Val: Difference between revisions

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Given an explicit or assumed limit, any [[patent val]] can simply be represented by stating its first coefficient - the digit representing how many generators map to 2/1. For example, the 5-limit patent val for 17edo, {{val| 17 27 39 }}, can be called simply, "17".

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 17edo 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".

The patent val for any EDO will use the most accurate mapping for each individual prime when pure octaves are assumed. 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 17edo 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| 17 27 38 }}, we'd write "17cc". In [[17edo]], 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.

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 Given an explicit or assumed limit, any [[patent val]] can simply be represented by stating its first coefficient - the digit representing how many generators map to 2/1. For example, the 5-limit patent val for 17edo, {{val| 17 27 39 }}, can be called simply, "17".
-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 17edo 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".
+The patent val for any EDO will use the most accurate mapping for each individual prime when pure octaves are assumed. 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 17edo 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| 17 27 38 }}, we'd write "17cc". In [[17edo]], 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.