240edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 145397585 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 145398845 - 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>2010-05-28 03: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-28 03:45:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>145398845</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 8: | Line 8: | ||
<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;white-space: pre-wrap ! important" class="old-revision-html">The 240edo divides the octave into 240 steps of exactly five cents each. Its primary purpose is in tuning marvel temperament and marvel's extension to spectacle temperament. | <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;white-space: pre-wrap ! important" class="old-revision-html">The 240edo divides the octave into 240 steps of exactly five cents each. Its primary purpose is in tuning marvel temperament and marvel's extension to spectacle temperament. | ||
If we round off to the nearest five cents, we end up with a [[Vals and Tuning Space|val]](mapping to primes) for 240edo of <240 380 557 674|. This tempers out the [[http://en.wikipedia.org/wiki/Septimal_kleisma|septimal kleisma]] of 225/224, with the resultant errors (two cents flat for the fifth, a little over a cent flat and sharp, respectively, for the major third and the 7/4) about as low as it is possible to achieve. Retuning 5-limit scales to 240edo is a simple and often very effective way to to make them function as 7-limit scales while retaining very accurate tuning. | If we round off to the nearest five cents, we end up with a [[Vals and Tuning Space|val]](mapping to primes) for 240edo of <240 380 557 674|. This tempers out the [[http://en.wikipedia.org/wiki/Septimal_kleisma|septimal kleisma]] of 225/224, with the resultant errors (two cents flat for the fifth, a little over a cent flat and sharp, respectively, for the major third and the 7/4) about as low as it is possible to achieve. Retuning 5-limit scales to 240edo is a simple and often very effective way to to make them function as 7-limit scales while retaining very accurate tuning. | ||
For higher limits, 240edo tempers out 243/242 in the 11-limit, 351/350 in the 13-limit, and 375/374 in the 17-limit, and adding these to the mix converts marvel temperament into spectacle temperament. This is still a planar temperament, but more complex as two unidecimal neutral thirds of 11/9 make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 the 350 cent interval often employed in 24edo versions of Arabic music.) Musical intervals are therefore generated by octaves, major thirds, and neutral thirds in spectacle. We have: | For higher limits, 240edo tempers out 243/242 in the 11-limit, 351/350 in the 13-limit, and 375/374 in the 17-limit, and adding these to the mix converts marvel temperament into spectacle temperament. This is still a planar temperament, but more complex as two unidecimal neutral thirds of 11/9 make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 the 350 cent interval often employed in 24edo versions of Arabic music.) Musical intervals are therefore generated by octaves, major thirds, and neutral thirds in spectacle. We have: | ||
| Line 81: | Line 81: | ||
15/8 | 15/8 | ||
2/1 | 2/1 | ||
! lumma5_240.scl | |||
! | |||
Carl Lumma's scale aka diadie1, 240edo version | |||
12 | |||
! | |||
115. | |||
200. | |||
270. | |||
385. | |||
500. | |||
585. | |||
700. | |||
815. | |||
885. | |||
970. | |||
1085. | |||
1200. | |||
! marvel chords | ! marvel chords | ||
! [-1, -1, 2]->[-1, 0, -2]||[0, -1, -1]->[0, 0, -1]->[0, 0, 0]->[0, 0, 1]->[0, 0, 2]</pre></div> | ! [-1, -1, 2]->[-1, 0, -2]||[0, -1, -1]->[0, 0, -1]->[0, 0, 0]->[0, 0, 1]->[0, 0, 2] | ||
! pum14.scl | |||
pum14 scale | |||
14 | |||
! | |||
25/24 | |||
16/15 | |||
10/9 | |||
75/64 | |||
5/4 | |||
4/3 | |||
64/45 | |||
3/2 | |||
25/16 | |||
8/5 | |||
5/3 | |||
16/9 | |||
15/8 | |||
2 | |||
! pum14_240.scl | |||
pum14 in 240edo | |||
14 | |||
! | |||
70. | |||
115. | |||
185. | |||
270. | |||
385. | |||
500. | |||
615. | |||
700. | |||
770. | |||
815. | |||
885. | |||
1000. | |||
1085. | |||
1200. | |||
! tetrads [[0, -1, 0], [0, -1, 1], [1, -1, 1], [1, -1, 2], | |||
! [0, 0, 2], [0, -1, -2], [0, 0, 1], [0, -1, -1]] | |||
