Domain basis: Difference between revisions
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= Basis elements and nonstandard domain bases = | = Basis elements and nonstandard domain bases = | ||
Bases are expressed as lists of '''[[basis | Bases are expressed as lists of '''[[basis element]]s''', the building blocks of the corresponding space, and domain bases are no different. They are notated by separating these basis elements with periods. The most common bases consist of prime numbers, which are the building blocks of the [[Wikipedia:Rational_number|rational numbers]] we use for [[just intonation|justly intoned]] interval ratios. Examples of such bases are 2.3.5, or 2.3.7.11. | ||
When left unspecified, the basis is the <math>d</math> [[prime limit]], or in other words, the sequence of the first <math>d</math> primes where <math>d</math> is the [[dimensionality]]. So, for example, given the [[mapping|regular temperament mapping]] {{rket|{{map|1 0 -4 -13 -25}} {{map|0 1 4 10 18}}}}, we should assume that its domain basis is 2.3.5.7.11. This is called a '''standard basis''', and any other basis would therefore be a '''nonstandard basis'''. | When left unspecified, the basis is the <math>d</math> [[prime limit]], or in other words, the sequence of the first <math>d</math> primes where <math>d</math> is the [[dimensionality]]. So, for example, given the [[mapping|regular temperament mapping]] {{rket|{{map|1 0 -4 -13 -25}} {{map|0 1 4 10 18}}}}, we should assume that its domain basis is 2.3.5.7.11. This is called a '''standard basis''', and any other basis would therefore be a '''nonstandard basis'''. | ||