Val: Difference between revisions
Wikispaces>genewardsmith **Imported revision 288625236 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 294107600 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-21 12:43:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>294107600</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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 ... 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 are important because they provide a way to mathematically formalize how, specifically, the intervals in a random chain of generators are viewed as the tempered versions of more fundamental just intonation intervals. They can also be viewed as a way to map JI "onto" the chain, imbuing it with a harmonic context. Vals will enable you to figure out what commas your temperament eliminates, what [[comma pump|comma pumps]] are available in the temperament, what the most consonant chords in the temperament are, how to optimize the octave stretch of the temperament to minimize tuning error, what EDOs support your temperament, and other operations as of yet undiscovered. | Vals are important because they provide a way to mathematically formalize how, specifically, the intervals in a random chain of generators are viewed as the tempered versions of more fundamental just intonation intervals. They can also be viewed as a way to map JI "onto" the chain, imbuing it with a harmonic context. Vals will enable you to figure out what commas your temperament eliminates, what [[comma pump|comma pumps]] are available in the temperament, what the most consonant chords in the temperament are, how to optimize the octave stretch of the temperament to minimize tuning error, what EDOs support your temperament, and other operations as of yet undiscovered. | ||
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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>.<br /> | 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>.<br /> | ||
<br /> | |||
For a more mathematically intensive introduction to vals, see <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">Vals and Tuning Space</a>.<br /> | |||
<br /> | <br /> | ||
Vals are important because they provide a way to mathematically formalize how, specifically, the intervals in a random chain of generators are viewed as the tempered versions of more fundamental just intonation intervals. They can also be viewed as a way to map JI &quot;onto&quot; the chain, imbuing it with a harmonic context. Vals will enable you to figure out what commas your temperament eliminates, what <a class="wiki_link" href="/comma%20pump">comma pumps</a> are available in the temperament, what the most consonant chords in the temperament are, how to optimize the octave stretch of the temperament to minimize tuning error, what EDOs support your temperament, and other operations as of yet undiscovered.<br /> | Vals are important because they provide a way to mathematically formalize how, specifically, the intervals in a random chain of generators are viewed as the tempered versions of more fundamental just intonation intervals. They can also be viewed as a way to map JI &quot;onto&quot; the chain, imbuing it with a harmonic context. Vals will enable you to figure out what commas your temperament eliminates, what <a class="wiki_link" href="/comma%20pump">comma pumps</a> are available in the temperament, what the most consonant chords in the temperament are, how to optimize the octave stretch of the temperament to minimize tuning error, what EDOs support your temperament, and other operations as of yet undiscovered.<br /> | ||