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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>~~2016~~-11-~~01 18~~:39:32 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-02-24 17:21:16 UTC</tt>.

: The original revision id was <tt>~~597693168~~</tt>.

: The original revision id was <tt>607131469</tt>.

: The revision comment was: <tt>~~removed tel links~~</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.

<h4>Original Wikitext content:</h4>

Line 24:

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

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

||~ **Degrees** ||~ **Cents size** ||~ **Armodue note** ||||~ [[xenharmonic/Ups and Downs Notation|ups and]]

[[xenharmonic/Ups and Downs Notation|downs]]

[[xenharmonic/Ups and Downs Notation|notation]] ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming

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

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

|| 0 || 0 || 1 ||= P1 ||= perfect unison || 1/1 || 0 || None || 1/1 ||

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

|| 1 || 30.7692 || 1‡ (9#) ||= ^1 ||= up unison || 57/56 || 30.6421 || +0.1271 || ||

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

|| 2 || 61.5385 || 2b ||= m2 ||= minor 2nd || 29/28 || 60.7513 || +0.7872 || ||

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

|| 3 || 92.3077 || 1# ||= ^m2 ||= upminor 2nd || 39/37 || 91.1386 || +1.1691 || ||

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

|| 4 || 123.0769 || 2v ||= v~2 ||= downmid 2nd || 44/41 || 122.2555 || +0.8214 || ||

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

|| 5 || 153.8462 || 2 ||= ^~2 ||= upmid 2nd || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||

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

|| 6 || 184.6154 || 2‡ ||= vM2 ||= downmajor 2nd || 10/9 || 182.4037 || +2.2117 || 10/9 ||

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

|| 7**·** || 215.3846 || 3b ||= M2 ||= major 2nd || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||

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

|| 8 || 246.1538 || 2# ||= ^M2,

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

vm3 ||= upmajor 2nd,

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

downminor 3rd || 15/13 || 247.7411 || -1.5873 || ||

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

|| 9 || 276.9231 || 3v ||= m3 ||= minor 3rd || 27/23 || 277.5907 || -0.6676 || 7/6 ||

|| 12**·** ~~|| 4b~~ || 369.2308 || ~~26/21~~ || ~~369~~.7468 || -0.516 || ||

|| 10 || 307.6923 || 3 ||= ^m3 ||= upminor 3rd || 43/36 || 307.6077 || +0.0846 || 6/5 ||

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

|| 11 || 338.4615 || 3‡ ||= v~3 ||= downmid 3rd || 17/14 || 336.1295 || +2.332 || 11/9 ||

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

|| 12**·** || 369.2308 || 4b ||= ^~3 ||= upmid 3rd || 26/21 || 369.7468 || -0.516 || ||

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

|| 13 || 400 || 3# ||= vM3 ||= downmajor 3rd || 34/27 || 399.0904 || +0.9096 || 5/4 ||

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

|| 14 || 430.7692 || 4v (5b) ||= M3 ||= major 3rd || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||

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

|| 15 || 461.5385 || 4 ||= v4 ||= down 4th || 30/23 || 459.9944 || +1.5441 || ||

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

|| 16 || 492.3077 || 4‡ (5v) ||= P4 ||= perfect 4th || 85/64 || 491.2691 || +1.0386 || 4/3 ||

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

|| 17**·** || 523.0769 || 5 ||= ^4 ||= up 4th || 23/17 || 523.3189 || -0.242 || ||

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

|| 18 || 553.8462 || 5‡ (4#) ||= ^^4 ||= double-up 4th || 11/8 || 551.3179 || +2.5283 || 11/8 ||

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

|| 19 || 584.6154 || 6b ||= vvA4,

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

^d5 ||= double-down aug 4th, updim 5th || 7/5 || 582.5122 || +2.1032 || 7/5 ||

|| 23 ~~|| 6‡~~ || 707.6923 || ~~128/85~~ || ~~708~~.7309 || -1.0386 || 3/2 ||

|| 20 || 615.3846 || 5# ||= vA4,

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

^^d5 ||= downaug 4th, double-up dim 5th || 10/7 || 617.4878 || -2.1032 || 10/7 ||

