Otones12-24: Difference between revisions

Revision as of 16:25, 5 May 2010

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Andrew_Heathwaite and made on 2010-05-05 16:25:41 UTC.

The original revision id was 139761229.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

A dedecatonic (12-note) scale borrowed from the [[OverToneSeries|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 expected 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. 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 || 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 ||

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.

==Compositions== 
[[http://soundclick.com/share?songid=8839059|ant lizard dragon man]], original song by Threshold of Pain, words by Scott Marshall (2006). This recording is an arrangement for otonal organ, otonal dulcimer, hand claps, and voice by Andrew Heathwaite in otones 12-24 (arranged & recorded 2010).

==Inventory of intervals from 0 to 1200 cents:== 

0 - 1/1 - ...
74 - 24/23 - B-C
77 - 23/22 - A#-B
81 - 22/21 - A-A#
84 - 21/20 - G#-A
89 - 20/19 - G-G#
94 - 19/18 - F#-G
99 - 18/17 - F-F#
105 - 17/16 - E-F
112 - 16/15 - D#-E
119 - 15/14 - D-D#
128 - 14/13 - C#-D
139 - 13/12 - C-C#
151 - 12/11 - A#-C
157 - 23/21 - A-B
165 - 11/10 - A#-B#
173 - 21/19 - G-A
182 - 10/9 - F#-G#
193 - 19/17 - F-G
204 - 9/8 - E-F#
212 - 26/23 - B-C#
217 - 17/15 - D#-F
231 - 8/7 - D-E ; A-C
242 - 23/20 - G#-B
248 - 15/13 - C#-D#
254 - 22/19 - G-A#
267 - 7/6 - C-D ; F#-A
281 - 20/17 - F-G#
289 - 13/11 - A#-C#
316 - 6/5 - D#-F# ; G#-C
331 - 23/19 - G-B
336 - 17/14 - D-F
347 - 11/9 - F#-A#
359 - 16/13 - C#-E
366 - 21/17 - F-A
370 - 26/21 - A-C#
386 - 5/4 - C-D# ; E-G#
404 - 24/19 - G-C
409 - 19/15 - D#-G
418 - 14/11 - A#-D
424 - 23/18 - F#-B
435 - 9/7 - D-F#
446 - 22/17 - F-A#
454 - 13/10 - G#-C#
460 - 30/23 - B-D#
464 - 17/13 - C#-F
471 - 21/16 - E-A
498 - 4/3 - C-E ; D#-G# ; F#-C ; A-D
523 - 23/17 - F-B
529 - 19/14 - D-G
537 - 15/11 - A#-D#
543 - 26/19 - G-C#
551 - 11/8 - E-A
563 - 18/13 - C#-F#
572 - 32/23 - B-E
583 - 7/5 - D#-A ; G#-D
597 - 24/17 - F-C

603 - 17/12 - C-F
617 - 10/7 - D-G# ; A-D#
628 - 23/16 - E-B
637 - 13/9 - F#-C#
649 - 16/11 - A-E
657 - 19/13 - C#-G
663 - 22/15 - D#-A#
671 - 28/19 - G-D
677 - 34/23 - B-F
...

Original HTML content:

<html><head><title>otones12-24</title></head><body>A dedecatonic (12-note) scale borrowed from the <a class="wiki_link" href="/OverToneSeries">overtone series</a>:<br />
<br />
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<br />
<br />
which reduces to:<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 />
in cents:<br />
0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200<br />
<br />
Intervals between adjacent steps gradually get smaller, as is expected for overtone chunks like this:<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 />
in cents:<br />
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-modes"></a><!-- ws:end:WikiTextHeadingRule:0 -->modes</h2>
 <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 />


