Generalized Tenney norms and Tp interval space
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It can be useful to define a notion of the "complexity" of an interval, so that small-integer ratios such as 3/2 are less complex and intervals such as 32805/32768 are more complex. This can be accomplished for any free abelian group of monzos or smonzos by embedding the group in a normed vector space, such that the norm of this space represents the complexity of each interval. , where the monzos then form a lattice of vectors with integer coefficients, and then defining a norm on the space. Alternatively, if one prefers thinking of monzos as a Z-module
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<html><head><title>Generalized Tenney Norms and Tp Interval Space</title></head><body>It can be useful to define a notion of the "complexity" of an interval, so that small-integer ratios such as 3/2 are less complex and intervals such as 32805/32768 are more complex. This can be accomplished for any free abelian group of monzos or smonzos by embedding the group in a normed vector space, such that the norm of this space represents the complexity of each interval. <br /> <br /> , where the monzos then form a lattice of vectors with integer coefficients, and then defining a norm on the space. Alternatively, if one prefers thinking of monzos as a Z-module</body></html>