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

|| 21 || 646.1538 || 6v ||= vv5 ||= double-down 5th || 16/11 || 648.6821 || -2.5283 || 16/11 ||

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

|| 22**·** || 676.9231 || 6 ||= v5 ||= down 5th || 34/23 || 676.6811 || +0.242 || ||

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

|| 23 || 707.6923 || 6‡ ||= P5 ||= perfect 5th || 128/85 || 708.7309 || -1.0386 || 3/2 ||

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

|| 24 || 738.4615 || 7b ||= ^5 ||= up 5th || 23/15 || 740.0056 || -1.5441 || ||

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

|| 25 || 769.2308 || 6# ||= m6 ||= minor 6th || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||

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

|| 26 || 800 || 7v ||= ^m6 ||= upminor 6th || 27/17 || 800.9096 || -0.9096 || 8/5 ||

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

|| 27**·** || 830.7692 || 7 ||= v~6 ||= downmid 6th || 21/13 || 830.2532 || +0.516 || ||

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

|| 28 || 861.5385 || 7‡ ||= ^~6 ||= upmid 6th || 28/17 || 863.8705 || -2.332 || 18/11 ||

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

|| 29 || 892.3077 || 8b ||= vM6 ||= downmajor 6th || 72/43 || 892.3923 || -0.0846 || 5/3 ||

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

|| 30 || 923.0769 || 7# ||= M6 ||= major 6th || 46/27 || 922.4093 || +0.6676 || 12/7 ||

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

|| 31 || 953.8462 || 8v ||= ^M6,

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

vm7 ||= upmajor 6th,

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

downminor 7th || 26/15 || 952.2589 || +1.5873 || ||

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

|| 32**·** || 984.6154 || 8 ||= m7 ||= minor 7th || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||

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

|| 33 || 1015.3846 || 8‡ ||= ^m7 ||= upminor 7th || 9/5 || 1017.5963 || -2.2117 || 9/5 ||

|| 34 || 1046.1538 || 9b ||= v~7 ||= downmid 7th || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||

|| 35 || 1076.9231 || 8# ||= ^~7 ||= upmid 7th || 41/22 || 1077.7445 || -0.8214 || ||

|| 36 || 1107.6923 || 9v (1b) ||= vM7 ||= downmajor 7th || 74/39 || 1108.8614 || -1.1691 || ||

|| 37 || 1138.4615 || 9 ||= M7 ||= major 7th || 56/29 || 1139.2487 || -0.7872 || ||

|| 38 || 1169.2308 || 9‡ (1v) ||= v8 ||= down-8ve || 112/57 || 1169.3579 || -0.1271 || ||

|| 39**··**(or 0) || 1200 || 1 ||= P8 ||= perfect 8ve || 2/1 || 1200 || None || ||

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].

==__Instruments (prototypes):__==

Line 183:

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<tr>

<th>Degrees

</th>

<th>Cents size

</th>

<th>Armodue note

</th>

<th><~~strong~~>~~Cents size~~</~~strong~~>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">downs</a>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">notation</a>

</th>

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

Line 199:

Line 212:

</tr>

<tr>

<td>0

</td>

<td>0

</td>

<td>1

</td>

<td>0

<td style="text-align: center;">P1

</td>

<td style="text-align: center;">perfect unison

</td>

<td>1/1

Line 216:

Line 233:

<tr>

<td>1

</td>

<td>30.7692

</td>

<td>1‡ (9#)

</td>

<td>~~30.7692~~

<td style="text-align: center;">^1

</td>

<td style="text-align: center;">up unison

</td>

<td>57/56

Line 232:

Line 253:

<tr>

<td>2

</td>

<td>61.5385

</td>

<td>2b

</td>

<td>~~61.5385~~

<td style="text-align: center;">m2

</td>

<td style="text-align: center;">minor 2nd

</td>

<td>29/28

Line 248:

Line 273:

<tr>

<td>3

</td>

<td>92.3077

</td>

<td>1#

</td>

<td>~~92.3077~~

<td style="text-align: center;">^m2

</td>

<td style="text-align: center;">upminor 2nd

</td>

<td>39/37

Line 264:

