39edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>2013-05-~~06 04~~:37:29 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-05-15 09:02:49 UTC</tt>.

: The original revision id was <tt>~~429130986~~</tt>.

: The original revision id was <tt>431722584</tt>.

: The revision comment was: <tt></tt>

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

Line 19:

* **v** = Semiflat (1/5-tone down) ||

|| **Degrees** || **Armodue note** || **Cents size** || **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** || **Cents value** || **Error** ||

||~ **Degrees** ||~ **Armodue note** ||~ **Cents size** ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming

|| 0 || **1** || 0 || **1/1** || 0 || **None** ||

<39 62 91 110 135| [[Val]] ||

|| 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 ||

|| 0 || 1 || 0 || 1/1 || 0 || None || 1/1 ||

|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||

|| 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 || ||

|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||

|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 || ||

|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||

|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 || ||

|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 ||

|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 || ||

|| 6 || 2‡ || 184.6154 || 10/9 || 182.4037 || +2.2117 ||

|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||

|| 7**·** || 3b || 215.3846 || 17/15 || 216.6867 || -1.3021 ||

|| 6 || 2‡ || 184.6154 || 10/9 || 182.4037 || +2.2117 || 10/9 ||

|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||

|| 7**·** || 3b || 215.3846 || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||

|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 ||

|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 || ||

|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 ||

|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 || 7/6 ||

|| 11 || 3‡ || 338.4615 || 17/14 || 336.1295 || +2.332 ||

|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 || 6/5 ||

|| 12**·** || 4b || 369.2308 || 26/21 || 369.7468 || -0.516 ||

|| 11 || 3‡ || 338.4615 || 17/14 || 336.1295 || +2.332 || 11/9 ||

|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 ||

|| 12**·** || 4b || 369.2308 || 26/21 || 369.7468 || -0.516 || ||

|| 14 || 4v (5b) || 430.7692 || 41/32 || 429.0624 || +1.7068 ||

|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 || 5/4 ||

|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||

|| 14 || 4v (5b) || 430.7692 || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||

|| 16 || 4‡ (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 ||

|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 || ||

|| 17**·** || 5 || 523.0769 || 23/17 || 523.3189 || -0.242 ||

|| 16 || 4‡ (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 || 4/3 ||

|| 18 || 5‡ (4#) || 553.8462 || 11/8 || 551.3179 || +2.5283 ||

|| 17**·** || 5 || 523.0769 || 23/17 || 523.3189 || -0.242 || ||

|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 ||

|| 18 || 5‡ (4#) || 553.8462 || 11/8 || 551.3179 || +2.5283 || 11/8 ||

|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 ||

|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 || 7/5 ||

|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 ||

|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 || 10/7 ||

|| 22**·** || 6 || 676.9231 || 34/23 || 676.6811 || +0.242 ||

|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 || 16/11 ||

|| 23 || 6‡ || 707.6923 || 128/85 || 708.7309 || -1.0386 ||

|| 22**·** || 6 || 676.9231 || 34/23 || 676.6811 || +0.242 || ||

|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||

|| 23 || 6‡ || 707.6923 || 128/85 || 708.7309 || -1.0386 || 3/2 ||

|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 ||

|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 || ||

|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 ||

|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||

|| 27**·** || 7 || 830.7692 || 21/13 || 830.2532 || +0.516 ||

|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 || 8/5 ||

|| 28 || 7‡ || 861.5385 || 28/17 || 863.8705 || -2.332 ||

|| 27**·** || 7 || 830.7692 || 21/13 || 830.2532 || +0.516 || ||

|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 ||

|| 28 || 7‡ || 861.5385 || 28/17 || 863.8705 || -2.332 || 18/11 ||

|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 ||

|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 || 5/3 ||

|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||

|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 || 12/7 ||

|| 32**·** || 8 || 984.6154 || 30/17 || 983.3133 || +1.3021 ||

|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 || ||

|| 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 ||

|| 32**·** || 8 || 984.6154 || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||

