Otones12-24: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>Andrew_Heathwaite
**Imported revision 68458245 - Original comment: **
Redirected page to 12afdo
Tag: New redirect
 
(10 intermediate revisions by 5 users not shown)
Line 1: Line 1:
<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 15:18:48 UTC</tt>.<br>
: The original revision id was <tt>68458245</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, 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).
 
||  || 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 || 0 || 139 || 267 || 386 || 498 || 603 || 702 || 796 || 884 || 969 || 1049 || 1126 ||
|| C#-13 || 1061 || 0 || 128 || 248 || 359 || 464 || 563 || 657 || 746 || 830 || 911 || 988 ||
|| D-14 || 933 || 1072 || 0 || 119 || 231 || 336 || 435 || 529 || 617 || 702 || 782 || 859 ||
|| D#-15 || 814 || 952 || 1081 || 0 || 112 || 217 || 316 || 409 || 498 || 583 || 663 || 740 ||
|| E-16 || 702 || 841 || 969 || 1088 || 0 || 105 || 204 || 298 || 386 || 471 || 551 || 628 ||
|| F-17 || 597 || 736 || 864 || 983 || 1095 || 0 || 99 || 193 || 281 || 366 || 446 || 523 ||
|| F#-18 || 498 || 637 || 765 || 884 || 996 || 1101 || 0 || 94 || 182 || 267 || 347 || 424 ||
|| G-19 || 404 || 543 || 671 || 791 || 902 || 1007 || 1106 || 0 || 89 || 173 || 254 || 331 ||
|| G#-20 || 316 || 454 || 583 || 702 || 814 || 919 || 1018 || 1111 || 0 || 84 || 165 || 242 ||
|| 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 ||
|| B-23 || 74 || 212 || 341 || 460 || 572 || 677 || 776 || 869 || 958 || 1043 || 1123 || 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, 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;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).&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C-12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C#-13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D#-15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F-17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F#-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G#-20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A#-22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B-23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;C-12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;139&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;267&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;603&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;796&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;969&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1049&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1126&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;C#-13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1061&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;248&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;359&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;464&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;563&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;657&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;746&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;830&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;911&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;988&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;D-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;933&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1072&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;231&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;336&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;435&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;529&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;617&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;782&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;859&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;D#-15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;814&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;952&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1081&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;217&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;409&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;583&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;663&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;740&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;E-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;841&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;969&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1088&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;204&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;298&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;471&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;551&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;628&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;F-17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;597&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;736&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;864&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;983&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1095&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;193&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;281&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;366&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;446&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;523&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;F#-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;637&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;765&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;996&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;267&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;347&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;424&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;G-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;404&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;671&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;791&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;902&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1007&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1106&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;173&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;254&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;331&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;G#-20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;454&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;583&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;814&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;919&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1018&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1111&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;84&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;242&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;A-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;231&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;370&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;617&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;729&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;834&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;933&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1027&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1116&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;A#-22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;151&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;289&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;418&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;537&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;649&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;754&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;853&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;946&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1035&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1119&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;77&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;B-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;74&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;341&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;460&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;572&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;677&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;776&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;869&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;958&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1043&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1123&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 10:52, 20 September 2023

Redirect to:

Retrieved from "https://en.xen.wiki/index.php?title=Otones12-24&oldid=124488"