Line 293:

<tr>

<td>4

</td>

<td>123.0769

</td>

<td>2v

</td>

<td>~~123.0769~~

<td style="text-align: center;">v~2

</td>

<td style="text-align: center;">downmid 2nd

</td>

<td>44/41

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Line 313:

<tr>

<td>5

</td>

<td>153.8462

</td>

<td>2

</td>

<td>~~153.8462~~

<td style="text-align: center;">^~2

</td>

<td style="text-align: center;">upmid 2nd

</td>

<td>35/32

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Line 333:

<tr>

<td>6

</td>

<td>184.6154

</td>

<td>2‡

</td>

<td>~~184.6154~~

<td style="text-align: center;">vM2

</td>

<td style="text-align: center;">downmajor 2nd

</td>

<td>10/9

Line 312:

Line 353:

<tr>

<td>7·

</td>

<td>215.3846

</td>

<td>3b

</td>

<td>~~215.3846~~

<td style="text-align: center;">M2

</td>

<td style="text-align: center;">major 2nd

</td>

<td>17/15

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Line 373:

<tr>

<td>8

</td>

<td>246.1538

</td>

<td>2#

</td>

<td>~~246.1538~~

<td style="text-align: center;">^M2,

vm3

</td>

<td style="text-align: center;">upmajor 2nd,

downminor 3rd

</td>

<td>15/13

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Line 395:

<tr>

<td>9

</td>

<td>276.9231

</td>

<td>3v

</td>

<td>~~276.9231~~

<td style="text-align: center;">m3

</td>

<td style="text-align: center;">minor 3rd

</td>

<td>27/23

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Line 415:

<tr>

<td>10

</td>

<td>307.6923

</td>

<td>3

</td>

<td>~~307.6923~~

<td style="text-align: center;">^m3

</td>

<td style="text-align: center;">upminor 3rd

</td>

<td>43/36

Line 376:

Line 435:

<tr>

<td>11

</td>

<td>338.4615

</td>

<td>3‡

</td>

<td>~~338.4615~~

<td style="text-align: center;">v~3

</td>

<td style="text-align: center;">downmid 3rd

</td>

<td>17/14

Line 392:

Line 455:

<tr>

<td>12·

</td>

<td>369.2308

</td>

<td>4b

</td>

<td>~~369.2308~~

<td style="text-align: center;">^~3

</td>

<td style="text-align: center;">upmid 3rd

</td>

<td>26/21

Line 408:

Line 475:

<tr>

<td>13

</td>

<td>400

</td>

<td>3#

</td>

<td>~~400~~

<td style="text-align: center;">vM3

</td>

<td style="text-align: center;">downmajor 3rd

</td>

<td>34/27

Line 424:

Line 495:

<tr>

<td>14

</td>

<td>430.7692

</td>

<td>4v (5b)

</td>

<td>~~430.7692~~

<td style="text-align: center;">M3

</td>

<td style="text-align: center;">major 3rd

</td>

<td>41/32

Line 440:

Line 515:

<tr>

<td>15

</td>

<td>461.5385

</td>

<td>4

</td>

<td>~~461.5385~~

<td style="text-align: center;">v4

</td>

<td style="text-align: center;">down 4th

</td>

<td>30/23

Line 456:

Line 535:

<tr>

<td>16

</td>

<td>492.3077

</td>

<td>4‡ (5v)

</td>

<td>~~492.3077~~

<td style="text-align: center;">P4

</td>

<td style="text-align: center;">perfect 4th

</td>

<td>85/64

Line 472:

Line 555:

<tr>

<td>17·

</td>

<td>523.0769

</td>

<td>5

</td>

<td>~~523.0769~~

<td style="text-align: center;">^4

</td>

<td style="text-align: center;">up 4th

</td>

<td>23/17

Line 488:

Line 575:

<tr>

<td>18

</td>

<td>553.8462

</td>

<td>5‡ (4#)

</td>

<td>~~553.8462~~

<td style="text-align: center;">^^4

</td>

<td style="text-align: center;">double-up 4th

</td>

<td>11/8

Line 504:

Line 595:

<tr>

<td>19

</td>

<td>584.6154

</td>

<td>6b

</td>

<td>~~584.6154~~

<td style="text-align: center;">vvA4,

^d5

</td>

<td style="text-align: center;">double-down aug 4th, updim 5th

</td>

<td>7/5

Line 520:

Line 616:

<tr>

<td>20

</td>

<td>615.3846

</td>

<td>5#

</td>

<td>~~615.3846~~

<td style="text-align: center;">vA4,

^^d5

</td>

<td style="text-align: center;">downaug 4th, double-up dim 5th

</td>

<td>10/7

Line 536:

Line 637:

<tr>

<td>21

</td>

<td>646.1538

</td>

<td>6v

</td>

<td>~~646.1538~~

<td style="text-align: center;">vv5

</td>

<td style="text-align: center;">double-down 5th

</td>

<td>16/11

Line 552:

Line 657:

<tr>

<td>22·

</td>

<td>676.9231

</td>

<td>6

</td>

<td>~~676.9231~~

<td style="text-align: center;">v5

</td>

<td style="text-align: center;">down 5th

</td>

<td>34/23

Line 568:

Line 677:

<tr>

<td>23

</td>

<td>707.6923

</td>

<td>6‡

</td>

<td>~~707.6923~~

<td style="text-align: center;">P5

</td>

<td style="text-align: center;">perfect 5th

</td>

<td>128/85

Line 584:

Line 697:

<tr>

<td>24

</td>

<td>738.4615

</td>

<td>7b

</td>

<td>~~738.4615~~

<td style="text-align: center;">^5

</td>

<td style="text-align: center;">up 5th

</td>

<td>23/15

Line 600:

Line 717:

<tr>

<td>25

</td>

<td>769.2308

</td>

<td>6#

</td>

<td>~~769.2308~~

<td style="text-align: center;">m6

</td>

<td style="text-align: center;">minor 6th

</td>

<td>64/41

Line 616:

Line 737:

<tr>

<td>26

</td>

<td>800

</td>

<td>7v

</td>

<td>~~800~~

<td style="text-align: center;">^m6

</td>

<td style="text-align: center;">upminor 6th

</td>

<td>27/17

Line 632:

Line 757:

<tr>

<td>27·

</td>

<td>830.7692

</td>

<td>7

</td>

<td>~~830.7692~~

<td style="text-align: center;">v~6

</td>

<td style="text-align: center;">downmid 6th

</td>

<td>21/13

Line 648:

Line 777:

<tr>

<td>28

</td>

<td>861.5385

</td>

<td>7‡

</td>

<td>~~861.5385~~

<td style="text-align: center;">^~6

</td>

<td style="text-align: center;">upmid 6th

</td>

<td>28/17

Line 664:

Line 797:

<tr>

<td>29

</td>

<td>892.3077

</td>

<td>8b

</td>

<td>~~892.3077~~

<td style="text-align: center;">vM6

</td>

<td style="text-align: center;">downmajor 6th

</td>

<td>72/43

Line 680:

Line 817:

<tr>

<td>30

</td>

<td>923.0769

</td>

<td>7#

</td>

<td>~~923.0769~~

<td style="text-align: center;">M6

</td>

<td style="text-align: center;">major 6th

</td>

<td>46/27

Line 696:

Line 837:

<tr>

<td>31

</td>

<td>953.8462

</td>

<td>8v

</td>

<td>~~953.8462~~

<td style="text-align: center;">^M6,

vm7

</td>

<td style="text-align: center;">upmajor 6th,

downminor 7th

</td>

<td>26/15

Line 712:

Line 859:

<tr>

<td>32·

</td>

<td>984.6154

</td>

<td>8

</td>

<td>~~984.6154~~

<td style="text-align: center;">m7

</td>

<td style="text-align: center;">minor 7th

</td>

<td>30/17

Line 728:

Line 879:

<tr>

<td>33

</td>

<td>1015.3846

</td>

<td>8‡

</td>

<td>~~1015.3846~~

<td style="text-align: center;">^m7

</td>

<td style="text-align: center;">upminor 7th

</td>

<td>9/5

Line 744:

Line 899:

<tr>

<td>34

</td>

<td>1046.1538

</td>

<td>9b

</td>

<td>~~1046.1538~~

<td style="text-align: center;">v~7

</td>

<td style="text-align: center;">downmid 7th

</td>

<td>64/35

Line 760:

Line 919:

<tr>

<td>35

</td>

<td>1076.9231

</td>

<td>8#

</td>

<td>~~1076.9231~~

<td style="text-align: center;">^~7

</td>

<td style="text-align: center;">upmid 7th

</td>

<td>41/22

Line 776:

Line 939:

<tr>

<td>36

</td>

<td>1107.6923

</td>

<td>9v (1b)

</td>

<td>~~1107.6923~~

<td style="text-align: center;">vM7

</td>

<td style="text-align: center;">downmajor 7th

</td>

<td>74/39

Line 792:

Line 959:

<tr>

<td>37

</td>

<td>1138.4615

</td>

<td>9

</td>

<td>~~1138.4615~~

<td style="text-align: center;">M7

</td>

<td style="text-align: center;">major 7th

</td>

<td>56/29

Line 808:

Line 979:

<tr>

<td>38

</td>

<td>1169.2308

</td>

<td>9‡ (1v)

</td>

<td>~~1169.2308~~

<td style="text-align: center;">v8

</td>

<td style="text-align: center;">down-8ve

</td>

<td>112/57

Line 824:

Line 999:

<tr>

<td>39··(or 0)

</td>

<td>1200

</td>

<td>1

</td>

<td>~~1200~~

<td style="text-align: center;">P8

</td>

<td style="text-align: center;">perfect 8ve

</td>

<td>2/1

Line 840:

Line 1,019:

</table>

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.

