Equal-step tuning: Difference between revisions
Wikispaces>keenanpepper **Imported revision 284376784 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 340234432 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term //EDO//(occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]]. More generally, the term //EDn// can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic). | There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term //EDO//(occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]]. More generally, the term //EDn// can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic). | ||
**As there are infinite intervals, there are infinite equal scales.** Barring technicalities there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET surveys|sequentially]] or [[Polymicrotonality|simultaneously]]. | **As the steps are tuned to be equal, equal scales may be taken to close anywhere composers wish them to.** Barring the convention of closing equal divisions of particular just intervals at those stated just intervals, there are infinite synonymous names for each equal scale. Barring further the large number of names which would be avoided in discourses on comparative modality and tonality, there is still a a great width to the universe of modes and keys which modal and tonal compositional art can access. | ||
**As there are infinite intervals, there are infinite equal scales.** Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET surveys|sequentially]] or [[Polymicrotonality|simultaneously]]. | |||
==Simultaneous equal divisions== | ==Simultaneous equal divisions== | ||
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There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term <em>EDO</em>(occasionally written ED2), meaning &quot;equal divisions of the octave&quot; (or &quot;equal divisions of 2/1&quot;), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Tonalsoft Encyclopedia</a>. More generally, the term <em>EDn</em> can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).<br /> | There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term <em>EDO</em>(occasionally written ED2), meaning &quot;equal divisions of the octave&quot; (or &quot;equal divisions of 2/1&quot;), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Tonalsoft Encyclopedia</a>. More generally, the term <em>EDn</em> can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).<br /> | ||
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<strong>As there are infinite intervals, there are infinite equal scales.</strong> Barring technicalities there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings <a class="wiki_link" href="/ET%20surveys">sequentially</a> or <a class="wiki_link" href="/Polymicrotonality">simultaneously</a>.<br /> | <strong>As the steps are tuned to be equal, equal scales may be taken to close anywhere composers wish them to.</strong> Barring the convention of closing equal divisions of particular just intervals at those stated just intervals, there are infinite synonymous names for each equal scale. Barring further the large number of names which would be avoided in discourses on comparative modality and tonality, there is still a a great width to the universe of modes and keys which modal and tonal compositional art can access.<br /> | ||
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<strong>As there are infinite intervals, there are infinite equal scales.</strong> Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings <a class="wiki_link" href="/ET%20surveys">sequentially</a> or <a class="wiki_link" href="/Polymicrotonality">simultaneously</a>.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Equal-Simultaneous equal divisions"></a><!-- ws:end:WikiTextHeadingRule:2 -->Simultaneous equal divisions</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Equal-Simultaneous equal divisions"></a><!-- ws:end:WikiTextHeadingRule:2 -->Simultaneous equal divisions</h2> | ||