|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||

|| 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || 9/5 ||

|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||

|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||

|| 36 || 9v (1b) || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||

|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 || ||

|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||

|| 36 || 9v (1b) || 1107.6923 || 74/39 || 1108.8614 || -1.1691 || ||

|| 38 || 9‡ (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||

|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 || ||

|| 39**··**(or 0) || 1 || 1200 || 2/1 || 1200 || None ||

|| 38 || 9‡ (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 || ||

|| 39**··**(or 0) || 1 || 1200 || 2/1 || 1200 || None || ||

==__Instruments (prototypes):__==

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<tr>

<td>Degrees

<th>Degrees

</td>

</th>

<td>Armodue note

<th>Armodue note

</td>

</th>

<td>Cents size

<th>Cents size

</td>

</th>

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nearest%20just%20interval">Nearest Just I</a>nterval

<th><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nearest%20just%20interval">Nearest Just I</a>nterval

</td>

</th>

<td>Cents value

<th>Cents value

</td>

</th>

<td>Error

<th>Error

</td>

</th>

<th>11-limit Ratio Assuming

&lt;39 62 91 110 135| <a class="wiki_link" href="/Val">Val</a>

</th>

</tr>

<tr>

<td>0

</td>

<td~~><strong~~>1~~~~

<td>1

</td>

<td>0

</td>

<td~~><strong~~>1/1~~~~

<td>1/1

</td>

<td>0

</td>

<td>None

</td>

<td>1/1

</td>

</tr>

Line 178:

Line 184:

</td>

<td>+0.1271

</td>

<td>

</td>

</tr>

Line 192:

Line 200:

</td>

<td>+0.7872

</td>

<td>

</td>

</tr>

Line 206:

Line 216:

</td>

<td>+1.1691

</td>

<td>

</td>

</tr>

Line 220:

Line 232:

</td>

<td>+0.8214

</td>

<td>

</td>

</tr>

Line 234:

Line 248:

</td>

<td>-1.2934

</td>

<td>12/11, 11/10

</td>

</tr>

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Line 264:

</td>

<td>+2.2117

</td>

<td>10/9

</td>

</tr>

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Line 280:

</td>

<td>-1.3021

</td>

<td>8/7, 9/8

</td>

</tr>

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Line 296:

</td>

<td>-1.5873

</td>

<td>

</td>

</tr>

Line 290:

Line 312:

</td>

<td>-0.6676

</td>

<td>7/6

</td>

</tr>

Line 304:

Line 328:

</td>

<td>+0.0846

</td>

<td>6/5

</td>

</tr>

Line 318:

Line 344:

</td>

<td>+2.332

</td>

<td>11/9

</td>

</tr>

Line 332:

Line 360:

</td>

<td>-0.516

</td>

<td>

</td>

</tr>

Line 346:

Line 376:

</td>

<td>+0.9096

</td>

<td>5/4

</td>

</tr>

Line 360:

Line 392:

</td>

<td>+1.7068

</td>

<td>9/7, 14/11

</td>

</tr>

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Line 408:

</td>

<td>+1.5441

</td>

<td>

</td>

</tr>

Line 388:

Line 424:

</td>

<td>+1.0386

</td>

<td>4/3

</td>

</tr>

Line 402:

Line 440:

</td>

<td>-0.242

</td>

<td>

</td>

</tr>

Line 416:

Line 456:

</td>

<td>+2.5283

</td>

<td>11/8

</td>

</tr>

Line 430:

Line 472:

</td>

<td>+2.1032

</td>

<td>7/5

</td>

</tr>

Line 444:

Line 488:

</td>

<td>-2.1032

</td>

<td>10/7

</td>

</tr>

Line 458:

Line 504:

</td>

<td>-2.5283

</td>

<td>16/11

</td>

</tr>

Line 472:

Line 520:

</td>

<td>+0.242

</td>

<td>

</td>

</tr>

Line 486:

Line 536:

</td>

<td>-1.0386

</td>

<td>3/2

</td>

</tr>

Line 500:

Line 552:

</td>

<td>-1.5441

</td>

<td>

</td>

</tr>

Line 514:

Line 568:

</td>

<td>-1.7068

</td>

<td>14/9, 11/7

</td>

</tr>

Line 528:

Line 584:

</td>

<td>-0.9096

</td>

<td>8/5

</td>

</tr>

Line 542:

Line 600:

</td>

<td>+0.516

</td>

<td>

</td>

</tr>

Line 556:

Line 616:

</td>

<td>-2.332

</td>

<td>18/11

</td>

</tr>

Line 570:

Line 632:

</td>

<td>-0.0846

</td>

<td>5/3

</td>

</tr>

Line 584:

Line 648:

</td>

<td>+0.6676

</td>

<td>12/7

</td>

</tr>

Line 598:

Line 664:

</td>

<td>+1.5873

</td>

<td>

</td>

</tr>

Line 612:

Line 680:

</td>

<td>+1.3021

</td>

<td>7/4, 16/9

</td>

</tr>

Line 626:

Line 696:

</td>

<td>-2.2117

</td>

<td>9/5

</td>

</tr>

Line 640:

Line 712:

</td>

<td>+1.2934

</td>

<td>11/6, 20/11

</td>

</tr>

Line 654:

Line 728:

</td>

<td>-0.8214

</td>

<td>

</td>

</tr>

Line 668:

Line 744:

</td>

<td>-1.1691

</td>

<td>

</td>

</tr>

Line 682:

Line 760:

</td>

<td>-0.7872

</td>

<td>

</td>

</tr>

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Line 776:

</td>

<td>-0.1271

</td>

<td>

</td>

</tr>

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Line 792:

</td>

<td>None

</td>

<td>

</td>

</tr>

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<h2 id="toc2"><a name="x39 tone equal temperament-Instruments (prototypes):"></a>Instruments (prototypes):</h2>

<img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" />

<img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" />

An illustrative image of a 39-ED2 keyboard

<table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /></td></tr><tr><td class="imageCaption">39-EDD fretboard visualization</td></tr></table>

<table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /></td></tr><tr><td class="imageCaption">39-EDD fretboard visualization</td></tr></table>