<table class="wiki_table">
    <tr>
        <td><br />
</td>
        <td>C-12<br />
</td>
        <td>C#-13<br />
</td>
        <td>D-14<br />
</td>
        <td>D#-15<br />
</td>
        <td>E-16<br />
</td>
        <td>F-17<br />
</td>
        <td>F#-18<br />
</td>
        <td>G-19<br />
</td>
        <td>G#-20<br />
</td>
        <td>A-21<br />
</td>
        <td>A#-22<br />
</td>
        <td>B-23<br />
</td>
    </tr>
    <tr>
        <td>C-12<br />
</td>
        <td>0<br />
</td>
        <td>139<br />
</td>
        <td>267<br />
</td>
        <td>386<br />
</td>
        <td>498<br />
</td>
        <td>603<br />
</td>
        <td>702<br />
</td>
        <td>796<br />
</td>
        <td>884<br />
</td>
        <td>969<br />
</td>
        <td>1049<br />
</td>
        <td>1126<br />
</td>
    </tr>
    <tr>
        <td>C#-13<br />
</td>
        <td>1061<br />
</td>
        <td>0<br />
</td>
        <td>128<br />
</td>
        <td>248<br />
</td>
        <td>359<br />
</td>
        <td>464<br />
</td>
        <td>563<br />
</td>
        <td>657<br />
</td>
        <td>746<br />
</td>
        <td>830<br />
</td>
        <td>911<br />
</td>
        <td>988<br />
</td>
    </tr>
    <tr>
        <td>D-14<br />
</td>
        <td>933<br />
</td>
        <td>1072<br />
</td>
        <td>0<br />
</td>
        <td>119<br />
</td>
        <td>231<br />
</td>
        <td>336<br />
</td>
        <td>435<br />
</td>
        <td>529<br />
</td>
        <td>617<br />
</td>
        <td>702<br />
</td>
        <td>782<br />
</td>
        <td>859<br />
</td>
    </tr>
    <tr>
        <td>D#-15<br />
</td>
        <td>814<br />
</td>
        <td>952<br />
</td>
        <td>1081<br />
</td>
        <td>0<br />
</td>
        <td>112<br />
</td>
        <td>217<br />
</td>
        <td>316<br />
</td>
        <td>409<br />
</td>
        <td>498<br />
</td>
        <td>583<br />
</td>
        <td>663<br />
</td>
        <td>740<br />
</td>
    </tr>
    <tr>
        <td>E-16<br />
</td>
        <td>702<br />
</td>
        <td>841<br />
</td>
        <td>969<br />
</td>
        <td>1088<br />
</td>
        <td>0<br />
</td>
        <td>105<br />
</td>
        <td>204<br />
</td>
        <td>298<br />
</td>
        <td>386<br />
</td>
        <td>471<br />
</td>
        <td>551<br />
</td>
        <td>628<br />
</td>
    </tr>
    <tr>
        <td>F-17<br />
</td>
        <td>597<br />
</td>
        <td>736<br />
</td>
        <td>864<br />
</td>
        <td>983<br />
</td>
        <td>1095<br />
</td>
        <td>0<br />
</td>
        <td>99<br />
</td>
        <td>193<br />
</td>
        <td>281<br />
</td>
        <td>366<br />
</td>
        <td>446<br />
</td>
        <td>523<br />
</td>
    </tr>
    <tr>
        <td>F#-18<br />
</td>
        <td>498<br />
</td>
        <td>637<br />
</td>
        <td>765<br />
</td>
        <td>884<br />
</td>
        <td>996<br />
</td>
        <td>1101<br />
</td>
        <td>0<br />
</td>
        <td>94<br />
</td>
        <td>182<br />
</td>
        <td>267<br />
</td>
        <td>347<br />
</td>
        <td>424<br />
</td>
    </tr>
    <tr>
        <td>G-19<br />
</td>
        <td>404<br />
</td>
        <td>543<br />
</td>
        <td>671<br />
</td>
        <td>791<br />
</td>
        <td>902<br />
</td>
        <td>1007<br />
</td>
        <td>1106<br />
</td>
        <td>0<br />
</td>
        <td>89<br />
</td>
        <td>173<br />
</td>
        <td>254<br />
</td>
        <td>331<br />
</td>
    </tr>
    <tr>
        <td>G#-20<br />
</td>
        <td>316<br />
</td>
        <td>454<br />
</td>
        <td>583<br />
</td>
        <td>702<br />
</td>
        <td>814<br />
</td>
        <td>919<br />
</td>
        <td>1018<br />
</td>
        <td>1111<br />
</td>
        <td>0<br />
</td>
        <td>84<br />
</td>
        <td>165<br />
</td>
        <td>242<br />
</td>
    </tr>
    <tr>
        <td>A-21<br />
</td>
        <td>231<br />
</td>
        <td>370<br />
</td>
        <td>498<br />
</td>
        <td>617<br />
</td>
        <td>729<br />
</td>
        <td>834<br />
</td>
        <td>933<br />
</td>
        <td>1027<br />
</td>
        <td>1116<br />
</td>
        <td>0<br />
</td>
        <td>81<br />
</td>
        <td>157<br />
</td>
    </tr>
    <tr>
        <td>A#-22<br />
</td>
        <td>151<br />
</td>
        <td>289<br />
</td>
        <td>418<br />
</td>
        <td>537<br />
</td>
        <td>649<br />
</td>
        <td>754<br />
</td>
        <td>853<br />
</td>
        <td>946<br />
</td>
        <td>1035<br />
</td>
        <td>1119<br />
</td>
        <td>0<br />
</td>
        <td>77<br />
</td>
    </tr>
    <tr>
        <td>B-23<br />
</td>
        <td>74<br />
</td>
        <td>212<br />
</td>
        <td>341<br />
</td>
        <td>460<br />
</td>
        <td>572<br />
</td>
        <td>677<br />
</td>
        <td>776<br />
</td>
        <td>869<br />
</td>
        <td>958<br />
</td>
        <td>1043<br />
</td>
        <td>1123<br />
</td>
        <td>0<br />
</td>
    </tr>
</table>

