Douglas Blumeyer's RTT How-To: Difference between revisions

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[[File:Map and vector.png|500px|thumb|right|'''Figure 1a.''' Mapping example]]

Covectors and vectors give us a way to bridge JI and EDOs. If the vector gives us a list of primes in a JI interval, and the covector tells us how many steps it takes to reach the approximation of each of those primes individually in an EDO, then when we put them together, we can see what step of the EDO should give the closest approximation of that JI interval. We say that the JI interval '''maps''' to that number of steps in the EDO. Calculating this looks like {{val|12 19 28}}{{monzo|4 -1 -1}}, and all that means is to multiply matching terms and sum the results.

Covectors and vectors give us a way to bridge JI and EDOs. If the vector gives us a list of primes in a JI interval, and the covector tells us how many steps it takes to reach the approximation of each of those primes individually in an EDO, then when we put them together, we can see what step of the EDO should give the closest approximation of that JI interval. We say that the JI interval '''maps''' to that number of steps in the EDO. Calculating this looks like {{val|12 19 28}}{{monzo|4 -1 -1}}, and all that means is to multiply matching terms and sum the results (this is called the dot product).

So, 16/15 maps to one step in 12-EDO ''(see Figure 1a)''.

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 [[File:Map and vector.png|500px|thumb|right|'''Figure 1a.''' Mapping example]]
-Covectors and vectors give us a way to bridge JI and EDOs. If the vector gives us a list of primes in a JI interval, and the covector tells us how many steps it takes to reach the approximation of each of those primes individually in an EDO, then when we put them together, we can see what step of the EDO should give the closest approximation of that JI interval. We say that the JI interval '''maps''' to that number of steps in the EDO. Calculating this looks like {{val|12 19 28}}{{monzo|4 -1 -1}}, and all that means is to multiply matching terms and sum the results.
+Covectors and vectors give us a way to bridge JI and EDOs. If the vector gives us a list of primes in a JI interval, and the covector tells us how many steps it takes to reach the approximation of each of those primes individually in an EDO, then when we put them together, we can see what step of the EDO should give the closest approximation of that JI interval. We say that the JI interval '''maps''' to that number of steps in the EDO. Calculating this looks like {{val|12 19 28}}{{monzo|4 -1 -1}}, and all that means is to multiply matching terms and sum the results (this is called the dot product).
 So, 16/15 maps to one step in 12-EDO ''(see Figure 1a)''.