<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:xenwolf|xenwolf]] and made on <tt>2016-11-01 18:39:32 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-02-24 17:21:16 UTC</tt>.<br>
-: The original revision id was <tt>597693168</tt>.<br>
+: The original revision id was <tt>607131469</tt>.<br>
-: The revision comment was: <tt>removed tel links</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>
 <h4>Original Wikitext content:</h4>
@@ Line 24: / Line 24: @@
 * **v** = Semiflat (1/5-tone down) ||
-||~ **Degrees** ||~ **Armodue note** ||~ **Cents size** ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
+||~ **Degrees** ||~ **Cents size** ||~ **Armodue note** ||||~ [[xenharmonic/Ups and Downs Notation|ups and]]
+[[xenharmonic/Ups and Downs Notation|downs]]
+[[xenharmonic/Ups and Downs Notation|notation]] ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
 &lt;39 62 91 110 135| [[Val]] ||
-|| 0 || 1 || 0 || 1/1 || 0 || None || 1/1 ||
+|| 0 || 0 || 1 ||= P1 ||= perfect unison || 1/1 || 0 || None || 1/1 ||
-|| 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 ||   ||
+|| 1 || 30.7692 || 1‡ (9#) ||= ^1 ||= up unison || 57/56 || 30.6421 || +0.1271 ||   ||
-|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||   ||
+|| 2 || 61.5385 || 2b ||= m2 ||= minor 2nd || 29/28 || 60.7513 || +0.7872 ||   ||
-|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||   ||
+|| 3 || 92.3077 || 1# ||= ^m2 ||= upminor 2nd || 39/37 || 91.1386 || +1.1691 ||   ||
-|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||   ||
+|| 4 || 123.0769 || 2v ||= v~2 ||= downmid 2nd || 44/41 || 122.2555 || +0.8214 ||   ||
-|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||
+|| 5 || 153.8462 || 2 ||= ^~2 ||= upmid 2nd || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||
-|| 6 || 2‡ || 184.6154 || 10/9 || 182.4037 || +2.2117 || 10/9 ||
+|| 6 || 184.6154 || 2‡ ||= vM2 ||= downmajor 2nd || 10/9 || 182.4037 || +2.2117 || 10/9 ||
-|| 7**·** || 3b || 215.3846 || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||
+|| 7**·** || 215.3846 || 3b ||= M2 ||= major 2nd || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||
-|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||   ||
+|| 8 || 246.1538 || 2# ||= ^M2,
-|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 || 7/6 ||
+vm3 ||= upmajor 2nd,
-|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 || 6/5 ||
+downminor 3rd || 15/13 || 247.7411 || -1.5873 ||   ||
-|| 11 || 3‡ || 338.4615 || 17/14 || 336.1295 || +2.332 || 11/9 ||
+|| 9 || 276.9231 || 3v ||= m3 ||= minor 3rd || 27/23 || 277.5907 || -0.6676 || 7/6 ||
-|| 12**·** || 4b || 369.2308 || 26/21 || 369.7468 || -0.516 ||   ||
+|| 10 || 307.6923 || 3 ||= ^m3 ||= upminor 3rd || 43/36 || 307.6077 || +0.0846 || 6/5 ||
-|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 || 5/4 ||
+|| 11 || 338.4615 || 3‡ ||= v~3 ||= downmid 3rd || 17/14 || 336.1295 || +2.332 || 11/9 ||
-|| 14 || 4v (5b) || 430.7692 || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||
+|| 12**·** || 369.2308 || 4b ||= ^~3 ||= upmid 3rd || 26/21 || 369.7468 || -0.516 ||   ||
-|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||   ||
+|| 13 || 400 || 3# ||= vM3 ||= downmajor 3rd || 34/27 || 399.0904 || +0.9096 || 5/4 ||
-|| 16 || 4‡ (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 || 4/3 ||
+|| 14 || 430.7692 || 4v (5b) ||= M3 ||= major 3rd || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||
-|| 17**·** || 5 || 523.0769 || 23/17 || 523.3189 || -0.242 ||   ||
+|| 15 || 461.5385 || 4 ||= v4 ||= down 4th || 30/23 || 459.9944 || +1.5441 ||   ||
-|| 18 || 5‡ (4#) || 553.8462 || 11/8 || 551.3179 || +2.5283 || 11/8 ||
+|| 16 || 492.3077 || 4‡ (5v) ||= P4 ||= perfect 4th || 85/64 || 491.2691 || +1.0386 || 4/3 ||
-|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 || 7/5 ||
+|| 17**·** || 523.0769 || 5 ||= ^4 ||= up 4th || 23/17 || 523.3189 || -0.242 ||   ||
-|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 || 10/7 ||
+|| 18 || 553.8462 || 5‡ (4#) ||= ^^4 ||= double-up 4th || 11/8 || 551.3179 || +2.5283 || 11/8 ||
-|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 || 16/11 ||
+|| 19 || 584.6154 || 6b ||= vvA4,
-|| 22**·** || 6 || 676.9231 || 34/23 || 676.6811 || +0.242 ||   ||
+^d5 ||= double-down aug 4th, updim 5th || 7/5 || 582.5122 || +2.1032 || 7/5 ||
-|| 23 || 6‡ || 707.6923 || 128/85 || 708.7309 || -1.0386 || 3/2 ||
+|| 20 || 615.3846 || 5# ||= vA4,
-|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||   ||
+^^d5 ||= downaug 4th, double-up dim 5th || 10/7 || 617.4878 || -2.1032 || 10/7 ||
-|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||
+|| 21 || 646.1538 || 6v ||= vv5 ||= double-down 5th || 16/11 || 648.6821 || -2.5283 || 16/11 ||
-|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 || 8/5 ||
+|| 22**·** || 676.9231 || 6 ||= v5 ||= down 5th || 34/23 || 676.6811 || +0.242 ||   ||
-|| 27**·** || 7 || 830.7692 || 21/13 || 830.2532 || +0.516 ||   ||
+|| 23 || 707.6923 || 6‡ ||= P5 ||= perfect 5th || 128/85 || 708.7309 || -1.0386 || 3/2 ||
-|| 28 || 7‡ || 861.5385 || 28/17 || 863.8705 || -2.332 || 18/11 ||
+|| 24 || 738.4615 || 7b ||= ^5 ||= up 5th || 23/15 || 740.0056 || -1.5441 ||   ||
-|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 || 5/3 ||
+|| 25 || 769.2308 || 6# ||= m6 ||= minor 6th || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||
-|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 || 12/7 ||
+|| 26 || 800 || 7v ||= ^m6 ||= upminor 6th || 27/17 || 800.9096 || -0.9096 || 8/5 ||
-|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||   ||
+|| 27**·** || 830.7692 || 7 ||= v~6 ||= downmid 6th || 21/13 || 830.2532 || +0.516 ||   ||
