Val: Difference between revisions

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* mapping of 5/4: {{val| 26 41 60 }}{{monzo| -2 0 1 }} = 26 × -2 + 41 × 0 + 60 × 1 = -52 + 0 + 60 = 8 (steps of 26edo)

* mapping of 45/32: {{val| 26 41 60 }}{{monzo| -5 2 1 }} = 26 × -5 + 41 × 2 + 60 × 1 = -130 + 82 + 60 = 12 (steps of 26edo)

This is all very tedious, but in practice using a val is much simpler, because you do not need to do this, all you need to know is [[5/4]] is mapped to 8\12 and [[3/2]] is mapped to 15\26, therefore [[9/4]] is mapped to 30\26, therefore [[9/8]] is mapped to (30 - 26)\26 = 4\26, so that since we know 9/8 × 5/4 = 45/32, the mapped version of 45/32 will just be 4 + 8 = 12. This method guarantees that you never contradict yourself, even if you are technically using suspicious approximations.

This is all very tedious, but in practice using a val is much simpler, because you do not need to do this, all you need to know is [[5/4]] is mapped to 8\26 and [[3/2]] is mapped to 15\26, therefore [[9/4]] is mapped to 30\26, therefore [[9/8]] is mapped to (30 - 26)\26 = 4\26, so that since we know 9/8 × 5/4 = 45/32, the mapped version of 45/32 will just be 4 + 8 = 12. This method guarantees that you never contradict yourself, even if you are technically using suspicious approximations.

For the mathematically inclined, note that this operation is the same as taking the {{w|dot product}} between the monzo and val interpreted as ordinary vectors.

@@ Line 56: / Line 56: @@
 * mapping of 5/4: {{val| 26 41 60 }}{{monzo| -2 0 1 }} = 26 × -2 + 41 × 0 + 60 × 1 = -52 + 0 + 60 = 8 (steps of 26edo)
 * mapping of 45/32: {{val| 26 41 60 }}{{monzo| -5 2 1 }} = 26 × -5 + 41 × 2 + 60 × 1 = -130 + 82 + 60 = 12 (steps of 26edo)
-This is all very tedious, but in practice using a val is much simpler, because you do not need to do this, all you need to know is [[5/4]] is mapped to 8\12 and [[3/2]] is mapped to 15\26, therefore [[9/4]] is mapped to 30\26, therefore [[9/8]] is mapped to (30 - 26)\26 = 4\26, so that since we know 9/8 × 5/4 = 45/32, the mapped version of 45/32 will just be 4 + 8 = 12. This method guarantees that you never contradict yourself, even if you are technically using suspicious approximations.
+This is all very tedious, but in practice using a val is much simpler, because you do not need to do this, all you need to know is [[5/4]] is mapped to 8\26 and [[3/2]] is mapped to 15\26, therefore [[9/4]] is mapped to 30\26, therefore [[9/8]] is mapped to (30 - 26)\26 = 4\26, so that since we know 9/8 × 5/4 = 45/32, the mapped version of 45/32 will just be 4 + 8 = 12. This method guarantees that you never contradict yourself, even if you are technically using suspicious approximations.
 For the mathematically inclined, note that this operation is the same as taking the {{w|dot product}} between the monzo and val interpreted as ordinary vectors.