Patent val: Difference between revisions

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The basic principle of ''using'' a patent val is that you round prime harmonics to edosteps, and then deduce the "mapping" of an arbitrary interval based on its prime factorization. The '''patent val''' (aka '''nearest edomapping''') for some edo is thus the ~~[[val]]~~ that you obtain by finding the closest rounded approximation to each [[prime]] in the tuning, assuming octaves are pure (or in other words, assuming the edo number is an integer).

The basic principle of ''using'' a patent val is that you round prime harmonics to edosteps, and then deduce the "mapping" of an arbitrary interval based on its prime factorization.

The '''patent [[val]]''' (aka '''nearest edomapping''') for some edo is thus the list of numbers you get that you obtain by finding the closest rounded approximation to each [[prime]] in the tuning, assuming octaves are pure (or in other words, assuming the edo number is an integer).

For example, the patent val for 17edo is {{val| 17 27 39 }}, indicating that the closest mapping for 2/1 is 17 steps, the closest mapping for 3/1 is 27 steps, and the closest mapping for 5/1 is 39 steps. This means, if octaves are pure, that 3/2 is 706 cents, which is what you get if you round off 3/2 to the closest location in 17-equal, and that 5/4 is 353 cents, which is what you get is you round off 5/4 to the closest location in 17-equal.

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-The basic principle of ''using'' a patent val is that you round prime harmonics to edosteps, and then deduce the "mapping" of an arbitrary interval based on its prime factorization. The '''patent val''' (aka '''nearest edomapping''') for some edo is thus the [[val]] that you obtain by finding the closest rounded approximation to each [[prime]] in the tuning, assuming octaves are pure (or in other words, assuming the edo number is an integer).
+The basic principle of ''using'' a patent val is that you round prime harmonics to edosteps, and then deduce the "mapping" of an arbitrary interval based on its prime factorization.
+The '''patent [[val]]''' (aka '''nearest edomapping''') for some edo is thus the list of numbers you get that you obtain by finding the closest rounded approximation to each [[prime]] in the tuning, assuming octaves are pure (or in other words, assuming the edo number is an integer).
 For example, the patent val for 17edo is {{val| 17 27 39 }}, indicating that the closest mapping for 2/1 is 17 steps, the closest mapping for 3/1 is 27 steps, and the closest mapping for 5/1 is 39 steps. This means, if octaves are pure, that 3/2 is 706 cents, which is what you get if you round off 3/2 to the closest location in 17-equal, and that 5/4 is 353 cents, which is what you get is you round off 5/4 to the closest location in 17-equal.