Val: Difference between revisions
→Generalized patent vals: rework |
→Shorthand notations: note some of the implementations |
||
| Line 114: | Line 114: | ||
* 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. | ||
* 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. | * 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. | ||
* In Graham Breed's | |||
* In Graham Breed's | [[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 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. | |||
=== Sparse Offset Val notation === | === Sparse Offset Val notation === | ||
In 2022 [[User:Mike Battaglia|Mike Battaglia]] proposed '''SOV notation''' as a way to be explicit about which primes are being affected and in which direction. In 2024 it was further refined by him and [[ | In 2022 [[User:Mike Battaglia|Mike Battaglia]] proposed '''SOV notation''' as a way to be explicit about which primes are being affected and in which direction. In 2024 it was further refined by him and [[Lumi Pakkanen]] to be more analogous to [[Ups and downs notation]]. | ||
In this notation, patent vals are notated using the number of divisions followed by square brackets e.g. 17[] for {{val| 17 27 39 }}. To indicate a wider mapping for a prime, it is prefixed with a carret (^) e.g. 17[^5] for {{val| 17 27 40 }}. To indicate a narrower mapping for a prime it is prefixed with a vee (v) e.g. 17[v5] for {{val| 17 27 38 }}. The prefixes stack e.g. 17[^^5] corresponds to {{val| 17 27 41 }}. Multiple modifications are separated by commas (and optionally spaces) e.g. 17[v3, ^5] for {{val| 17 26 40 }}. | In this notation, patent vals are notated using the number of divisions followed by square brackets e.g. 17[] for {{val| 17 27 39 }}. To indicate a wider mapping for a prime, it is prefixed with a carret (^) e.g. 17[^5] for {{val| 17 27 40 }}. To indicate a narrower mapping for a prime it is prefixed with a vee (v) e.g. 17[v5] for {{val| 17 27 38 }}. The prefixes stack e.g. 17[^^5] corresponds to {{val| 17 27 41 }}. Multiple modifications are separated by commas (and optionally spaces) e.g. 17[v3, ^5] for {{val| 17 26 40 }}. | ||
| Line 129: | Line 131: | ||
For patent vals the empty square brackets are optional when using an "at" sign. The subgroup itself is optional if its obvious from context e.g. 12@ for {{val| 12 19 28 }} (subgroup 2.3.5). | For patent vals the empty square brackets are optional when using an "at" sign. The subgroup itself is optional if its obvious from context e.g. 12@ for {{val| 12 19 28 }} (subgroup 2.3.5). | ||
The 2022 version used a plus sign (+) in place of the caret and a minus sign (-) in place of the vee. | The 2022 version used a plus sign (+) in place of the caret and a minus sign (-) in place of the vee. Sintel's Temperament Calculator is a notable implementation of this version of the notation. | ||
== Vals vs. mappings == | == Vals vs. mappings == | ||