Val: Difference between revisions

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The patent val for any EDO will use the most accurate mapping for each individual prime. However, it may often be the case that one wants to refer to vals other than the patent val. For example, the 5-limit val {{val| 17 27 40 }}, which maps the 5/4 to the 424 cent interval rather than the 353 cent interval, is not the patent val for 17-EDO but may be preferred because it is lower in overall error. Non-patent vals are specified by adding a “wart” to the end of their name which specifies their deviation from the patent val. In this case, we want to specify that the 5/1 has been changed to use its second-most accurate mapping. Since 5 is the third prime number, we add the third letter of the alphabet to the end of the EDO number, to form "17c".

If we wanted to use the third-most accurate mapping for 5, {{val| 7 27 38 }}, we'd write "17cc". In [[17-EDO]], the approximation of the prime-5 component is raised for an odd, and lowered for an even, amount of c letters: <code></code> = 39, <code>c</code> = 40, <code>cc</code> = 38, <code>ccc</code> = 41, <code>cccc</code> = 37.

If we wanted to use the third-most accurate mapping for 5, {{val| 17 27 38 }}, we'd write "17cc". In [[17edo|17-EDO]], the approximation of the prime-5 component is raised for an odd, and lowered for an even, amount of c letters: <code></code> = 39, <code>c</code> = 40, <code>cc</code> = 38, <code>ccc</code> = 41, <code>cccc</code> = 37.

The general rules:

* Wart letters specify prime approximations being altered from the patent val

* Wart letters specify prime approximations being altered from the patent val.

* The ''n''-th letter of the alphabet refers to the ''n''-th prime: a~2, b~3, c~5, d~7, e~11 etc.

* A letter which appears m times refers to the (''m'' + 1)-th most accurate mapping for that prime.

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 The patent val for any EDO will use the most accurate mapping for each individual prime. However, it may often be the case that one wants to refer to vals other than the patent val. For example, the 5-limit val {{val| 17 27 40 }}, which maps the 5/4 to the 424 cent interval rather than the 353 cent interval, is not the patent val for 17-EDO but may be preferred because it is lower in overall error. Non-patent vals are specified by adding a “wart” to the end of their name which specifies their deviation from the patent val. In this case, we want to specify that the 5/1 has been changed to use its second-most accurate mapping. Since 5 is the third prime number, we add the third letter of the alphabet to the end of the EDO number, to form "17c".
-If we wanted to use the third-most accurate mapping for 5, {{val| 7 27 38 }}, we'd write "17cc". In [[17-EDO]], the approximation of the prime-5 component is raised for an odd, and lowered for an even, amount of c letters: <code></code> = 39, <code>c</code> = 40, <code>cc</code> = 38, <code>ccc</code> = 41, <code>cccc</code> = 37.
+If we wanted to use the third-most accurate mapping for 5, {{val| 17 27 38 }}, we'd write "17cc". In [[17edo|17-EDO]], the approximation of the prime-5 component is raised for an odd, and lowered for an even, amount of c letters: <code></code> = 39, <code>c</code> = 40, <code>cc</code> = 38, <code>ccc</code> = 41, <code>cccc</code> = 37.
 The general rules:
-* Wart letters specify prime approximations being altered from the patent val
+* Wart letters specify prime approximations being altered from the patent val.
 * The ''n''-th letter of the alphabet refers to the ''n''-th prime: a~2, b~3, c~5, d~7, e~11 etc.
 * A letter which appears m times refers to the (''m'' + 1)-th most accurate mapping for that prime.