@@ 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-05-06 04:37:29 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-05-15 09:02:49 UTC</tt>.<br>
-: The original revision id was <tt>429130986</tt>.<br>
+: The original revision id was <tt>431722584</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 19: / Line 19: @@
 * **v** = Semiflat (1/5-tone down) ||
-|| **Degrees** || **Armodue note** || **Cents size** || **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** || **Cents value** || **Error** ||
+||~ **Degrees** ||~ **Armodue note** ||~ **Cents size** ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
-|| 0 || **1** || 0 || **1/1** || 0 || **None** ||
+&lt;39 62 91 110 135| [[Val]] ||
-|| 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 ||
+|| 0 || 1 || 0 || 1/1 || 0 || None || 1/1 ||
-|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||
+|| 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 ||   ||
-|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||
+|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||   ||
-|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||
+|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||   ||
-|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 ||
+|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||   ||
-|| 6 || 2‡ || 184.6154 || 10/9 || 182.4037 || +2.2117 ||
+|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||
-|| 7**·** || 3b || 215.3846 || 17/15 || 216.6867 || -1.3021 ||
+|| 6 || 2‡ || 184.6154 || 10/9 || 182.4037 || +2.2117 || 10/9 ||
-|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||
+|| 7**·** || 3b || 215.3846 || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||
-|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 ||
+|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||   ||
-|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 ||
+|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 || 7/6 ||
-|| 11 || 3‡ || 338.4615 || 17/14 || 336.1295 || +2.332 ||
+|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 || 6/5 ||
-|| 12**·** || 4b || 369.2308 || 26/21 || 369.7468 || -0.516 ||
+|| 11 || 3‡ || 338.4615 || 17/14 || 336.1295 || +2.332 || 11/9 ||
-|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 ||
+|| 12**·** || 4b || 369.2308 || 26/21 || 369.7468 || -0.516 ||   ||
-|| 14 || 4v (5b) || 430.7692 || 41/32 || 429.0624 || +1.7068 ||
+|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 || 5/4 ||
-|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||
+|| 14 || 4v (5b) || 430.7692 || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||
-|| 16 || 4‡ (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 ||
+|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||   ||
-|| 17**·** || 5 || 523.0769 || 23/17 || 523.3189 || -0.242 ||
+|| 16 || 4‡ (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 || 4/3 ||
-|| 18 || 5‡ (4#) || 553.8462 || 11/8 || 551.3179 || +2.5283 ||
+|| 17**·** || 5 || 523.0769 || 23/17 || 523.3189 || -0.242 ||   ||
-|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 ||
+|| 18 || 5‡ (4#) || 553.8462 || 11/8 || 551.3179 || +2.5283 || 11/8 ||
-|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 ||
+|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 || 7/5 ||
-|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 ||
+|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 || 10/7 ||
-|| 22**·** || 6 || 676.9231 || 34/23 || 676.6811 || +0.242 ||
+|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 || 16/11 ||
-|| 23 || 6‡ || 707.6923 || 128/85 || 708.7309 || -1.0386 ||
+|| 22**·** || 6 || 676.9231 || 34/23 || 676.6811 || +0.242 ||   ||
-|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||
+|| 23 || 6‡ || 707.6923 || 128/85 || 708.7309 || -1.0386 || 3/2 ||
-|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 ||
+|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||   ||
-|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 ||
+|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||
-|| 27**·** || 7 || 830.7692 || 21/13 || 830.2532 || +0.516 ||
+|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 || 8/5 ||
-|| 28 || 7‡ || 861.5385 || 28/17 || 863.8705 || -2.332 ||
+|| 27**·** || 7 || 830.7692 || 21/13 || 830.2532 || +0.516 ||   ||
-|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 ||
+|| 28 || 7‡ || 861.5385 || 28/17 || 863.8705 || -2.332 || 18/11 ||
-|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 ||
+|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 || 5/3 ||
-|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||
+|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 || 12/7 ||
-|| 32**·** || 8 || 984.6154 || 30/17 || 983.3133 || +1.3021 ||
+|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||   ||
-|| 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 ||
+|| 32**·** || 8 || 984.6154 || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||
-|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||
+|| 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
-|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||
+|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
-|| 36 || 9v (1b) || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||
+|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||   ||
-|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||
+|| 36 || 9v (1b) || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||   ||
-|| 38 || 9‡ (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||
+|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||   ||
-|| 39**··**(or 0) || 1 || 1200 || 2/1 || 1200 || None ||
+|| 38 || 9‡ (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||   ||
+|| 39**··**(or 0) || 1 || 1200 || 2/1 || 1200 || None ||   ||
 ==__Instruments (prototypes):__==
@@ Line 139: / Line 140: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;Degrees&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;strong&gt;Degrees&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;&lt;strong&gt;Armodue note&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;strong&gt;Armodue note&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;&lt;strong&gt;Cents size&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;strong&gt;Cents size&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nearest%20just%20interval"&gt;Nearest Just I&lt;/a&gt;nterval&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;strong&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nearest%20just%20interval"&gt;Nearest Just I&lt;/a&gt;nterval&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;&lt;strong&gt;Cents value&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;strong&gt;Cents value&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;&lt;strong&gt;Error&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;strong&gt;Error&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
+        &lt;th&gt;11-limit Ratio Assuming&lt;br /&gt;
+&amp;lt;39 62 91 110 135| &lt;a class="wiki_link" href="/Val"&gt;Val&lt;/a&gt;&lt;br /&gt;
