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>2009-10-17 12:28:10 UTC</tt>.<br>
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| : The original revision id was <tt>95821348</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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]]:
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| 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
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| which reduces to:
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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
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| in cents:
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| 0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200
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| | |
| Intervals between adjacent steps gradually get smaller, as is expected for overtone chunks like this:
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| 13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23
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| in cents:
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| 139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74
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| ==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).
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| || || 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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| || C-12 || 0 || 139 || 267 || 386 || 498 || 603 || 702 || 796 || 884 || 969 || 1049 || 1126 ||
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| || C#-13 || 1061 || 0 || 128 || 248 || 359 || 464 || 563 || 657 || 746 || 830 || 911 || 988 ||
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| || D-14 || 933 || 1072 || 0 || 119 || 231 || 336 || 435 || 529 || 617 || 702 || 782 || 859 ||
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| || D#-15 || 814 || 952 || 1081 || 0 || 112 || 217 || 316 || 409 || 498 || 583 || 663 || 740 ||
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| || E-16 || 702 || 841 || 969 || 1088 || 0 || 105 || 204 || 298 || 386 || 471 || 551 || 628 ||
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| || F-17 || 597 || 736 || 864 || 983 || 1095 || 0 || 99 || 193 || 281 || 366 || 446 || 523 ||
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| || F#-18 || 498 || 637 || 765 || 884 || 996 || 1101 || 0 || 94 || 182 || 267 || 347 || 424 ||
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| || G-19 || 404 || 543 || 671 || 791 || 902 || 1007 || 1106 || 0 || 89 || 173 || 254 || 331 ||
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| || G#-20 || 316 || 454 || 583 || 702 || 814 || 919 || 1018 || 1111 || 0 || 84 || 165 || 242 ||
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| || A-21 || 231 || 370 || 498 || 617 || 729 || 834 || 933 || 1027 || 1116 || 0 || 81 || 157 ||
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| || A#-22 || 151 || 289 || 418 || 537 || 649 || 754 || 853 || 946 || 1035 || 1119 || 0 || 77 ||
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| || B-23 || 74 || 212 || 341 || 460 || 572 || 677 || 776 || 869 || 958 || 1043 || 1123 || 0 ||
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| 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.
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| ===Inventory of intervals from 0 to 1200 cents:===
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| 0 - 1/1 - ...
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| 74 - 24/23 - B-C
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| 77 - 23/22 - A#-B
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| 81 - 22/21 - A-A#
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| 84 - 21/20 - G#-A
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| 89 - 20/19 - G-G#
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| 94 - 19/18 - F#-G
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| 99 - 18/17 - F-F#
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| 105 - 17/16 - E-F
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| 112 - 16/15 - D#-E
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| 119 - 15/14 - D-D#
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| 128 - 14/13 - C#-D
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| 139 - 13/12 - C-C#
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| 151 - 12/11 - A#-C
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| 157 - 23/21 - A-B
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| 165 - 11/10 - A#-B#
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| 173 - 21/19 - G-A
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| 182 - 10/9 - F#-G#
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| 193 - 19/17 - F-G
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| 204 - 9/8 - E-F#
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| 212 - 26/23 - B-C#
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| 217 - 17/15 - D#-F
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| 231 - 8/7 - D-E ; A-C
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| 242 - 23/20 - G#-B
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| 248 - 15/13 - C#-D#
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| 254 - 22/19 - G-A#
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| 267 - 7/6 - C-D ; F#-A
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| 281 - 20/17 - F-G#
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| 289 - 13/11 - A#-C#
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| 316 - 6/5 - D#-F# ; G#-C
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| 331 - 23/19 - G-B
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| 336 - 17/14 - D-F
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| 347 - 11/9 - F#-A#
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| 359 - 16/13 - C#-E
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| 366 - 21/17 - F-A
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| 370 - 26/21 - A-C#
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| 386 - 5/4 - C-D# ; E-G#
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| 404 - 24/19 - G-C
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| 409 - 19/15 - D#-G
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| 418 - 14/11 - A#-D
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| 424 - 23/18 - F#-B
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| 435 - 9/7 - D-F#
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| 446 - 22/17 - F-A#
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| 454 - 13/10 - G#-C#
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| 460 - 30/23 - B-D#
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| 464 - 17/13 - C#-F
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| 471 - 21/16 - E-A
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| 498 - 4/3 - C-E ; D#-G# ; F#-C ; A-D
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| 523 - 23/17 - F-B
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| 529 - 19/14 - D-G
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| 537 - 15/11 - A#-D#
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| 543 - 26/19 - G-C#
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| 551 - 11/8 - E-A
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| 563 - 18/13 - C#-F#
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| 572 - 32/23 - B-E
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| 583 - 7/5 - D#-A ; G#-D
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| 597 - 24/17 - F-C
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| 603 - 17/12 - C-F
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| 617 - 10/7 - D-G# ; A-D#
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| 628 - 23/16 - E-B
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| 637 - 13/9 - F#-C#
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| 649 - 16/11 - A-E
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| 657 - 19/13 - C#-G
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| 663 - 22/15 - D#-A#
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| 671 - 28/19 - G-D
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| 677 - 34/23 - B-F
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| ...</pre></div>
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| <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="/overtone%20series">overtone series</a>:<br />
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| <br />
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| 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 />
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| <br />
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| which reduces to:<br />
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| <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<br />
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| in cents:<br />
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| 0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200<br />
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| <br />
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| Intervals between adjacent steps gradually get smaller, as is expected for overtone chunks like this:<br />
| |
| <br />
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| 13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23<br />
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| in cents:<br />
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| 139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-modes"></a><!-- ws:end:WikiTextHeadingRule:0 -->modes</h2>
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| <br />
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| 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 />
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| <br />
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| <table class="wiki_table">
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| <tr>
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| <td><br />
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| </td>
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| <td>C-12<br />
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| </td>
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| <td>C#-13<br />
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| </td>
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| <td>D-14<br />
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| </td>
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| <td>D#-15<br />
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| </td>
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| <td>E-16<br />
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| </td>
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| <td>F-17<br />
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| </td>
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| <td>F#-18<br />
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| </td>
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| <td>G-19<br />
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| </td>
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| <td>G#-20<br />
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| </td>
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| <td>A-21<br />
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| </td>
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| <td>A#-22<br />
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| </td>
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| <td>B-23<br />
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| </td>
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| </tr>
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| <tr>
