Equal-step tuning
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- This revision was by author hstraub and made on 2007-08-06 06:17:37 UTC.
- The original revision id was 6584503.
- The revision comment was: 24edo
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Original Wikitext content:
An Equal Temperament, in the most general sense, is a tuning in which every single step is the same interval; an equal-step scale. This single-step interval is often described as a fraction of another interval—the divisions paradigm, if you will—but it can also be explicitly given. There is a convention which takes "X tone equal temperament" to mean "X divisions of 2/1, the octave"; this is abbreviated tET or some variant. Because "equal //temperament//" literally refers to treating these scales as [[temperament|temperaments]] of JI, the less loaded term //EDO//, meaning "equal divisions of the octave", introduced by Dan Stearns and later popularized by Joe Monzo, is helpful especially for denoting scales that do not even //try// to resemble JI. There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]]. ---- == == =The Divisions Paradigm= From a [[JustIntonation|Just Intonation]] perspective, it is important to note that if the large interval being divided is just, none of its divisions will be just—you can only have one! and its multiples... ===Equal Divisions of the Octave (2/1)=== [[5edo|5]] [[7edo|7]] [[8edo|8]] [[9edo|9]] [[10edo|10]] [[11edo|11]] [[13edo|13]] [[14edo|14]] [[15edo|15]] [[16edo|16]] [[17edo|17]] [[19edo|19]] [[22edo|22]] [[24edo|24 (Skryabin, Ives, Ligeti)]] [[31edo|31]] ===Equal Divisions of the Tritave (3/1)=== 12 [[BohlenPierce|13 (Bohlen-Pierce)]] ===Equal Divisions of the Perfect Fifth (3/2)=== [[88cET|8 (88-cET)]] ===Equal Divisions of the Just Major 17th (5/1)=== 25 (Stockhausen, McLaren) =The explicit paradigm= 88-cET, Alpha, Beta, Gamma =The stretch paradigm= ...coming soon... ---- =Equal temperament surveys= A rather strange emerging genre. Some curious composers, wishing to test the Darregian notion that each equal temperament, to a certain extent, possesses a certain quality or mood to it, endeavor to compose entire series of pieces which sample the field, often sequentially. Easley Blackwood's rather neoclassical //Microtonal Etudes// (1980-1), in EDO's 13 through 24, was one of the first such surveys. [[McLaren|Brian McLaren]]'s idiosyncratic //240 Piano Pieces// from the 90's, with 5 pieces in each tuning from 5/oct to 53/oct (excepting 12!), might be the most extensive, so much that each set of 5 pieces might be thought of as a whole. [[Warren Burt]]'s //39 Dissonant Etudes// (1992-8) (5/oct to 43/oct) all use the same basic technique to generate "dissonance." Daniel Wolf has a series of etudes from ET's 8 through 23, excepting 10, 12, and 20, written between 1994 and 2004. Jacob Barton's //Moods// and //Xenharmonic Variations on a Theme by Mozart// from 2004 progress sequentially in sections (ET's 1-13 and 12-19). Igliashon Jones is currently at work on an album of electronic pop songs in 13-24 (right?) EDOs in which the time signature matches the tuning(!), an idea from Hans Straub, who has written such works in 5- and 17-EDO. In addition to the proper surveys, many individuals have pieces in a wide range of EDOs that don't necessarily constitute suites or "thorough" surveys. Ivor Darreg, Marc Jones, Dan Stearns, Gene Ward Smith, X. J. Scott, Andrew Heathwaite, and Aaron Hunt come to mind, as well as more music by Brian McLaren and Warren Burt. =[[Polymicrotonality]] with equal temperaments= You are invited to share your experiences with combining equal temperaments with each other and with unequal temperaments.
