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Wikispaces>Andrew_Heathwaite **Imported revision 95821348 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 95821418 - Original comment: ** |
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| 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-10-17 12: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-10-17 12:29:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>95821418</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> | ||
<h4>Original Wikitext content:</h4> | <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]]: | <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 [[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 | 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 | ||
| Line 113: | Line 113: | ||
...</pre></div> | ...</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 <a class="wiki_link" href="/ | <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 <a class="wiki_link" href="/OverToneSeries">overtone series</a>:<br /> | ||
<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 /> | 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 /> | ||
Revision as of 12:29, 17 October 2009
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 2009-10-17 12:29:17 UTC.
- The original revision id was 95821418.
- 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. ===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:<h2> --><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, & 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:<h3> --><h3 id="toc1"><a name="x-modes-Inventory of intervals from 0 to 1200 cents:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Inventory of intervals from 0 to 1200 cents:</h3>
<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>