Ed7/3: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 602114698 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 602115010 - Original comment: ** |
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<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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-13 18: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-13 18:25:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602115010</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> | ||
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Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally [[Pseudo-traditional harmonic functions of enneatonic scale degrees|enneatonic scales]], especially those equivalent at e. g. 7:3, can take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. | Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally [[Pseudo-traditional harmonic functions of enneatonic scale degrees|enneatonic scales]], especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. | ||
Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet. | Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet. | ||
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Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of <a class="wiki_link" href="/equivalence">equivalence</a> has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the &quot;Middletown valley&quot;, the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally <a class="wiki_link" href="/Pseudo-traditional%20harmonic%20functions%20of%20enneatonic%20scale%20degrees">enneatonic scales</a>, especially those equivalent at e. g. 7:3, can take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.<br /> | Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of <a class="wiki_link" href="/equivalence">equivalence</a> has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the &quot;Middletown valley&quot;, the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally <a class="wiki_link" href="/Pseudo-traditional%20harmonic%20functions%20of%20enneatonic%20scale%20degrees">enneatonic scales</a>, especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.<br /> | ||
<br /> | <br /> | ||
Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. &quot;Macrobichromatic&quot; might be a practically perfect term for it if it hasn't been named yet.<br /> | Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. &quot;Macrobichromatic&quot; might be a practically perfect term for it if it hasn't been named yet.<br /> | ||
Revision as of 18:25, 13 December 2016
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2016-12-13 18:25:13 UTC.
- The original revision id was 602115010.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
<span style="font-size: 19.5px;">Division of a tenth (e. g. 7/3) into n equal parts</span> Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally [[Pseudo-traditional harmonic functions of enneatonic scale degrees|enneatonic scales]], especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet. The branches of the Middletown family are named thus: 3&6: Tritetrachordal 4&5: Montrose 2&7: Terra Rubra The family of interlaced octatonic scale based temperaments in the "Middletown valley" is called Vesuvius (i. e. the volcano east of Naples). [[8edX]] [[9edX]] [[15edX]] [[16edX]]
Original HTML content:
<html><head><title>edX</title></head><body><span style="font-size: 19.5px;">Division of a tenth (e. g. 7/3) into n equal parts</span><br /> <br /> <br /> Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of <a class="wiki_link" href="/equivalence">equivalence</a> has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally <a class="wiki_link" href="/Pseudo-traditional%20harmonic%20functions%20of%20enneatonic%20scale%20degrees">enneatonic scales</a>, especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.<br /> <br /> Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet.<br /> <br /> The branches of the Middletown family are named thus:<br /> <br /> 3&6: Tritetrachordal<br /> 4&5: Montrose<br /> 2&7: Terra Rubra<br /> <br /> The family of interlaced octatonic scale based temperaments in the "Middletown valley" is called Vesuvius (i. e. the volcano east of Naples).<br /> <br /> <a class="wiki_link" href="/8edX">8edX</a><br /> <a class="wiki_link" href="/9edX">9edX</a><br /> <a class="wiki_link" href="/15edX">15edX</a><br /> <a class="wiki_link" href="/16edX">16edX</a></body></html>