Vals and tuning space: Difference between revisions

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== Vals and Monzos ==

If V is a val and M is a monzo of the same rank, then the [http://mathworld.wolfram.com/AngleBracket.html angle bracket] {{val|V}}M~~>~~, which can also be written V(M), is the result of applying the [http://en.wikipedia.org/wiki/Group_homomorphism homomorphism] V to M. For example, if V = {{val|12 19 28 34}} and M = {{monzo|-5 2 2 -1}} then {{val|V}}{{monzo|M}} ~~(or ⟨V|M⟩)~~ equals 12*(-5) + 19*2 + 28*2 - 34 = 0.

If V is a val and M is a monzo of the same rank, then the [http://mathworld.wolfram.com/AngleBracket.html angle bracket] {{val|V}}{{monzo|M}}, which can also be written ⟨V|M⟩ or V(M), is the result of applying the [http://en.wikipedia.org/wiki/Group_homomorphism homomorphism] V to M. For example, if V = {{val|12 19 28 34}} and M = {{monzo|-5 2 2 -1}} then {{val|V}}{{monzo|M}} equals 12*(-5) + 19*2 + 28*2 - 34 = 0.

This tells us that in septimal 12 equal, represented by V, the interval 225/224, represented by M, is mapped to 0, which represents 1. Hence, 225/224 vanishes in septimal 12 equal; it is in the [http://mathworld.wolfram.com/GroupKernel.html kernel] of V. One should note in particular that the coordinates of V represent where the successive primes 2, 3, 5 and 7 are mapped.

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 == Vals and Monzos ==
-If V is a val and M is a monzo of the same rank, then the [http://mathworld.wolfram.com/AngleBracket.html angle bracket] {{val|V}}M&gt;, which can also be written V(M), is the result of applying the [http://en.wikipedia.org/wiki/Group_homomorphism homomorphism] V to M. For example, if V = {{val|12 19 28 34}} and M = {{monzo|-5 2 2 -1}} then {{val|V}}{{monzo|M}} (or ⟨V|M⟩) equals 12*(-5) + 19*2 + 28*2 - 34 = 0.
+If V is a val and M is a monzo of the same rank, then the [http://mathworld.wolfram.com/AngleBracket.html angle bracket] {{val|V}}{{monzo|M}}, which can also be written ⟨V|M⟩ or V(M), is the result of applying the [http://en.wikipedia.org/wiki/Group_homomorphism homomorphism] V to M. For example, if V = {{val|12 19 28 34}} and M = {{monzo|-5 2 2 -1}} then {{val|V}}{{monzo|M}} equals 12*(-5) + 19*2 + 28*2 - 34 = 0.
 This tells us that in septimal 12 equal, represented by V, the interval 225/224, represented by M, is mapped to 0, which represents 1. Hence, 225/224 vanishes in septimal 12 equal; it is in the [http://mathworld.wolfram.com/GroupKernel.html kernel] of V. One should note in particular that the coordinates of V represent where the successive primes 2, 3, 5 and 7 are mapped.