-|| 32**·** || 8 || 984.6154 || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||
+|| 28 || 861.5385 || 7‡ ||= ^~6 ||= upmid 6th || 28/17 || 863.8705 || -2.332 || 18/11 ||
-|| 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
+|| 29 || 892.3077 || 8b ||= vM6 ||= downmajor 6th || 72/43 || 892.3923 || -0.0846 || 5/3 ||
-|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
+|| 30 || 923.0769 || 7# ||= M6 ||= major 6th || 46/27 || 922.4093 || +0.6676 || 12/7 ||
-|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||   ||
+|| 31 || 953.8462 || 8v ||= ^M6,
-|| 36 || 9v (1b) || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||   ||
+vm7 ||= upmajor 6th,
-|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||   ||
+downminor 7th || 26/15 || 952.2589 || +1.5873 ||   ||
-|| 38 || 9‡ (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||   ||
+|| 32**·** || 984.6154 || 8 ||= m7 ||= minor 7th || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||
-|| 39**··**(or 0) || 1 || 1200 || 2/1 || 1200 || None ||   ||
+|| 33 || 1015.3846 || 8‡ ||= ^m7 ||= upminor 7th || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
+|| 34 || 1046.1538 || 9b ||= v~7 ||= downmid 7th || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
+|| 35 || 1076.9231 || 8# ||= ^~7 ||= upmid 7th || 41/22 || 1077.7445 || -0.8214 ||   ||
+|| 36 || 1107.6923 || 9v (1b) ||= vM7 ||= downmajor 7th || 74/39 || 1108.8614 || -1.1691 ||   ||
+|| 37 || 1138.4615 || 9 ||= M7 ||= major 7th || 56/29 || 1139.2487 || -0.7872 ||   ||
+|| 38 || 1169.2308 || 9‡ (1v) ||= v8 ||= down-8ve || 112/57 || 1169.3579 || -0.1271 ||   ||
+|| 39**··**(or 0) || 1200 || 1 ||= P8 ||= perfect 8ve || 2/1 || 1200 || None ||   ||
+Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].
 ==__Instruments (prototypes):__==
@@ Line 183: / Line 192: @@
      &lt;tr&gt;
          &lt;th&gt;&lt;strong&gt;Degrees&lt;/strong&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;strong&gt;Cents size&lt;/strong&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;&lt;strong&gt;Armodue note&lt;/strong&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;&lt;strong&gt;Cents size&lt;/strong&gt;&lt;br /&gt;
+         &lt;th colspan="2"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;ups and&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;downs&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
 &lt;/th&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;
@@ Line 199: / Line 212: @@
      &lt;/tr&gt;
      &lt;tr&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1/1&lt;br /&gt;
@@ Line 216: / Line 233: @@
      &lt;tr&gt;
          &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;30.7692&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1‡ (9#)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;30.7692&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;57/56&lt;br /&gt;
@@ Line 232: / Line 253: @@
      &lt;tr&gt;
          &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;61.5385&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;61.5385&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;29/28&lt;br /&gt;
@@ Line 248: / Line 273: @@
      &lt;tr&gt;
          &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;92.3077&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92.3077&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;39/37&lt;br /&gt;
@@ Line 264: / Line 293: @@
      &lt;tr&gt;
          &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;123.0769&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;123.0769&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmid 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;44/41&lt;br /&gt;
@@ Line 280: / Line 313: @@
      &lt;tr&gt;
          &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;153.8462&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;153.8462&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmid 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;35/32&lt;br /&gt;
@@ Line 296: / Line 333: @@
      &lt;tr&gt;
          &lt;td&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;184.6154&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;184.6154&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/9&lt;br /&gt;
@@ Line 312: / Line 353: @@
      &lt;tr&gt;
          &lt;td&gt;7&lt;strong&gt;·&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;215.3846&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;215.3846&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/15&lt;br /&gt;
@@ Line 328: / Line 373: @@
      &lt;tr&gt;
          &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;246.1538&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;246.1538&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M2,&lt;br /&gt;
+vm3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmajor 2nd,&lt;br /&gt;
+downminor 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/13&lt;br /&gt;
@@ Line 344: / Line 395: @@
      &lt;tr&gt;
          &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;276.9231&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;276.9231&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/23&lt;br /&gt;
@@ Line 360: / Line 415: @@
      &lt;tr&gt;
          &lt;td&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;307.6923&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;307.6923&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;43/36&lt;br /&gt;
@@ Line 376: / Line 435: @@
      &lt;tr&gt;
