Val: Difference between revisions

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The general rules:

* 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.

* Wart letters that ''suffix'' the number 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. So, if a number representing a val is wartless, it is taken to mean the patent val.

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

* A wart letter that ''prefixes'' the number specifies the corresponding prime as the [[interval of equivalence]] to be divided by the following number. For example, b13 refers to the patent val of [[13edt|13ed3]]. The octave is assumed, so "a" is typically not written out.

* So, if a number representing a val is wartless, it is taken to mean the patent val.

* A wart letter ~~may~~ ''~~prefix~~'' the number~~, in which case it~~ specifies the corresponding prime as the [[interval of equivalence]] to be divided by the following number. For example, b13 refers to the patent val of [[13edt|13ed3]]. The octave is assumed, so "a" is typically not written out.

[[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder], [[Sintel]]'s [https://sintel.pythonanywhere.com Temperament Calculator], and [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] have implementations of wart notation that differ from each other slightly. For example:

[[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder], [[Sintel]]'s [https://sintel.pythonanywhere.com Temperament Calculator], and [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] have implementations of wart notation that differ from each other slightly. For example, in the Temperament Finder, the wart letter "p" is used to make explicit that the number refers to the patent val (though the letter originally was intended to stand for "prime"), despite that "p" is logically the letter for prime 53, and the wart letter "q" and after refers to each non-prime basis element of composite/fractional subgroup, respectively and temporarily.

* In Graham Breed's Temperament Finder, the wart letter "p" is used to make explicit that the number refers to the patent val (though the letter originally was intended to stand for "prime")~~. Note~~ that "p" is logically the letter for prime 53.

* In Graham Breed's Temperament Finder, the wart letter "q" and after refers to each non-prime basis element of composite/fractional subgroup, respectively and temporarily.

For a full specification and a deeper dive into the nuances in each implementation, see Flora's [https://github.com/FloraCanou/temperament_evaluator/wiki/Commonwart Commonwart] document.

=== Sparse Offset Val notation ===

@@ Line 115: / Line 115: @@
 The general rules:
-* 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.
+* Wart letters that ''suffix'' the number 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. So, if a number representing a val is wartless, it is taken to mean the patent val.
-* A letter which appears ''m'' times refers to the (''m'' + 1)-th most accurate mapping for that prime.
+* A wart letter that ''prefixes'' the number specifies the corresponding prime as the [[interval of equivalence]] to be divided by the following number. For example, b13 refers to the patent val of [[13edt|13ed3]]. The octave is assumed, so "a" is typically not written out.
-* So, if a number representing a val is wartless, it is taken to mean the patent val.
-* A wart letter may ''prefix'' the number, in which case it specifies the corresponding prime as the [[interval of equivalence]] to be divided by the following number. For example, b13 refers to the patent val of [[13edt|13ed3]]. The octave is assumed, so "a" is typically not written out.
-[[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder], [[Sintel]]'s [https://sintel.pythonanywhere.com Temperament Calculator], and [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] have implementations of wart notation that differ from each other slightly. For example:
+[[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder], [[Sintel]]'s [https://sintel.pythonanywhere.com Temperament Calculator], and [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] have implementations of wart notation that differ from each other slightly. For example, in the Temperament Finder, the wart letter "p" is used to make explicit that the number refers to the patent val (though the letter originally was intended to stand for "prime"), despite that "p" is logically the letter for prime 53, and the wart letter "q" and after refers to each non-prime basis element of composite/fractional subgroup, respectively and temporarily.
-* In Graham Breed's Temperament Finder, the wart letter "p" is used to make explicit that the number refers to the patent val (though the letter originally was intended to stand for "prime"). Note that "p" is logically the letter for prime 53.
-* In Graham Breed's Temperament Finder, the wart letter "q" and after refers to each non-prime basis element of composite/fractional subgroup, respectively and temporarily.
+For a full specification and a deeper dive into the nuances in each implementation, see Flora's [https://github.com/FloraCanou/temperament_evaluator/wiki/Commonwart Commonwart] document.
 === Sparse Offset Val notation ===