<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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Compositions"></a><!-- ws:end:WikiTextHeadingRule:2 -->Compositions</h2>
 <a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839059" rel="nofollow">ant lizard dragon man</a>, original song by Threshold of Pain, words by Scott Marshall (2006). This recording is an arrangement for otonal organ, otonal dulcimer, hand claps, and voice by Andrew Heathwaite in otones 12-24 (arranged &amp; recorded 2010).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Inventory of intervals from 0 to 1200 cents:"></a><!-- ws:end:WikiTextHeadingRule:4 -->Inventory of intervals from 0 to 1200 cents:</h2>
 <br />
0 - 1/1 - ...<br />
74 - 24/23 - B-C<br />
77 - 23/22 - A#-B<br />
81 - 22/21 - A-A#<br />
84 - 21/20 - G#-A<br />
89 - 20/19 - G-G#<br />
94 - 19/18 - F#-G<br />
99 - 18/17 - F-F#<br />
105 - 17/16 - E-F<br />
112 - 16/15 - D#-E<br />
119 - 15/14 - D-D#<br />
128 - 14/13 - C#-D<br />
139 - 13/12 - C-C#<br />
151 - 12/11 - A#-C<br />
157 - 23/21 - A-B<br />
165 - 11/10 - A#-B#<br />
173 - 21/19 - G-A<br />
182 - 10/9 - F#-G#<br />
193 - 19/17 - F-G<br />
204 - 9/8 - E-F#<br />
212 - 26/23 - B-C#<br />
217 - 17/15 - D#-F<br />
231 - 8/7 - D-E ; A-C<br />
242 - 23/20 - G#-B<br />
248 - 15/13 - C#-D#<br />
254 - 22/19 - G-A#<br />
267 - 7/6 - C-D ; F#-A<br />
281 - 20/17 - F-G#<br />
289 - 13/11 - A#-C#<br />
316 - 6/5 - D#-F# ; G#-C<br />
331 - 23/19 - G-B<br />
336 - 17/14 - D-F<br />
347 - 11/9 - F#-A#<br />
359 - 16/13 - C#-E<br />
366 - 21/17 - F-A<br />
370 - 26/21 - A-C#<br />
386 - 5/4 - C-D# ; E-G#<br />
404 - 24/19 - G-C<br />
409 - 19/15 - D#-G<br />
418 - 14/11 - A#-D<br />
424 - 23/18 - F#-B<br />
435 - 9/7 - D-F#<br />
446 - 22/17 - F-A#<br />
454 - 13/10 - G#-C#<br />
460 - 30/23 - B-D#<br />
464 - 17/13 - C#-F<br />
471 - 21/16 - E-A<br />
498 - 4/3 - C-E ; D#-G# ; F#-C ; A-D<br />
523 - 23/17 - F-B<br />
529 - 19/14 - D-G<br />
537 - 15/11 - A#-D#<br />
543 - 26/19 - G-C#<br />
551 - 11/8 - E-A<br />
563 - 18/13 - C#-F#<br />
572 - 32/23 - B-E<br />
583 - 7/5 - D#-A ; G#-D<br />
597 - 24/17 - F-C<br />
<br />
603 - 17/12 - C-F<br />
617 - 10/7 - D-G# ; A-D#<br />
628 - 23/16 - E-B<br />
637 - 13/9 - F#-C#<br />
649 - 16/11 - A-E<br />
657 - 19/13 - C#-G<br />
663 - 22/15 - D#-A#<br />
671 - 28/19 - G-D<br />
677 - 34/23 - B-F<br />
...</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2009-10-17 12:29:17 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-05-05 16:25:41 UTC</tt>.<br>
-: The original revision id was <tt>95821418</tt>.<br>
+: The original revision id was <tt>139761229</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>
@@ Line 42: / Line 42: @@
 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.
-===Inventory of intervals from 0 to 1200 cents:===
+==Compositions==
+[[http://soundclick.com/share?songid=8839059|ant lizard dragon man]], original song by Threshold of Pain, words by Scott Marshall (2006). This recording is an arrangement for otonal organ, otonal dulcimer, hand claps, and voice by Andrew Heathwaite in otones 12-24 (arranged &amp; recorded 2010).
+==Inventory of intervals from 0 to 1200 cents:==
 - 1/1 - ...
@@ Line 505: / Line 508: @@
 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.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-modes-Inventory of intervals from 0 to 1200 cents:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Inventory of intervals from 0 to 1200 cents:&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Compositions&lt;/h2&gt;
+ &lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839059" rel="nofollow"&gt;ant lizard dragon man&lt;/a&gt;, original song by Threshold of Pain, words by Scott Marshall (2006). This recording is an arrangement for otonal organ, otonal dulcimer, hand claps, and voice by Andrew Heathwaite in otones 12-24 (arranged &amp;amp; recorded 2010).&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Inventory of intervals from 0 to 1200 cents:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Inventory of intervals from 0 to 1200 cents:&lt;/h2&gt;
   &lt;br /&gt;
 - 1/1 - ...&lt;br /&gt;

Otones12-24: Difference between revisions

Revision as of 16:25, 5 May 2010

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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