Val: Difference between revisions

Line 26:

==Shorthand Notation==

Given an explicit or assumed limit, any [[Patent_val|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 17-EDO, <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 <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.

(also known as '''“warts”''' or '''“wart” notation''')

~~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, ~~<~~17 27 ~~38]~~, ~~we'd write~~ "~~17cc~~".

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 17-EDO, {{val| 17 27 39 }}, can be called simply, "17".

The ~~general rule~~ is:

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".

~~<ul><li>For each wart~~, the ~~letter specifies which~~ prime ~~approximation~~ is ~~being altered~~, ~~so that the nth letter~~ of ~~the alphabet refers to the nth prime.~~</li><li>~~A letter which appears m times refers to the (m+1)th most accurate mapping for that prime.~~</li><li>~~If a number representing a val is wartless~~, ~~it is taken to mean the patent val.~~</li></ul>

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

See also: [[~~Monzos_and_Interval_Space|~~Monzos and Interval Space]], [[~~Patent_val|Patent val]], [[Vals_and_Tuning_Space|~~Vals and Tuning Space]], [[~~Optimal_patent_val|~~Optimal patent val]]

The general rules:

[[Category:~~definition~~]]

[[Category:~~intervals~~]]

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

[[Category:~~theory~~]]

* The nth letter of the alphabet refers to the nth prime: a=2, b=3, c=5, d=7, e=11 etc.

[[Category:~~tuning~~]]

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

[[Category:~~val~~]]

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

== See also ==

* [[Monzos and Interval Space]]

* [[Vals and Tuning Space]]

* [[Optimal patent val]]

[[Category:Definition]]

[[Category:Intervals]]

[[Category:Theory]]

[[Category:Tuning]]

[[Category:Val]]

[[Category:Notation]]

@@ Line 26: / Line 26: @@
 ==Shorthand Notation==
-Given an explicit or assumed limit, any [[Patent_val|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 17-EDO, &lt;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 &lt;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.
+(also known as '''“warts”''' or '''“wart” notation''')
-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, &lt;17 27 38], we'd write "17cc".
+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 17-EDO, {{val| 17 27 39 }}, can be called simply, "17".
-The general rule is:
+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".
-<ul><li>For each wart, the letter specifies which prime approximation is being altered, so that the nth letter of the alphabet refers to the nth prime.</li><li>A letter which appears m times refers to the (m+1)th most accurate mapping for that prime.</li><li>If a number representing a val is wartless, it is taken to mean the patent val.</li></ul>
+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
-See also: [[Monzos_and_Interval_Space|Monzos and Interval Space]], [[Patent_val|Patent val]], [[Vals_and_Tuning_Space|Vals and Tuning Space]], [[Optimal_patent_val|Optimal patent val]]
+The general rules:
-[[Category:definition]]
-[[Category:intervals]]
+* Wart letters specify prime approximations being altered from the patent val
-[[Category:theory]]
+* The nth letter of the alphabet refers to the nth prime: a=2, b=3, c=5, d=7, e=11 etc.
-[[Category:tuning]]
+* A letter which appears m times refers to the (m+1)th most accurate mapping for that prime
-[[Category:val]]
+* ''So, if a number representing a val is wartless, it is taken to mean the patent val''
+== See also ==
+* [[Monzos and Interval Space]]
+* [[Vals and Tuning Space]]
+* [[Optimal patent val]]
+[[Category:Definition]]
+[[Category:Intervals]]
+[[Category:Theory]]
+[[Category:Tuning]]
+[[Category:Val]]
+[[Category:Notation]]