Otones12-24: Difference between revisions

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Wikispaces>Andrew_Heathwaite
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
#redirect [[12afdo]]
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 14:45:10 UTC</tt>.<br>
: The original revision id was <tt>68454333</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">A dedecatonic (12-note) scale borrowed from the overtone series:
 
12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12, 20/12, 21/12, 22/12, 23/12, 24/12
 
which reduces to:
 
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:
 
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
= in cents:
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74
 
==modes==
 
For your tuning pleasure, all 12 modes. Note that the names "C", "C#", refer to a keyboard mapping that begins the scale on C. Such a mapping &amp; naming system are, I admit, quite arbitrary.
=== ===
===|| || 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 || 1/1 = 0 || 13/12 = 139 || 7/6 = 267 || 5/4 = 389 || 4/3 = 498 || 17/12 = 603 || 3/2 = 702 || 19/12 = 796 || 5/3 = 884 || 7/4 = 969 || 11/6 = 1049 || 23/12 = 1126 || || C# = 13 || 24/13 = 1061 || 1/1 = 0 || 14/13 = 128 || 15/13 = 248 || 16/13 = 359 || 17/13 = 464 || 18/13 = 563 || 19/13 = 657 || 20/13 = 746 || 21/13 = 830 || 22/13 = 911 || 23/13 = 988 || || D = 14 || 12/7 = 933 || 13/7 = 1072 || 1/1 = 0 || 15/14 = 119 || 8/7 = 231 || 17/14 = 336 || 9/7 = 435 || 19/14 = 529 || 10/7 = 617 || 3/2 = 702 || 11/7 = 782 || 23/14 = 859 || || D# = 15 || 8/5 = 814 || 26/15 = 952 || 28/15 = 1081 || 1/1 = 0 || 16/15 = 112 || 17/15 = 217 || 6/5 = 316 || 19/15 = 409 || 4/3 = 498 || 7/5 = 583 || 22/15 = 663 || 23/15 = 740 || || E = 16 || 3/2 = 702 || 13/8 = 841 || 7/4 = 969 || 15/8 = 1088 || 1/1 = 0 || 17/16 = 105 || 9/8 = 204 || 19/16 = 298 || 5/4 = 386 || 21/16 = 471 || 11/8 = 551 || 23/16 = 628 || || F = 17 || 24/17 = 597 || 26/17 = 736 || 28/17 = 864 || 30/17 = 983 || 32/17 = 1095 || 1/1 = 0 || 18/17 = 99 || 19/17 = 193 || 20/17 = 281 || 21/17 = 366 || 22/17 = 446 || 23/17 = 523 || || F# = 18 || 4/3 = 498 || 13/9 = 637 || 14/9 = 765 || 5/3 = 884 || 16/9 = 996 || 17/9 = 1101 || 1/1 = 0 || 19/18 = 94 || 10/9 = 182 || 7/6 = 267 || 11/9 = 347 || 23/18 = 424 || || G = 19 || 24/19 = 404 || 26/19 = 543 || 28/19 = 671 || 30/19 = 791 || 32/19 = 902 || 34/19 = 1007 || 36/19 = 1106 || 1/1 = 0 || 20/19 = 89 || 21/19 = 173 || 22/19 = 254 || 23/19 = 331 || || G# = 20 || 6/5 = 316 || 13/10 = 454 || 7/5 = 583 || 3/2 = 702 || 8/5 = 814 || 17/10 = 919 || 9/5 = 1018 || 19/10 = 1111 || 1/1 = 0 || 21/20 = 84 || 11/10 = 165 || 23/20 = 242 || || A = 21 || 8/7 = 231 || 26/21 = 370 || 4/3 = 498 || 10/7 = 617 || 32/21 = 729 || 34/21 = 834 || 12/7 = 933 || 38/21 = 1027 || 40/21 = 1116 || 1/1 = 0 || 22/21 = 81 || 23/21 = 157 || || A# = 22 || 12/11 = 151 || 13/11 = 289 || 14/11 = 418 || 15/11 = 537 || 16/11 = 649 || 17/11 = 754 || 18/11 = 853 || 19/11 = 946 || 20/11 = 1035 || 21/11 = 1119 || 1/1 = 0 || 23/22 = 77 || || B = 23 || 24/23 = 74 || 26/23 = 212 || 28/23 = 341 || 30/23 = 460 || 32/23 = 572 || 34/23 = 677 || 36/23 = 776 || 38/23 = 869 || 40/23 = 958 || 42/23 = 1043 || 44/23 = 1123 || 1/1 = 0 ||=== </pre></div>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;otones12-24&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A dedecatonic (12-note) scale borrowed from the overtone series:&lt;br /&gt;
