EDO vs ET: Difference between revisions
Wikispaces>igliashon **Imported revision 241616237 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 241855209 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-18 19:58:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>241855209</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> | ||
| Line 12: | Line 12: | ||
==Why bother making this distinction?== | ==Why bother making this distinction?== | ||
There are many EDOs which, by virtue of some freak miracle of mathematics, happen to sound a lot like Just Intonation. Some say this is the case with 12-EDO, and that one of the reasons for its popularity is because it sounds enough like 5-limit (or perhaps even 7-limit) JI to please the masses, while being incredibly practical and convenient. Some also say that EDOs like 19, 22, 31, 34, | There are many EDOs which, by virtue of some freak miracle of mathematics, happen to sound a lot like Just Intonation. Some say this is the case with 12-EDO, and that one of the reasons for its popularity is because it sounds enough like 5-limit (or perhaps even 7-limit) JI to please the masses, while being incredibly practical and convenient. Some also say that EDOs like 19, 22, 31, 34, 41, 46 or 53 sound even more like JI than 12-EDO, and this indeed seems to be the case. Because of this acoustic similarity between equal tunings and Just tunings, lots of people like to treat equal tunings as //approximations// to JI--in other words, temperaments. With EDOs such as these, it is possible to gain some level of insight into their harmonic structures by thinking in terms of approximate JI, and thus this approach has been very useful to many people. | ||
However, it is not always true that those using EDOs are interested in approximating JI, nor is it true that describing all EDOs in terms of approximate JI is universally helpful or illuminating. As an example of the former, consider the atonalists, a loose school of 20th-century composers who sought to embrace the "equality" of equal temperament by treating every note as having equal musical importance, and thereby escape connotations of tonality that had previously defined Western classical music. As an example of the latter, consider 7-EDO: there is not a single triadic sonority within the EDO that is concordant enough to plausibly be conflated with Just Intonation, and attempts to describe its harmonic structures in terms of Just ratios is often more confusing than it is illuminating. It is not impossible to treat 7-EDO as an equal temperament, but doing so begs the question of what is being gained in the process, which cannot be had by ignoring JI all together. | However, it is not always true that those using EDOs are interested in approximating JI, nor is it true that describing all EDOs in terms of approximate JI is universally helpful or illuminating. As an example of the former, consider the atonalists, a loose school of 20th-century composers who sought to embrace the "equality" of equal temperament by treating every note as having equal musical importance, and thereby escape connotations of tonality that had previously defined Western classical music. As an example of the latter, consider 7-EDO: there is not a single triadic sonority within the EDO that is concordant enough to plausibly be conflated with Just Intonation, and attempts to describe its harmonic structures in terms of Just ratios is often more confusing than it is illuminating. It is not impossible to treat 7-EDO as an equal temperament, but doing so begs the question of what is being gained in the process, which cannot be had by ignoring JI all together. | ||
| Line 30: | Line 30: | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="EDOs vs. Equal Temperaments-Why bother making this distinction?"></a><!-- ws:end:WikiTextHeadingRule:2 -->Why bother making this distinction?</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="EDOs vs. Equal Temperaments-Why bother making this distinction?"></a><!-- ws:end:WikiTextHeadingRule:2 -->Why bother making this distinction?</h2> | ||
<br /> | <br /> | ||
There are many EDOs which, by virtue of some freak miracle of mathematics, happen to sound a lot like Just Intonation. Some say this is the case with 12-EDO, and that one of the reasons for its popularity is because it sounds enough like 5-limit (or perhaps even 7-limit) JI to please the masses, while being incredibly practical and convenient. Some also say that EDOs like 19, 22, 31, 34, | There are many EDOs which, by virtue of some freak miracle of mathematics, happen to sound a lot like Just Intonation. Some say this is the case with 12-EDO, and that one of the reasons for its popularity is because it sounds enough like 5-limit (or perhaps even 7-limit) JI to please the masses, while being incredibly practical and convenient. Some also say that EDOs like 19, 22, 31, 34, 41, 46 or 53 sound even more like JI than 12-EDO, and this indeed seems to be the case. Because of this acoustic similarity between equal tunings and Just tunings, lots of people like to treat equal tunings as <em>approximations</em> to JI--in other words, temperaments. With EDOs such as these, it is possible to gain some level of insight into their harmonic structures by thinking in terms of approximate JI, and thus this approach has been very useful to many people.<br /> | ||
<br /> | <br /> | ||
However, it is not always true that those using EDOs are interested in approximating JI, nor is it true that describing all EDOs in terms of approximate JI is universally helpful or illuminating. As an example of the former, consider the atonalists, a loose school of 20th-century composers who sought to embrace the &quot;equality&quot; of equal temperament by treating every note as having equal musical importance, and thereby escape connotations of tonality that had previously defined Western classical music. As an example of the latter, consider 7-EDO: there is not a single triadic sonority within the EDO that is concordant enough to plausibly be conflated with Just Intonation, and attempts to describe its harmonic structures in terms of Just ratios is often more confusing than it is illuminating. It is not impossible to treat 7-EDO as an equal temperament, but doing so begs the question of what is being gained in the process, which cannot be had by ignoring JI all together.<br /> | However, it is not always true that those using EDOs are interested in approximating JI, nor is it true that describing all EDOs in terms of approximate JI is universally helpful or illuminating. As an example of the former, consider the atonalists, a loose school of 20th-century composers who sought to embrace the &quot;equality&quot; of equal temperament by treating every note as having equal musical importance, and thereby escape connotations of tonality that had previously defined Western classical music. As an example of the latter, consider 7-EDO: there is not a single triadic sonority within the EDO that is concordant enough to plausibly be conflated with Just Intonation, and attempts to describe its harmonic structures in terms of Just ratios is often more confusing than it is illuminating. It is not impossible to treat 7-EDO as an equal temperament, but doing so begs the question of what is being gained in the process, which cannot be had by ignoring JI all together.<br /> | ||