+&lt;/th&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;1&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;1/1&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;None&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;None&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 178: / Line 184: @@
 &lt;/td&gt;
          &lt;td&gt;+0.1271&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 192: / Line 200: @@
 &lt;/td&gt;
          &lt;td&gt;+0.7872&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 206: / Line 216: @@
 &lt;/td&gt;
          &lt;td&gt;+1.1691&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 220: / Line 232: @@
 &lt;/td&gt;
          &lt;td&gt;+0.8214&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 234: / Line 248: @@
 &lt;/td&gt;
          &lt;td&gt;-1.2934&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12/11, 11/10&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 248: / Line 264: @@
 &lt;/td&gt;
          &lt;td&gt;+2.2117&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10/9&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 262: / Line 280: @@
 &lt;/td&gt;
          &lt;td&gt;-1.3021&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8/7, 9/8&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 276: / Line 296: @@
 &lt;/td&gt;
          &lt;td&gt;-1.5873&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 290: / Line 312: @@
 &lt;/td&gt;
          &lt;td&gt;-0.6676&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/6&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 304: / Line 328: @@
 &lt;/td&gt;
          &lt;td&gt;+0.0846&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 318: / Line 344: @@
 &lt;/td&gt;
          &lt;td&gt;+2.332&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/9&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 332: / Line 360: @@
 &lt;/td&gt;
          &lt;td&gt;-0.516&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 346: / Line 376: @@
 &lt;/td&gt;
          &lt;td&gt;+0.9096&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 360: / Line 392: @@
 &lt;/td&gt;
          &lt;td&gt;+1.7068&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/7, 14/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 374: / Line 408: @@
 &lt;/td&gt;
          &lt;td&gt;+1.5441&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 388: / Line 424: @@
 &lt;/td&gt;
          &lt;td&gt;+1.0386&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 402: / Line 440: @@
 &lt;/td&gt;
          &lt;td&gt;-0.242&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 416: / Line 456: @@
 &lt;/td&gt;
          &lt;td&gt;+2.5283&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/8&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 430: / Line 472: @@
 &lt;/td&gt;
          &lt;td&gt;+2.1032&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 444: / Line 488: @@
 &lt;/td&gt;
          &lt;td&gt;-2.1032&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 458: / Line 504: @@
 &lt;/td&gt;
          &lt;td&gt;-2.5283&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 472: / Line 520: @@
 &lt;/td&gt;
          &lt;td&gt;+0.242&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 486: / Line 536: @@
 &lt;/td&gt;
          &lt;td&gt;-1.0386&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 500: / Line 552: @@
 &lt;/td&gt;
          &lt;td&gt;-1.5441&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 514: / Line 568: @@
 &lt;/td&gt;
          &lt;td&gt;-1.7068&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/9, 11/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 528: / Line 584: @@
 &lt;/td&gt;
          &lt;td&gt;-0.9096&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 542: / Line 600: @@
 &lt;/td&gt;
          &lt;td&gt;+0.516&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 556: / Line 616: @@
 &lt;/td&gt;
          &lt;td&gt;-2.332&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;18/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 570: / Line 632: @@
 &lt;/td&gt;
          &lt;td&gt;-0.0846&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5/3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 584: / Line 648: @@
 &lt;/td&gt;
          &lt;td&gt;+0.6676&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 598: / Line 664: @@
 &lt;/td&gt;
          &lt;td&gt;+1.5873&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 612: / Line 680: @@
 &lt;/td&gt;
          &lt;td&gt;+1.3021&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/4, 16/9&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 626: / Line 696: @@
 &lt;/td&gt;
          &lt;td&gt;-2.2117&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 640: / Line 712: @@
 &lt;/td&gt;
          &lt;td&gt;+1.2934&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/6, 20/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 654: / Line 728: @@
 &lt;/td&gt;
          &lt;td&gt;-0.8214&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 668: / Line 744: @@
 &lt;/td&gt;
          &lt;td&gt;-1.1691&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 682: / Line 760: @@
 &lt;/td&gt;
          &lt;td&gt;-0.7872&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 696: / Line 776: @@
 &lt;/td&gt;
          &lt;td&gt;-0.1271&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 710: / Line 792: @@
 &lt;/td&gt;
          &lt;td&gt;None&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 717: / Line 801: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x39 tone equal temperament-Instruments (prototypes):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;Instruments (prototypes):&lt;/u&gt;&lt;/h2&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:604:&amp;lt;img src=&amp;quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 467px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:604 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:686:&amp;lt;img src=&amp;quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 467px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:686 --&gt;&lt;br /&gt;
 &lt;em&gt;An illustrative image of a 39-ED2 keyboard&lt;/em&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:605:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;39-EDD fretboard visualization&amp;quot; title=&amp;quot;39-EDD fretboard visualization&amp;quot; style=&amp;quot;height: 203px; width: 826px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDD fretboard visualization&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:605 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:687:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;39-EDD fretboard visualization&amp;quot; title=&amp;quot;39-EDD fretboard visualization&amp;quot; style=&amp;quot;height: 203px; width: 826px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDD fretboard visualization&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:687 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;