EDT
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Kosmorsky and made on 2011-08-17 22:32:46 UTC.
- The original revision id was 246623789.
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Original Wikitext content:
=Division of the tritave (3/1) into n equal parts= After the octave (roughly 2:1 but it has been tuned sharp and flat for various reasons), the next simple "frame interval" available is the ratio 3:1. Among other names, the third harmonic has been called the "perfect twelfth" "triple" or "tritave". There has been argument whether pitches a tritave removed can be heard as equivalent, but with proper context and/or experience, at least some people find that they can. Arguably that is the single criterion for calling the tritave a true frame interval. But it is certain that musically valuable organizations of pitch can arise through the equal division of non-octave intervals regardless of equivalence, and either way, the multitude of equal divisions of the tritave are rich and ripe for exploration. The Bohlen-Pierce (BP) scale seems to have been the first such arrangement to be seriously studied and made into music. As the equivalent harmonics are 1:3:9:27 etc., filling in 3-9 isoharmonically, one arrives at the fundamental consonant triad of BP music - 3:5:7:(9). The MOS that are most naturally formed from these harmonics are of the forms 4L+1s (pentatonic) and 4L+5s (nonatonic). Which brings forward one analogy with diatonic music (3rd and 5th harmonics under octaves) or diatonic function in general: that 4edt and 9edt can be directly compared to 5edo and 7edo (and indeed they sound like they can). In contrast to the state of meantone temperaments, the simplest L=2 s=1 (13edt, the traditional tempered BP scale) is the most accurate and evenly-tempered for a long way. But the formations with Large and small steps of different relative sizes are no less important, for example by being capable of representing other intervals and harmonics. [[5edt]] (Tritave counterpart of Magic) [[6edt]] (Tritave counterpart of Hanson) [[7edt]] (Tritave counterpart of Orwell) [[8edt]] (Tritave counterpart of Blacksmith) [[9edt]] [[10edt]] [[11edt]] (Euler Temperament) [[12edt]] [[BP|13 (Bohlen-Pierce)]] [[14edt]] (Contains the Anti-Lambda MOS) [[15edt]] [[16edt]] [[17edt]] [[18edt]] [[19ED3|19 (Bernhard Stopper)]] [[20edt]] [[21edt]] [[22edt]] [[23edt]] [[24edt]] [[25edt]] [[26edt]] [[27edt]] [[28edt]] ... [[39edt]] Triple Bohlen-Pierce (Erlich)
Original HTML content:
<html><head><title>edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Division of the tritave (3/1) into n equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the tritave (3/1) into n equal parts</h1> <br /> <br /> After the octave (roughly 2:1 but it has been tuned sharp and flat for various reasons), the next simple "frame interval" available is the ratio 3:1. Among other names, the third harmonic has been called the "perfect twelfth" "triple" or "tritave". There has been argument whether pitches a tritave removed can be heard as equivalent, but with proper context and/or experience, at least some people find that they can. Arguably that is the single criterion for calling the tritave a true frame interval. But it is certain that musically valuable organizations of pitch can arise through the equal division of non-octave intervals regardless of equivalence, and either way, the multitude of equal divisions of the tritave are rich and ripe for exploration.<br /> <br /> The Bohlen-Pierce (BP) scale seems to have been the first such arrangement to be seriously studied and made into music. As the equivalent harmonics are 1:3:9:27 etc., filling in 3-9 isoharmonically, one arrives at the fundamental consonant triad of BP music - 3:5:7:(9). The MOS that are most naturally formed from these harmonics are of the forms 4L+1s (pentatonic) and 4L+5s (nonatonic). Which brings forward one analogy with diatonic music (3rd and 5th harmonics under octaves) or diatonic function in general: that 4edt and 9edt can be directly compared to 5edo and 7edo (and indeed they sound like they can). In contrast to the state of meantone temperaments, the simplest L=2 s=1 (13edt, the traditional tempered BP scale) is the most accurate and evenly-tempered for a long way. But the formations with Large and small steps of different relative sizes are no less important, for example by being capable of representing other intervals and harmonics.<br /> <br /> <a class="wiki_link" href="/5edt">5edt</a> (Tritave counterpart of Magic)<br /> <a class="wiki_link" href="/6edt">6edt</a> (Tritave counterpart of Hanson)<br /> <a class="wiki_link" href="/7edt">7edt</a> (Tritave counterpart of Orwell)<br /> <a class="wiki_link" href="/8edt">8edt</a> (Tritave counterpart of Blacksmith)<br /> <a class="wiki_link" href="/9edt">9edt</a><br /> <a class="wiki_link" href="/10edt">10edt</a><br /> <a class="wiki_link" href="/11edt">11edt</a> (Euler Temperament)<br /> <a class="wiki_link" href="/12edt">12edt</a><br /> <a class="wiki_link" href="/BP">13 (Bohlen-Pierce)</a><br /> <a class="wiki_link" href="/14edt">14edt</a> (Contains the Anti-Lambda MOS)<br /> <a class="wiki_link" href="/15edt">15edt</a><br /> <a class="wiki_link" href="/16edt">16edt</a><br /> <a class="wiki_link" href="/17edt">17edt</a><br /> <a class="wiki_link" href="/18edt">18edt</a><br /> <a class="wiki_link" href="/19ED3">19 (Bernhard Stopper)</a><br /> <a class="wiki_link" href="/20edt">20edt</a><br /> <a class="wiki_link" href="/21edt">21edt</a><br /> <a class="wiki_link" href="/22edt">22edt</a><br /> <a class="wiki_link" href="/23edt">23edt</a><br /> <a class="wiki_link" href="/24edt">24edt</a><br /> <a class="wiki_link" href="/25edt">25edt</a><br /> <a class="wiki_link" href="/26edt">26edt</a><br /> <a class="wiki_link" href="/27edt">27edt</a><br /> <a class="wiki_link" href="/28edt">28edt</a><br /> ...<br /> <a class="wiki_link" href="/39edt">39edt</a> Triple Bohlen-Pierce (Erlich)</body></html>