Val: Difference between revisions
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== Shorthand notation == | == Shorthand notation == | ||
This is also known as '''warts''' or '''wart notation'''. | This is also known as '''warts''' or '''wart notation'''. It was developed by [[Herman Miller]] and [[Graham Breed]]. | ||
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". | 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". | ||
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* The ''n''-th letter of the alphabet refers to the ''n''-th prime: a~2, b~3, c~5, d~7, e~11 etc. | * 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. | * A letter which appears m times refers to the (''m'' + 1)-th most accurate mapping for that prime. | ||
* ''So, if a number representing a val is wartless, it is taken to mean the patent val''. | * ''So, if a number representing a val is wartless, it is taken to mean the patent val''. | ||
* The wart letter p is used to make explicit that the number refers to the patent val (however, the letter p was not chosen to stand for "patent val"; that is a coincidence. The creators of wart notation do not use the term "patent val". The letter originally was intended to stand for "prime".) | |||
== Vals in JI subgroups == | == Vals in JI subgroups == | ||