Val: Difference between revisions

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== Definition ==

A [[val]] is a list of numbers telling you the approximation of each [[prime harmonic]] used in an edo in terms of steps, where by ''prime harmonic'' we mean each frequency ratio ''p''/1 (where ''p'' is a {{w|prime number}}. This list of integers by convention corresponds to all primes up to some largest prime (the [[limit]]) so that we can tell what number represents the ''mapping'' of what prime by its place in the list (1st place is prime 2's mapping (a.k.a. the edo), 2nd place is prime 3's mapping, 3rd place is prime 5's mapping, 4th is prime 7's, etc.). The val is used to understand the edo's approximations to ratios involving those primes, like 2 × 5 / 3 / 3 = [[10/9]] for primes {2, 3, 5}. This list [[#Warts|does not have to be the closest approximation]] for each prime, but it usually is. Thus a val is essentially just a list of numbers that we are interpreting as having a certain meaning.

A [[val]] is a list of numbers telling you the approximation of each [[prime harmonic]] used in an edo in terms of steps, where by ''prime harmonic'' we mean each frequency ratio ''p''/1 (where ''p'' is a {{w|prime number}}. This list of integers by convention corresponds to all primes up to some largest prime (the [[limit]]) so that we can tell what number represents the ''mapping'' of what prime by its place in the list (1st place is prime 2's mapping (a.k.a. the edo), 2nd place is prime 3's mapping, 3rd place is prime 5's mapping, 4th is prime 7's, etc.). The val is used to understand the edo's approximations to ratios involving those primes, like 2 × 5 / 3 / 3 = [[10/9]] for primes {2, 3, 5}. This list [[#Warts and generalized patent vals|does not have to be the closest approximation]] for each prime, but it usually is. Thus a val is essentially just a list of numbers that we are interpreting as having a certain meaning.

=== Example ===

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Note that when we take the closest approximation of each prime (corresponding to rounding rather than e.g. using the second-best approximation possible) we call it a ''[[patent val]]'', therefore, the "5-limit patent val" of 26edo is {{val| 26 41 60 }}, where the limit is 5 because that is the highest prime we are considering.

, not sure if i broke it or someone else

== Using a val ==

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 == Definition ==
-A [[val]] is a list of numbers telling you the approximation of each [[prime harmonic]] used in an edo in terms of steps, where by ''prime harmonic'' we mean each frequency ratio ''p''/1 (where ''p'' is a {{w|prime number}}. This list of integers by convention corresponds to all primes up to some largest prime (the [[limit]]) so that we can tell what number represents the ''mapping'' of what prime by its place in the list (1st place is prime 2's mapping (a.k.a. the edo), 2nd place is prime 3's mapping, 3rd place is prime 5's mapping, 4th is prime 7's, etc.). The val is used to understand the edo's approximations to ratios involving those primes, like 2 × 5 / 3 / 3 = [[10/9]] for primes {2, 3, 5}. This list [[#Warts|does not have to be the closest approximation]] for each prime, but it usually is. Thus a val is essentially just a list of numbers that we are interpreting as having a certain meaning.
+A [[val]] is a list of numbers telling you the approximation of each [[prime harmonic]] used in an edo in terms of steps, where by ''prime harmonic'' we mean each frequency ratio ''p''/1 (where ''p'' is a {{w|prime number}}. This list of integers by convention corresponds to all primes up to some largest prime (the [[limit]]) so that we can tell what number represents the ''mapping'' of what prime by its place in the list (1st place is prime 2's mapping (a.k.a. the edo), 2nd place is prime 3's mapping, 3rd place is prime 5's mapping, 4th is prime 7's, etc.). The val is used to understand the edo's approximations to ratios involving those primes, like 2 × 5 / 3 / 3 = [[10/9]] for primes {2, 3, 5}. This list [[#Warts and generalized patent vals|does not have to be the closest approximation]] for each prime, but it usually is. Thus a val is essentially just a list of numbers that we are interpreting as having a certain meaning.
 === Example ===
@@ Line 25: / Line 25: @@
 Note that when we take the closest approximation of each prime (corresponding to rounding rather than e.g. using the second-best approximation possible) we call it a ''[[patent val]]'', therefore, the "5-limit patent val" of 26edo is {{val| 26 41 60 }}, where the limit is 5 because that is the highest prime we are considering.
+, not sure if i broke it or someone else
 == Using a val ==