</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>240edo</title></head><body>The 240edo divides the octave into 240 steps of exactly five cents each. Its primary purpose is in tuning marvel temperament and marvel's extension to spectacle temperament.<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>240edo</title></head><body>The 240edo divides the octave into 240 steps of exactly five cents each. Its primary purpose is in tuning marvel temperament and marvel's extension to spectacle temperament.<br /> | ||
<br /> | <br /> | ||
If we round off to the nearest five cents, we end up with a <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">val</a>(mapping to primes) for 240edo of &lt;240 380 557 674|. This tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_kleisma" rel="nofollow">septimal kleisma</a> of 225/224, with the resultant errors (two cents flat for the fifth, a little over a cent flat and sharp, respectively, for the major third and the 7/4) about as low as it is possible to achieve. Retuning 5-limit scales to 240edo is a simple and often very effective way to to make them function as 7-limit scales while retaining very accurate tuning.<br /> | If we round off to the nearest five cents, we end up with a <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">val</a>(mapping to primes) for 240edo of &lt;240 380 557 674|. This tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_kleisma" rel="nofollow">septimal kleisma</a> of 225/224, with the resultant errors (two cents flat for the fifth, a little over a cent flat and sharp, respectively, for the major third and the 7/4) about as low as it is possible to achieve. Retuning 5-limit scales to 240edo is a simple and often very effective way to to make them function as 7-limit scales while retaining very accurate tuning.<br /> | ||
<br /> | <br /> | ||
For higher limits, 240edo tempers out 243/242 in the 11-limit, 351/350 in the 13-limit, and 375/374 in the 17-limit, and adding these to the mix converts marvel temperament into spectacle temperament. This is still a planar temperament, but more complex as two unidecimal neutral thirds of 11/9 make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 the 350 cent interval often employed in 24edo versions of Arabic music.) Musical intervals are therefore generated by octaves, major thirds, and neutral thirds in spectacle. We have:<br /> | For higher limits, 240edo tempers out 243/242 in the 11-limit, 351/350 in the 13-limit, and 375/374 in the 17-limit, and adding these to the mix converts marvel temperament into spectacle temperament. This is still a planar temperament, but more complex as two unidecimal neutral thirds of 11/9 make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 the 350 cent interval often employed in 24edo versions of Arabic music.) Musical intervals are therefore generated by octaves, major thirds, and neutral thirds in spectacle. We have:<br /> | ||
| Line 159: | Line 219: | ||
15/8<br /> | 15/8<br /> | ||
2/1<br /> | 2/1<br /> | ||
<br /> | |||
<br /> | |||
! lumma5_240.scl<br /> | |||
!<br /> | |||
Carl Lumma's scale aka diadie1, 240edo version<br /> | |||
12<br /> | |||
!<br /> | |||
115.<br /> | |||
200.<br /> | |||
270.<br /> | |||
385.<br /> | |||
500.<br /> | |||
585.<br /> | |||
700.<br /> | |||
815.<br /> | |||
885.<br /> | |||
970.<br /> | |||
1085.<br /> | |||
1200.<br /> | |||
! marvel chords<br /> | ! marvel chords<br /> | ||
! [-1, -1, 2]-&gt;[-1, 0, -2]||[0, -1, -1]-&gt;[0, 0, -1]-&gt;[0, 0, 0]-&gt;[0, 0, 1]-&gt;[0, 0, 2]</body></html></pre></div> | ! [-1, -1, 2]-&gt;[-1, 0, -2]||[0, -1, -1]-&gt;[0, 0, -1]-&gt;[0, 0, 0]-&gt;[0, 0, 1]-&gt;[0, 0, 2]<br /> | ||
<br /> | |||
! pum14.scl<br /> | |||
pum14 scale<br /> | |||
14<br /> | |||
!<br /> | |||
25/24<br /> | |||
16/15<br /> | |||
10/9<br /> | |||
75/64<br /> | |||
5/4<br /> | |||
4/3<br /> | |||
64/45<br /> | |||
3/2<br /> | |||
25/16<br /> | |||
8/5<br /> | |||
5/3<br /> | |||
16/9<br /> | |||
15/8<br /> | |||
2<br /> | |||
<br /> | |||
! pum14_240.scl<br /> | |||
pum14 in 240edo<br /> | |||
14<br /> | |||
!<br /> | |||
70.<br /> | |||
115.<br /> | |||
185.<br /> | |||
270.<br /> | |||
385.<br /> | |||
500.<br /> | |||
615.<br /> | |||
700.<br /> | |||
770.<br /> | |||
815.<br /> | |||
885.<br /> | |||
1000.<br /> | |||
1085.<br /> | |||
1200.<br /> | |||
! tetrads [[0, -1, 0], [0, -1, 1], [1, -1, 1], [1, -1, 2], ! [0, 0, 2], [0, -1, -2], [0, 0, 1], [0, -1, -1]]</body></html></pre></div> | |||