Just intonation: Difference between revisions
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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(In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, "Differential Coherence", //1/1// vol. 11, no. 2: p.1): | (In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, "Differential Coherence", //1/1// vol. 11, no. 2: p.1): | ||
//1. The principle of "[[harmonic limits]]," which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's "psycharithmes" and his ordering by complexity; Gioseffe Zarlino's five-limit "senario," and the like; Helmholtz's theory of consonance with its "blending of partials," which, like the others, results in giving priority to the lowest prime numbers). | //1. The principle of "[[Harmonic Limit|harmonic limits]]," which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's "psycharithmes" and his ordering by complexity; Gioseffe Zarlino's five-limit "senario," and the like; Helmholtz's theory of consonance with its "blending of partials," which, like the others, results in giving priority to the lowest prime numbers). | ||
2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the "monophonic" system of Harry Partch's [[tonality diamond]]. This, incidentially, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1,3 5 7 9, 11, or their octaves. | 2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the "monophonic" system of Harry Partch's [[tonality diamond]]. This, incidentially, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1,3 5 7 9, 11, or their octaves. | ||
3. Other theorists who, in contrast to the above, advocate the use of the [[ | 3. Other theorists who, in contrast to the above, advocate the use of the [[http://en.wikipedia.org/wiki/Hexany|products]] of a given set of prime numbers, such as Robert Dussaut, Ervin Wilson, and others. | ||
4. Restrictions on the variety of prime numbers used within a system, for example, 3 used with only one other prime ([[3and7JI|7]], 11, or 13...). This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation. | 4. Restrictions on the variety of prime numbers used within a system, for example, 3 used with only one other prime ([[3and7JI|7]], 11, or 13...). This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation. | ||
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(In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, &quot;Differential Coherence&quot;, <em>1/1</em> vol. 11, no. 2: p.1):<br /> | (In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, &quot;Differential Coherence&quot;, <em>1/1</em> vol. 11, no. 2: p.1):<br /> | ||
<br /> | <br /> | ||
<em>1. The principle of &quot;<a class="wiki_link" href="/ | <em>1. The principle of &quot;<a class="wiki_link" href="/Harmonic%20Limit">harmonic limits</a>,&quot; which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's &quot;psycharithmes&quot; and his ordering by complexity; Gioseffe Zarlino's five-limit &quot;senario,&quot; and the like; Helmholtz's theory of consonance with its &quot;blending of partials,&quot; which, like the others, results in giving priority to the lowest prime numbers).<br /> | ||
<br /> | <br /> | ||
2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the &quot;monophonic&quot; system of Harry Partch's <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a>. This, incidentially, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1,3 5 7 9, 11, or their octaves.<br /> | 2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the &quot;monophonic&quot; system of Harry Partch's <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a>. This, incidentially, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1,3 5 7 9, 11, or their octaves.<br /> | ||
<br /> | <br /> | ||
3. Other theorists who, in contrast to the above, advocate the use of the <a class=" | 3. Other theorists who, in contrast to the above, advocate the use of the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexany" rel="nofollow">products</a> of a given set of prime numbers, such as Robert Dussaut, Ervin Wilson, and others.<br /> | ||
<br /> | <br /> | ||
4. Restrictions on the variety of prime numbers used within a system, for example, 3 used with only one other prime (<a class="wiki_link" href="/3and7JI">7</a>, 11, or 13...). This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation.<br /> | 4. Restrictions on the variety of prime numbers used within a system, for example, 3 used with only one other prime (<a class="wiki_link" href="/3and7JI">7</a>, 11, or 13...). This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation.<br /> | ||