Generalized Tenney norms and Tp interval space: Difference between revisions
smonzo |
clarity on subgroup monzos |
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\end{bmatrix}</math> | \end{bmatrix}</math> | ||
Given these matrices, the T1 norm of our | Given these matrices, the T1 norm of our subgroup basis monzo |0 -2 1>, which we will call '''v''', can be found by taking the L1 norm of the resulting real vector '''W<span style="font-size: 10px; vertical-align: sub;">L</span>''' · '''V<span style="font-size: 10px; vertical-align: sub;">G</span>''' · '''v'''. This expression works out to | ||
<math>\left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.9/7.5/3} = \left \| | <math>\left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.9/7.5/3} = \left \| | ||
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Note that the value 15.861 is obtained by |0| + |-7.925| + |2.322| + |5.615|, which is the L1 norm of the vector. | Note that the value 15.861 is obtained by |0| + |-7.925| + |2.322| + |5.615|, which is the L1 norm of the vector. | ||
To confirm this, we can put | To confirm this, we can put the subgroup basis monzo |0 -2 1> back into rational form to see that it represents the interval 245/243. As the L1 norm is supposed to give log(n·d) for any interval n/d, we can confirm that we have the right answer above by noting that log(245·243) is indeed equal to 15.861. | ||
[[Category:height]] | [[Category:height]] | ||
[[Category:measure]] | [[Category:measure]] | ||