Val: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-~~19 05~~:17:45 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-28 10:47:31 UTC</tt>.

: The original revision id was <tt>~~255538752~~</tt>.

: The original revision id was <tt>259040340</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 11:

A val is a map representing how to view the intervals in a single [[periods and generators|chain of generators]] as the tempered versions of intervals in just intonation. They form the link between things like EDOs and JI, and by doing so form the basis for all of regular temperament theory. It's very common for vals to refer to EDOs specifically, although they also show us how to relate larger chains of generators to JI as well (such as a stack of meantone fifths).

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 limit~~'s primes~~. 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.

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]].

Line 33:

A val is a map representing how to view the intervals in a single <a class="wiki_link" href="/periods%20and%20generators">chain of generators</a> as the tempered versions of intervals in just intonation. They form the link between things like EDOs and JI, and by doing so form the basis for all of regular temperament theory. It's very common for vals to refer to EDOs specifically, although they also show us how to relate larger chains of generators to JI as well (such as a stack of meantone fifths).

A val accomplishes the goal of mapping all intervals in some <a class="wiki_link" href="/harmonic%20limit">harmonic limit </a>by simply notating how many steps in the chain it takes to get to each of the limit~~'s primes~~. 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.

A val accomplishes the goal of mapping all intervals in some <a class="wiki_link" href="/harmonic%20limit">harmonic limit </a>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 <a class="wiki_link" href="/harmonic%20limit">prime limit p</a>.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-19 05:17:45 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-28 10:47:31 UTC</tt>.<br>
-: The original revision id was <tt>255538752</tt>.<br>
+: The original revision id was <tt>259040340</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 11: / Line 11: @@
 A val is a map representing how to view the intervals in a single [[periods and generators|chain of generators]] as the tempered versions of intervals in just intonation. They form the link between things like EDOs and JI, and by doing so form the basis for all of regular temperament theory. It's very common for vals to refer to EDOs specifically, although they also show us how to relate larger chains of generators to JI as well (such as a stack of meantone fifths).
-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 limit's primes. 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.
+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]].
@@ Line 33: / Line 33: @@
   A val is a map representing how to view the intervals in a single &lt;a class="wiki_link" href="/periods%20and%20generators"&gt;chain of generators&lt;/a&gt; as the tempered versions of intervals in just intonation. They form the link between things like EDOs and JI, and by doing so form the basis for all of regular temperament theory. It's very common for vals to refer to EDOs specifically, although they also show us how to relate larger chains of generators to JI as well (such as a stack of meantone fifths).&lt;br /&gt;
 &lt;br /&gt;
-A val accomplishes the goal of mapping all intervals in some &lt;a class="wiki_link" href="/harmonic%20limit"&gt;harmonic limit &lt;/a&gt;by simply notating how many steps in the chain it takes to get to each of the limit's primes. 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.&lt;br /&gt;
+A val accomplishes the goal of mapping all intervals in some &lt;a class="wiki_link" href="/harmonic%20limit"&gt;harmonic limit &lt;/a&gt;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.&lt;br /&gt;
 &lt;br /&gt;
 Vals are usually written in the notation &amp;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 &lt;a class="wiki_link" href="/harmonic%20limit"&gt;prime limit p&lt;/a&gt;.&lt;br /&gt;