TOP tuning: Difference between revisions

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__FORCETOC__

=Proportional error=

A ''tuning'' for a regular temperament is defined by a vector T in [[Vals_and_Tuning_Space#Vals and Monzos|Tenney tuning space]] whose entries are the sizes of the intervals, in cents, which the k generators of the regular temperament (often the first k primes) are mapped to. T is denoted by a [http://en.wikipedia.org/wiki/Bra-ket_notation bra vector], and if M is a monzo then <T|M> is the size, in cents, of the interval defined by M in the tuning T. If k is the rational number which M represents, then we may also write this quantity as T(k).

A ''tuning'' for a regular temperament is defined by a vector T in [[Vals_and_Tuning_Space#Vals and Monzos|Tenney tuning space]] whose entries are the sizes of the intervals, in cents, which the n generators of the regular temperament (often the first n primes) are mapped to. T is denoted by a [http://en.wikipedia.org/wiki/Bra-ket_notation bra vector], and if M is a monzo then <T|M> is the size, in cents, of the interval defined by M in the tuning T. If k is the rational number which M represents, then we may also write this quantity as T(k).

For example, if M is |-4 4 -1> then k = 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(k) = 21.506290, T(k) = 0 (i.e., the tuning tempers away the syntonic comma).

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 __FORCETOC__
 =Proportional error=
-A ''tuning'' for a regular temperament is defined by a vector T in [[Vals_and_Tuning_Space#Vals and Monzos|Tenney tuning space]] whose entries are the sizes of the intervals, in cents, which the k generators of the regular temperament (often the first k primes) are mapped to. T is denoted by a [http://en.wikipedia.org/wiki/Bra-ket_notation bra vector], and if M is a monzo then &lt;T|M&gt; is the size, in cents, of the interval defined by M in the tuning T. If k is the rational number which M represents, then we may also write this quantity as T(k).
+A ''tuning'' for a regular temperament is defined by a vector T in [[Vals_and_Tuning_Space#Vals and Monzos|Tenney tuning space]] whose entries are the sizes of the intervals, in cents, which the n generators of the regular temperament (often the first n primes) are mapped to. T is denoted by a [http://en.wikipedia.org/wiki/Bra-ket_notation bra vector], and if M is a monzo then &lt;T|M&gt; is the size, in cents, of the interval defined by M in the tuning T. If k is the rational number which M represents, then we may also write this quantity as T(k).
 For example, if M is |-4 4 -1&gt; then k = 81/80 (a [[syntonic comma]]). If T is &lt;1200 1900 2800| (a multiple of [[12edo]]) then &lt;T|M&gt; = -4800 + 7600 - 2800 = 0. Thus, while cents(k) = 21.506290, T(k) = 0 (i.e., the tuning tempers away the syntonic comma).