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| <td>C-12<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td>139<br />
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| </td>
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| <td>267<br />
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| </td>
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| <td>386<br />
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| </td>
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| <td>498<br />
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| </td>
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| <td>603<br />
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| </td>
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| <td>702<br />
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| </td>
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| <td>796<br />
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| </td>
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| <td>884<br />
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| </td>
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| <td>969<br />
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| </td>
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| <td>1049<br />
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| </td>
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| <td>1126<br />
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| </td>
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| </tr>
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| <tr>
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| <td>C#-13<br />
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| </td>
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| <td>1061<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td>128<br />
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| </td>
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| <td>248<br />
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| </td>
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| <td>359<br />
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| </td>
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| <td>464<br />
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| </td>
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| <td>563<br />
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| </td>
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| <td>657<br />
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| </td>
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| <td>746<br />
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| </td>
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| <td>830<br />
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| </td>
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| <td>911<br />
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| </td>
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| <td>988<br />
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| </td>
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| </tr>
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| <tr>
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| <td>D-14<br />
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| </td>
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| <td>933<br />
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| </td>
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| <td>1072<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td>119<br />
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| </td>
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| <td>231<br />
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| </td>
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| <td>336<br />
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| </td>
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| <td>435<br />
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| </td>
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| <td>529<br />
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| </td>
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| <td>617<br />
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| </td>
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| <td>702<br />
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| </td>
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| <td>782<br />
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| </td>
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| <td>859<br />
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| </td>
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| </tr>
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| <tr>
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| <td>D#-15<br />
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| </td>
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| <td>814<br />
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| </td>
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| <td>952<br />
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| </td>
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| <td>1081<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td>112<br />
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| </td>
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| <td>217<br />
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| </td>
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| <td>316<br />
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| </td>
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| <td>409<br />
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| </td>
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| <td>498<br />
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| </td>
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| <td>583<br />
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| </td>
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| <td>663<br />
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| </td>
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| <td>740<br />
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| </td>
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| </tr>
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| <tr>
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| <td>E-16<br />
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| </td>
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| <td>702<br />
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| </td>
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| <td>841<br />
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| </td>
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| <td>969<br />
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| </td>
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| <td>1088<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td>105<br />
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| </td>
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| <td>204<br />
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| </td>
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| <td>298<br />
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| </td>
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| <td>386<br />
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| </td>
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| <td>471<br />
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| </td>
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| <td>551<br />
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| </td>
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| <td>628<br />
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| </td>
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| </tr>
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| <tr>
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| <td>F-17<br />
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| </td>
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| <td>597<br />
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| </td>
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| <td>736<br />
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| </td>
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| <td>864<br />
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| </td>
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| <td>983<br />
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| </td>
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| <td>1095<br />
| |
| </td>
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| <td>0<br />
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| </td>
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| <td>99<br />
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| </td>
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| <td>193<br />
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| </td>
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| <td>281<br />
| |
| </td>
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| <td>366<br />
| |
| </td>
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| <td>446<br />
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| </td>
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| <td>523<br />
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| </td>
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| </tr>
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| <tr>
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| <td>F#-18<br />
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| </td>
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| <td>498<br />
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| </td>
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| <td>637<br />
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| </td>
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| <td>765<br />
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| </td>
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| <td>884<br />
| |
| </td>
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| <td>996<br />
| |
| </td>
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| <td>1101<br />
| |
| </td>
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| <td>0<br />
| |
| </td>
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| <td>94<br />
| |
| </td>
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| <td>182<br />
| |
| </td>
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| <td>267<br />
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| </td>
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| <td>347<br />
| |
| </td>
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| <td>424<br />
| |
| </td>
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| </tr>
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| <tr>
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| <td>G-19<br />
| |
| </td>
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| <td>404<br />
| |
| </td>
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| <td>543<br />
| |
| </td>
| |
| <td>671<br />
| |
| </td>
| |
| <td>791<br />
| |
| </td>
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| <td>902<br />
| |
| </td>
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| <td>1007<br />
| |
| </td>
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| <td>1106<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| <td>89<br />
| |
| </td>
| |
| <td>173<br />
| |
| </td>
| |
| <td>254<br />
| |
| </td>
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| <td>331<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <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;h3&gt; --><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></pre></div>
| |