Otones12-24
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Andrew_Heathwaite and made on 2009-04-19 15:18:48 UTC.
- The original revision id was 68458245.
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Original Wikitext content:
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, & 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 ||
Original HTML content:
<html><head><title>otones12-24</title></head><body>A dedecatonic (12-note) scale borrowed from the overtone series:<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 />
<br />
in cents:<br />
<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 usual 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. 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>
</body></html>