Devadoot: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 585002961 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 585770747 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-06- | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 21:51:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>585770747</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 14: | Line 14: | ||
There are 13 steps in a period (i. e., a major third), and the generator is 2 steps. This generates a large number of different MOSes, most of which are improper. The smallest proper MOSes are those with 1, 2, 6, and 7 notes per period. The last two are by far the most interesting, and they are closely related to magic[19] and magic[22] respectively. While they are not octave-repeating, they do have relatively long chains of octaves (five or six of them, respectively) which makes the non-octave-repeating quality less obvious than it otherwise would be. | There are 13 steps in a period (i. e., a major third), and the generator is 2 steps. This generates a large number of different MOSes, most of which are improper. The smallest proper MOSes are those with 1, 2, 6, and 7 notes per period. The last two are by far the most interesting, and they are closely related to magic[19] and magic[22] respectively. While they are not octave-repeating, they do have relatively long chains of octaves (five or six of them, respectively) which makes the non-octave-repeating quality less obvious than it otherwise would be. | ||
The devadoot[7] scale derived from 41edo has step pattern 2 2 2 2 2 2 1 (per period). Since octaves are no longer exactly equivalent, we must evaluate the Graham complexity of the entire N-integer-limit chord of nature (rather than just odd limits). The Graham complexity of the complete 10-limit otonality is 4; this means that devadoot[7] allows for 3 each (up to period equivalency) of the basic "major-like" (otonal) and "minor-like" (utonal) 10-limit chords. Since there are slightly more than three periods in an octave, this actually means that there are around 9 such chords per octave, which allows considerable freedom of modulation. Much like angel, it handles the 10-integer-limit amazingly but doesn't handle 12-integer-limit harmonies as well.</pre></div> | The devadoot[7] scale derived from 41edo has step pattern 2 2 2 2 2 2 1 (per period). Since octaves are no longer exactly equivalent, we must evaluate the Graham complexity of the entire N-integer-limit chord of nature (rather than just odd limits). The Graham complexity of the complete 10-limit otonality is 4; this means that devadoot[7] allows for 3 each (up to period equivalency) of the basic "major-like" (otonal) and "minor-like" (utonal) 10-limit chords. Since there are slightly more than three periods in an octave, this actually means that there are around 9 such chords per octave, which allows considerable freedom of modulation. Much like angel, it handles the 10-integer-limit amazingly but doesn't handle 12-integer-limit harmonies as well. | ||
Straight-fretted devadoot guitars would be a possibility; they would need to be tuned in [[https://en.wikipedia.org/wiki/Major_thirds_tuning|all-thirds]] since the period is a major third.</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>devadoot</title></head><body><strong>Devadoot</strong> is the name proposed by Mason Green for the non-octave-equivalent variant of <a class="wiki_link" href="/magic">magic</a> temperament that has a period of a flattened major third, five of which make a tritave (3:1), and a generator which can equivalently be designated as an octave, a perfect fifth, or a large quarter tone (i. e., an octave minus three periods).<br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>devadoot</title></head><body><strong>Devadoot</strong> is the name proposed by Mason Green for the non-octave-equivalent variant of <a class="wiki_link" href="/magic">magic</a> temperament that has a period of a flattened major third, five of which make a tritave (3:1), and a generator which can equivalently be designated as an octave, a perfect fifth, or a large quarter tone (i. e., an octave minus three periods).<br /> | ||
| Line 24: | Line 26: | ||
There are 13 steps in a period (i. e., a major third), and the generator is 2 steps. This generates a large number of different MOSes, most of which are improper. The smallest proper MOSes are those with 1, 2, 6, and 7 notes per period. The last two are by far the most interesting, and they are closely related to magic[19] and magic[22] respectively. While they are not octave-repeating, they do have relatively long chains of octaves (five or six of them, respectively) which makes the non-octave-repeating quality less obvious than it otherwise would be.<br /> | There are 13 steps in a period (i. e., a major third), and the generator is 2 steps. This generates a large number of different MOSes, most of which are improper. The smallest proper MOSes are those with 1, 2, 6, and 7 notes per period. The last two are by far the most interesting, and they are closely related to magic[19] and magic[22] respectively. While they are not octave-repeating, they do have relatively long chains of octaves (five or six of them, respectively) which makes the non-octave-repeating quality less obvious than it otherwise would be.<br /> | ||
<br /> | <br /> | ||
The devadoot[7] scale derived from 41edo has step pattern 2 2 2 2 2 2 1 (per period). Since octaves are no longer exactly equivalent, we must evaluate the Graham complexity of the entire N-integer-limit chord of nature (rather than just odd limits). The Graham complexity of the complete 10-limit otonality is 4; this means that devadoot[7] allows for 3 each (up to period equivalency) of the basic &quot;major-like&quot; (otonal) and &quot;minor-like&quot; (utonal) 10-limit chords. Since there are slightly more than three periods in an octave, this actually means that there are around 9 such chords per octave, which allows considerable freedom of modulation. Much like angel, it handles the 10-integer-limit amazingly but doesn't handle 12-integer-limit harmonies as well.</body></html></pre></div> | The devadoot[7] scale derived from 41edo has step pattern 2 2 2 2 2 2 1 (per period). Since octaves are no longer exactly equivalent, we must evaluate the Graham complexity of the entire N-integer-limit chord of nature (rather than just odd limits). The Graham complexity of the complete 10-limit otonality is 4; this means that devadoot[7] allows for 3 each (up to period equivalency) of the basic &quot;major-like&quot; (otonal) and &quot;minor-like&quot; (utonal) 10-limit chords. Since there are slightly more than three periods in an octave, this actually means that there are around 9 such chords per octave, which allows considerable freedom of modulation. Much like angel, it handles the 10-integer-limit amazingly but doesn't handle 12-integer-limit harmonies as well.<br /> | ||
<br /> | |||
Straight-fretted devadoot guitars would be a possibility; they would need to be tuned in <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Major_thirds_tuning" rel="nofollow">all-thirds</a> since the period is a major third.</body></html></pre></div> | |||