Relative cent: Difference between revisions
Wikispaces>genewardsmith **Imported revision 256869644 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 313713116 - 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:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-22 15:39:36 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>313713116</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: | ||
Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat. | Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat. | ||
If you want to quantify the approximation of a given [[JI]] interval in an equal-stepped tonal systems, you can consider the absolute distance of 50 relative cent as the worst possible and 0 relative cent as the best possible. For example, [[5edo]] has a relatively good approximated [[natural seventh]] with the ratio [[7_4|7/4]]: the absolute distance of | If you want to quantify the approximation of a given [[JI]] interval in an equal-stepped tonal systems, you can consider the absolute distance of 50 relative cent as the worst possible and 0 relative cent as the best possible. For example, [[5edo]] has a relatively good approximated [[natural seventh]] with the ratio [[7_4|7/4]]: the absolute distance of 4\5 in 5edo is 8.826 ¢ or 3.677 r¢ flat of 7/4. But the approximations of its multiple edos [[10edo]] (7.355 r¢), [[15edo]] (11.032 r¢) ... gets relatively worse. [[65edo]] has the 7/4 approximately between adjacent pitches, at 47.807 r¢ flat, but its absolute approximation of this interval in cents is still the same as for 5edo: 8.826 ¢ flat. | ||
---- | ---- | ||
| Line 27: | Line 27: | ||
Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of <a class="wiki_link" href="/41edo">41edo</a> is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.<br /> | Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of <a class="wiki_link" href="/41edo">41edo</a> is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.<br /> | ||
<br /> | <br /> | ||
If you want to quantify the approximation of a given <a class="wiki_link" href="/JI">JI</a> interval in an equal-stepped tonal systems, you can consider the absolute distance of 50 relative cent as the worst possible and 0 relative cent as the best possible. For example, <a class="wiki_link" href="/5edo">5edo</a> has a relatively good approximated <a class="wiki_link" href="/natural%20seventh">natural seventh</a> with the ratio <a class="wiki_link" href="/7_4">7/4</a>: the absolute distance of | If you want to quantify the approximation of a given <a class="wiki_link" href="/JI">JI</a> interval in an equal-stepped tonal systems, you can consider the absolute distance of 50 relative cent as the worst possible and 0 relative cent as the best possible. For example, <a class="wiki_link" href="/5edo">5edo</a> has a relatively good approximated <a class="wiki_link" href="/natural%20seventh">natural seventh</a> with the ratio <a class="wiki_link" href="/7_4">7/4</a>: the absolute distance of 4\5 in 5edo is 8.826 ¢ or 3.677 r¢ flat of 7/4. But the approximations of its multiple edos <a class="wiki_link" href="/10edo">10edo</a> (7.355 r¢), <a class="wiki_link" href="/15edo">15edo</a> (11.032 r¢) ... gets relatively worse. <a class="wiki_link" href="/65edo">65edo</a> has the 7/4 approximately between adjacent pitches, at 47.807 r¢ flat, but its absolute approximation of this interval in cents is still the same as for 5edo: 8.826 ¢ flat.<br /> | ||
<br /> | <br /> | ||
<hr /> | <hr /> | ||
<em>...also the term <a class="wiki_link" href="/centidegree">centidegree</a> was suggested, but this seems to be used already as a unit for temperature.</em></body></html></pre></div> | <em>...also the term <a class="wiki_link" href="/centidegree">centidegree</a> was suggested, but this seems to be used already as a unit for temperature.</em></body></html></pre></div> | ||