Val: Difference between revisions

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A val accomplishes the goal of mapping all intervals in some [[Harmonic_Limit|harmonic limit ]]by simply notating how many steps in the chain it takes to get to each of the primes within the limit. Since every positive rational number can be described as a product of primes, any mapping for the primes hence implies a mapping for all of the positive rational numbers within the prime limit. By mapping the primes and letting the composite rationals fall where they may, a val tells us which interval in the chain represents the tempered 3/2, which interval represents the tempered 5/4, and so forth.

Vals are usually written in the notation <a b c d e f ~~...~~ p], where each successive column represents a successive prime, such as 2, 3, 5, 7, 11, 13... etc, in that order, up to some [[Harmonic_Limit|prime limit p]].

Vals are usually written in the notation <a b c d e f g h i j k l m n o p], where each successive column represents a successive prime, such as 2, 3, 5, 7, 11, 13... etc, in that order, up to some [[Harmonic_Limit|prime limit p]].

For a more mathematically intensive introduction to vals, see [[Vals_and_Tuning_Space|Vals and Tuning Space]].

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 A val accomplishes the goal of mapping all intervals in some [[Harmonic_Limit|harmonic limit ]]by simply notating how many steps in the chain it takes to get to each of the primes within the limit. Since every positive rational number can be described as a product of primes, any mapping for the primes hence implies a mapping for all of the positive rational numbers within the prime limit. By mapping the primes and letting the composite rationals fall where they may, a val tells us which interval in the chain represents the tempered 3/2, which interval represents the tempered 5/4, and so forth.
-Vals are usually written in the notation &lt;a b c d e f ... p], where each successive column represents a successive prime, such as 2, 3, 5, 7, 11, 13... etc, in that order, up to some [[Harmonic_Limit|prime limit p]].
+Vals are usually written in the notation &lt;a b c d e f g h i j k l m n o p], where each successive column represents a successive prime, such as 2, 3, 5, 7, 11, 13... etc, in that order, up to some [[Harmonic_Limit|prime limit p]].
 For a more mathematically intensive introduction to vals, see [[Vals_and_Tuning_Space|Vals and Tuning Space]].