₂(nd) | ||