&lt;br /&gt;
12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12, 20/12, 21/12, 22/12, 23/12, 24/12&lt;br /&gt;
&lt;br /&gt;
which reduces to:&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
in cents:&lt;br /&gt;
&lt;br /&gt;
0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200&lt;br /&gt;
&lt;br /&gt;
intervals between adjacent steps gradually get smaller, as is usual for overtone chunks like this:&lt;br /&gt;
&lt;br /&gt;
13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23&lt;br /&gt;
= in cents:&lt;br /&gt;
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;modes&lt;/h2&gt;
&lt;br /&gt;
For your tuning pleasure, all 12 modes. Note that the names &amp;quot;C&amp;quot;, &amp;quot;C#&amp;quot;, refer to a keyboard mapping that begins the scale on C. Such a mapping &amp;amp; naming system are, I admit, quite arbitrary.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-modes-|| || 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 || 1/1 = 0 || 13/12 = 139 || 7/6 = 267 || 5/4 = 389 || 4/3 = 498 || 17/12 = 603 || 3/2 = 702 || 19/12 = 796 || 5/3 = 884 || 7/4 = 969 || 11/6 = 1049 || 23/12 = 1126 || || C# = 13 || 24/13 = 1061 || 1/1 = 0 || 14/13 = 128 || 15/13 = 248 || 16/13 = 359 || 17/13 = 464 || 18/13 = 563 || 19/13 = 657 || 20/13 = 746 || 21/13 = 830 || 22/13 = 911 || 23/13 = 988 || || D = 14 || 12/7 = 933 || 13/7 = 1072 || 1/1 = 0 || 15/14 = 119 || 8/7 = 231 || 17/14 = 336 || 9/7 = 435 || 19/14 = 529 || 10/7 = 617 || 3/2 = 702 || 11/7 = 782 || 23/14 = 859 || || D# = 15 || 8/5 = 814 || 26/15 = 952 || 28/15 = 1081 || 1/1 = 0 || 16/15 = 112 || 17/15 = 217 || 6/5 = 316 || 19/15 = 409 || 4/3 = 498 || 7/5 = 583 || 22/15 = 663 || 23/15 = 740 || || E = 16 || 3/2 = 702 || 13/8 = 841 || 7/4 = 969 || 15/8 = 1088 || 1/1 = 0 || 17/16 = 105 || 9/8 = 204 || 19/16 = 298 || 5/4 = 386 || 21/16 = 471 || 11/8 = 551 || 23/16 = 628 || || F = 17 || 24/17 = 597 || 26/17 = 736 || 28/17 = 864 || 30/17 = 983 || 32/17 = 1095 || 1/1 = 0 || 18/17 = 99 || 19/17 = 193 || 20/17 = 281 || 21/17 = 366 || 22/17 = 446 || 23/17 = 523 || || F# = 18 || 4/3 = 498 || 13/9 = 637 || 14/9 = 765 || 5/3 = 884 || 16/9 = 996 || 17/9 = 1101 || 1/1 = 0 || 19/18 = 94 || 10/9 = 182 || 7/6 = 267 || 11/9 = 347 || 23/18 = 424 || || G = 19 || 24/19 = 404 || 26/19 = 543 || 28/19 = 671 || 30/19 = 791 || 32/19 = 902 || 34/19 = 1007 || 36/19 = 1106 || 1/1 = 0 || 20/19 = 89 || 21/19 = 173 || 22/19 = 254 || 23/19 = 331 || || G# = 20 || 6/5 = 316 || 13/10 = 454 || 7/5 = 583 || 3/2 = 702 || 8/5 = 814 || 17/10 = 919 || 9/5 = 1018 || 19/10 = 1111 || 1/1 = 0 || 21/20 = 84 || 11/10 = 165 || 23/20 = 242 || || A = 21 || 8/7 = 231 || 26/21 = 370 || 4/3 = 498 || 10/7 = 617 || 32/21 = 729 || 34/21 = 834 || 12/7 = 933 || 38/21 = 1027 || 40/21 = 1116 || 1/1 = 0 || 22/21 = 81 || 23/21 = 157 || || A# = 22 || 12/11 = 151 || 13/11 = 289 || 14/11 = 418 || 15/11 = 537 || 16/11 = 649 || 17/11 = 754 || 18/11 = 853 || 19/11 = 946 || 20/11 = 1035 || 21/11 = 1119 || 1/1 = 0 || 23/22 = 77 || || B = 23 || 24/23 = 74 || 26/23 = 212 || 28/23 = 341 || 30/23 = 460 || 32/23 = 572 || 34/23 = 677 || 36/23 = 776 || 38/23 = 869 || 40/23 = 958 || 42/23 = 1043 || 44/23 = 1123 || 1/1 = 0 ||"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;|| || 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 || 1/1 = 0 || 13/12 = 139 || 7/6 = 267 || 5/4 = 389 || 4/3 = 498 || 17/12 = 603 || 3/2 = 702 || 19/12 = 796 || 5/3 = 884 || 7/4 = 969 || 11/6 = 1049 || 23/12 = 1126 || || C# = 13 || 24/13 = 1061 || 1/1 = 0 || 14/13 = 128 || 15/13 = 248 || 16/13 = 359 || 17/13 = 464 || 18/13 = 563 || 19/13 = 657 || 20/13 = 746 || 21/13 = 830 || 22/13 = 911 || 23/13 = 988 || || D = 14 || 12/7 = 933 || 13/7 = 1072 || 1/1 = 0 || 15/14 = 119 || 8/7 = 231 || 17/14 = 336 || 9/7 = 435 || 19/14 = 529 || 10/7 = 617 || 3/2 = 702 || 11/7 = 782 || 23/14 = 859 || || D# = 15 || 8/5 = 814 || 26/15 = 952 || 28/15 = 1081 || 1/1 = 0 || 16/15 = 112 || 17/15 = 217 || 6/5 = 316 || 19/15 = 409 || 4/3 = 498 || 7/5 = 583 || 22/15 = 663 || 23/15 = 740 || || E = 16 || 3/2 = 702 || 13/8 = 841 || 7/4 = 969 || 15/8 = 1088 || 1/1 = 0 || 17/16 = 105 || 9/8 = 204 || 19/16 = 298 || 5/4 = 386 || 21/16 = 471 || 11/8 = 551 || 23/16 = 628 || || F = 17 || 24/17 = 597 || 26/17 = 736 || 28/17 = 864 || 30/17 = 983 || 32/17 = 1095 || 1/1 = 0 || 18/17 = 99 || 19/17 = 193 || 20/17 = 281 || 21/17 = 366 || 22/17 = 446 || 23/17 = 523 || || F# = 18 || 4/3 = 498 || 13/9 = 637 || 14/9 = 765 || 5/3 = 884 || 16/9 = 996 || 17/9 = 1101 || 1/1 = 0 || 19/18 = 94 || 10/9 = 182 || 7/6 = 267 || 11/9 = 347 || 23/18 = 424 || || G = 19 || 24/19 = 404 || 26/19 = 543 || 28/19 = 671 || 30/19 = 791 || 32/19 = 902 || 34/19 = 1007 || 36/19 = 1106 || 1/1 = 0 || 20/19 = 89 || 21/19 = 173 || 22/19 = 254 || 23/19 = 331 || || G# = 20 || 6/5 = 316 || 13/10 = 454 || 7/5 = 583 || 3/2 = 702 || 8/5 = 814 || 17/10 = 919 || 9/5 = 1018 || 19/10 = 1111 || 1/1 = 0 || 21/20 = 84 || 11/10 = 165 || 23/20 = 242 || || A = 21 || 8/7 = 231 || 26/21 = 370 || 4/3 = 498 || 10/7 = 617 || 32/21 = 729 || 34/21 = 834 || 12/7 = 933 || 38/21 = 1027 || 40/21 = 1116 || 1/1 = 0 || 22/21 = 81 || 23/21 = 157 || || A# = 22 || 12/11 = 151 || 13/11 = 289 || 14/11 = 418 || 15/11 = 537 || 16/11 = 649 || 17/11 = 754 || 18/11 = 853 || 19/11 = 946 || 20/11 = 1035 || 21/11 = 1119 || 1/1 = 0 || 23/22 = 77 || || B = 23 || 24/23 = 74 || 26/23 = 212 || 28/23 = 341 || 30/23 = 460 || 32/23 = 572 || 34/23 = 677 || 36/23 = 776 || 38/23 = 869 || 40/23 = 958 || 42/23 = 1043 || 44/23 = 1123 || 1/1 = 0 ||&lt;/h3&gt;
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 10:52, 20 September 2023

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