Val: Difference between revisions
Not sure why giving a "bad" example in the first place so that you have to include the twist of logic. Amend it by plainly stating what we mind and what we don't. Cleanup +1 |
I don't think you should try explaining backslash notation when you can link. You should also declare it before using it. |
||
| Line 31: | Line 31: | ||
* 5/4 = 5/(2 × 2) | * 5/4 = 5/(2 × 2) | ||
* 45/32 = (3 × 3 × 5)/(2 × 2 × 2 × 2 × 2) | * 45/32 = (3 × 3 × 5)/(2 × 2 × 2 × 2 × 2) | ||
Now all we do is substitute each occurrence of each prime with adding (or subtracting if we are dividing) the corresponding number of ''steps'' for that prime given by our val: | Now all we do is substitute each occurrence of each prime with adding (or subtracting if we are dividing) the corresponding number of ''steps'' for that prime given by our val: | ||
* 9/8 is mapped to (41 + 41) - (26 + 26 + 26) = 82 - 78 = 4 steps | * 9/8 is mapped to (41 + 41) - (26 + 26 + 26) = 82 - 78 = 4 steps | ||
* 5/4 is mapped to 60 - (26 + 26) = 60 - 52 = 8 steps | * 5/4 is mapped to 60 - (26 + 26) = 60 - 52 = 8 steps | ||
* 45/32 is mapped to (41 + 41 + 60) - (26 + 26 + 26 + 26 + 26) = 142 - 130 = 12 steps | * 45/32 is mapped to (41 + 41 + 60) - (26 + 26 + 26 + 26 + 26) = 142 - 130 = 12 steps | ||
That is a successful use of a val. The arithmetic works out nicely: the approximation of 5/4 times the approximation of 9/8 is the approximation of 45/32. | |||
That is a successful use of a val. The arithmetic works out nicely: the approximation of 5/4 times the approximation of 9/8 is the approximation of 45/32. Using [[backslash notation]] to denote the number of steps in an edo, these are 4\26, 8\26, and 12\26, respectively. | |||
Now let us compare to the closest approximations: | Now let us compare to the closest approximations: | ||