Otones12-24: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 68458245 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 68458829 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-04-19 15: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-04-19 15:23:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>68458829</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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1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1 | 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1 | ||
in cents: | in cents: | ||
0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200 | 0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200 | ||
Intervals between adjacent steps gradually get smaller, as is usual for overtone chunks like this: | |||
13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23 | 13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23 | ||
in cents: | |||
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74 | 139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74 | ||
==modes== | ==modes== | ||
For your tuning pleasure, all 12 modes, arranged in a handy-dandy table. The following matrix uses a keyboard mapping that starts the scale on C. To find an interval, say the interval from C to F#, first find the lower pitch on the left, C, & follow it across the row to the column of the higher pitch, F# to find 702 cents. To find the name of the interval in just intonation, use the number of the higher pitch as the numerator (18) and the number of the lower pitch (12) as the denominator, then reduce (3/2). | For your tuning pleasure, all 12 modes, arranged in a handy-dandy table. The following matrix uses a keyboard mapping that starts the scale on C. Thus, C=1/1, C#=13/12, etc. To find an interval, say the interval from C to F#, first find the lower pitch on the left, C, & follow it across the row to the column of the higher pitch, F# to find 702 cents. To find the name of the interval in just intonation, use the number of the higher pitch as the numerator (18) and the number of the lower pitch (12) as the denominator, then reduce (3/2). | ||
|| || C-12 || C#-13 || D-14 || D#-15 || E-16 || F-17 || F#-18 || G-19 || G#-20 || A-21 || A#-22 || B-23 || | || || C-12 || C#-13 || D-14 || D#-15 || E-16 || F-17 || F#-18 || G-19 || G#-20 || A-21 || A#-22 || B-23 || | ||
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|| A-21 || 231 || 370 || 498 || 617 || 729 || 834 || 933 || 1027 || 1116 || 0 || 81 || 157 || | || A-21 || 231 || 370 || 498 || 617 || 729 || 834 || 933 || 1027 || 1116 || 0 || 81 || 157 || | ||
|| A#-22 || 151 || 289 || 418 || 537 || 649 || 754 || 853 || 946 || 1035 || 1119 || 0 || 77 || | || A#-22 || 151 || 289 || 418 || 537 || 649 || 754 || 853 || 946 || 1035 || 1119 || 0 || 77 || | ||
|| B-23 || 74 || 212 || 341 || 460 || 572 || 677 || 776 || 869 || 958 || 1043 || 1123 || 0 ||</pre></div> | || B-23 || 74 || 212 || 341 || 460 || 572 || 677 || 776 || 869 || 958 || 1043 || 1123 || 0 || | ||
You can see that, due to the varying step sizes, this relatively small scale contains a large number of unique rational intervals up to the 23-limit.</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>otones12-24</title></head><body>A dedecatonic (12-note) scale borrowed from the overtone series:<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>otones12-24</title></head><body>A dedecatonic (12-note) scale borrowed from the overtone series:<br /> | ||
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<br /> | <br /> | ||
1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1<br /> | 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1<br /> | ||
in cents:<br /> | in cents:<br /> | ||
0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200<br /> | 0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200<br /> | ||
<br /> | <br /> | ||
Intervals between adjacent steps gradually get smaller, as is usual for overtone chunks like this:<br /> | |||
<br /> | <br /> | ||
13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23<br /> | 13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23<br /> | ||
in cents:<br /> | |||
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74<br /> | 139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-modes"></a><!-- ws:end:WikiTextHeadingRule:0 -->modes</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-modes"></a><!-- ws:end:WikiTextHeadingRule:0 -->modes</h2> | ||
<br /> | <br /> | ||
For your tuning pleasure, all 12 modes, arranged in a handy-dandy table. The following matrix uses a keyboard mapping that starts the scale on C. To find an interval, say the interval from C to F#, first find the lower pitch on the left, C, &amp; follow it across the row to the column of the higher pitch, F# to find 702 cents. To find the name of the interval in just intonation, use the number of the higher pitch as the numerator (18) and the number of the lower pitch (12) as the denominator, then reduce (3/2).<br /> | For your tuning pleasure, all 12 modes, arranged in a handy-dandy table. The following matrix uses a keyboard mapping that starts the scale on C. Thus, C=1/1, C#=13/12, etc. To find an interval, say the interval from C to F#, first find the lower pitch on the left, C, &amp; follow it across the row to the column of the higher pitch, F# to find 702 cents. To find the name of the interval in just intonation, use the number of the higher pitch as the numerator (18) and the number of the lower pitch (12) as the denominator, then reduce (3/2).<br /> | ||
<br /> | <br /> | ||
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</table> | </table> | ||
</body></html></pre></div> | <br /> | ||
You can see that, due to the varying step sizes, this relatively small scale contains a large number of unique rational intervals up to the 23-limit.</body></html></pre></div> | |||