Original HTML content:
<html><head><title>Equal-step Tuning</title></head><body>An Equal Temperament, in the most general sense, is a tuning in which every single step is the same interval; an equal-step scale. This single-step interval is often described as a fraction of another interval—the divisions paradigm, if you will—but it can also be explicitly given.<br /> <br /> There is a convention which takes "X tone equal temperament" to mean "X divisions of 2/1, the octave"; this is abbreviated tET or some variant. Because "equal <em>temperament</em>" literally refers to treating these scales as <a class="wiki_link" href="/temperament">temperaments</a> of JI, the less loaded term <em>EDO</em>, meaning "equal divisions of the octave", introduced by Dan Stearns and later popularized by Joe Monzo, is helpful especially for denoting scales that do not even <em>try</em> to resemble JI.<br /> <br /> 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>.<br /> <br /> <hr /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h2> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="The Divisions Paradigm"></a><!-- ws:end:WikiTextHeadingRule:2 -->The Divisions Paradigm</h1> From a <a class="wiki_link" href="/JustIntonation">Just Intonation</a> perspective, it is important to note that if the large interval being divided is just, none of its divisions will be just—you can only have one! and its multiples...<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="The Divisions Paradigm--Equal Divisions of the Octave (2/1)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Equal Divisions of the Octave (2/1)</h3> <a class="wiki_link" href="/5edo">5</a> <a class="wiki_link" href="/7edo">7</a> <a class="wiki_link" href="/8edo">8</a> <a class="wiki_link" href="/9edo">9</a> <a class="wiki_link" href="/10edo">10</a> <a class="wiki_link" href="/11edo">11</a> <a class="wiki_link" href="/13edo">13</a> <a class="wiki_link" href="/14edo">14</a> <a class="wiki_link" href="/15edo">15</a> <a class="wiki_link" href="/16edo">16</a> <a class="wiki_link" href="/17edo">17</a><br /> <a class="wiki_link" href="/19edo">19</a> <a class="wiki_link" href="/22edo">22</a> <a class="wiki_link" href="/24edo">24 (Skryabin, Ives, Ligeti)</a> <a class="wiki_link" href="/31edo">31</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="The Divisions Paradigm--Equal Divisions of the Tritave (3/1)"></a><!-- ws:end:WikiTextHeadingRule:6 -->Equal Divisions of the Tritave (3/1)</h3> 12<br /> <a class="wiki_link" href="/BohlenPierce">13 (Bohlen-Pierce)</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="The Divisions Paradigm--Equal Divisions of the Perfect Fifth (3/2)"></a><!-- ws:end:WikiTextHeadingRule:8 -->Equal Divisions of the Perfect Fifth (3/2)</h3> <a class="wiki_link" href="/88cET">8 (88-cET)</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="The Divisions Paradigm--Equal Divisions of the Just Major 17th (5/1)"></a><!-- ws:end:WikiTextHeadingRule:10 -->Equal Divisions of the Just Major 17th (5/1)</h3> 25 (Stockhausen, McLaren)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="The explicit paradigm"></a><!-- ws:end:WikiTextHeadingRule:12 -->The explicit paradigm</h1> 88-cET, Alpha, Beta, Gamma<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="The stretch paradigm"></a><!-- ws:end:WikiTextHeadingRule:14 -->The stretch paradigm</h1> <br /> ...coming soon...<br /> <br /> <hr /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Equal temperament surveys"></a><!-- ws:end:WikiTextHeadingRule:16 -->Equal temperament surveys</h1> A rather strange emerging genre. Some curious composers, wishing to test the Darregian notion that each equal temperament, to a certain extent, possesses a certain quality or mood to it, endeavor to compose entire series of pieces which sample the field, often sequentially. Easley Blackwood's rather neoclassical <em>Microtonal Etudes</em> (1980-1), in EDO's 13 through 24, was one of the first such surveys. <a class="wiki_link" href="/McLaren">Brian McLaren</a>'s idiosyncratic <em>240 Piano Pieces</em> from the 90's, with 5 pieces in each tuning from 5/oct to 53/oct (excepting 12!), might be the most extensive, so much that each set of 5 pieces might be thought of as a whole. <a class="wiki_link" href="/Warren%20Burt">Warren Burt</a>'s <em>39 Dissonant Etudes</em> (1992-8) (5/oct to 43/oct) all use the same basic technique to generate "dissonance."<br /> <br /> Daniel Wolf has a series of etudes from ET's 8 through 23, excepting 10, 12, and 20, written between 1994 and 2004. Jacob Barton's <em>Moods</em> and <em>Xenharmonic Variations on a Theme by Mozart</em> from 2004 progress sequentially in sections (ET's 1-13 and 12-19). Igliashon Jones is currently at work on an album of electronic pop songs in 13-24 (right?) EDOs in which the time signature matches the tuning(!), an idea from Hans Straub, who has written such works in 5- and 17-EDO.<br /> <br /> In addition to the proper surveys, many individuals have pieces in a wide range of EDOs that don't necessarily constitute suites or "thorough" surveys. Ivor Darreg, Marc Jones, Dan Stearns, Gene Ward Smith, X. J. Scott, Andrew Heathwaite, and Aaron Hunt come to mind, as well as more music by Brian McLaren and Warren Burt.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Polymicrotonality with equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:18 --><a class="wiki_link" href="/Polymicrotonality">Polymicrotonality</a> with equal temperaments</h1> You are invited to share your experiences with combining equal temperaments with each other and with unequal temperaments.</body></html>