          &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;338.4615&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;338.4615&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmid 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/14&lt;br /&gt;
@@ Line 392: / Line 455: @@
      &lt;tr&gt;
          &lt;td&gt;12&lt;strong&gt;·&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;369.2308&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;4b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;369.2308&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmid 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;26/21&lt;br /&gt;
@@ Line 408: / Line 475: @@
      &lt;tr&gt;
          &lt;td&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;400&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;400&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;34/27&lt;br /&gt;
@@ Line 424: / Line 495: @@
      &lt;tr&gt;
          &lt;td&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;430.7692&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;4v (5b)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;430.7692&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;41/32&lt;br /&gt;
@@ Line 440: / Line 515: @@
      &lt;tr&gt;
          &lt;td&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;461.5385&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;461.5385&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;30/23&lt;br /&gt;
@@ Line 456: / Line 535: @@
      &lt;tr&gt;
          &lt;td&gt;16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;492.3077&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;4‡ (5v)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;492.3077&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;85/64&lt;br /&gt;
@@ Line 472: / Line 555: @@
      &lt;tr&gt;
          &lt;td&gt;17&lt;strong&gt;·&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;523.0769&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;523.0769&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;23/17&lt;br /&gt;
@@ Line 488: / Line 575: @@
      &lt;tr&gt;
          &lt;td&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;553.8462&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5‡ (4#)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;553.8462&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;11/8&lt;br /&gt;
@@ Line 504: / Line 595: @@
      &lt;tr&gt;
          &lt;td&gt;19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;584.6154&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;6b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;584.6154&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vvA4,&lt;br /&gt;
+^d5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-down aug 4th, updim 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
@@ Line 520: / Line 616: @@
      &lt;tr&gt;
          &lt;td&gt;20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;615.3846&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;615.3846&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vA4,&lt;br /&gt;
+^^d5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downaug 4th, double-up dim 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/7&lt;br /&gt;
@@ Line 536: / Line 637: @@
      &lt;tr&gt;
          &lt;td&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;646.1538&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;6v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;646.1538&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-down 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;16/11&lt;br /&gt;
@@ Line 552: / Line 657: @@
      &lt;tr&gt;
          &lt;td&gt;22&lt;strong&gt;·&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;676.9231&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;676.9231&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;34/23&lt;br /&gt;
@@ Line 568: / Line 677: @@
      &lt;tr&gt;
          &lt;td&gt;23&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;707.6923&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;6‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;707.6923&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;128/85&lt;br /&gt;
@@ Line 584: / Line 697: @@
      &lt;tr&gt;
          &lt;td&gt;24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;738.4615&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;738.4615&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;23/15&lt;br /&gt;
@@ Line 600: / Line 717: @@
      &lt;tr&gt;
          &lt;td&gt;25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;769.2308&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;6#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;769.2308&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;64/41&lt;br /&gt;
@@ Line 616: / Line 737: @@
      &lt;tr&gt;
          &lt;td&gt;26&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;800&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;800&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/17&lt;br /&gt;
@@ Line 632: / Line 757: @@
      &lt;tr&gt;
          &lt;td&gt;27&lt;strong&gt;·&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;830.7692&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;830.7692&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;21/13&lt;br /&gt;
@@ Line 648: / Line 777: @@
      &lt;tr&gt;
          &lt;td&gt;28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;861.5385&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;861.5385&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmid 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;28/17&lt;br /&gt;
@@ Line 664: / Line 797: @@
      &lt;tr&gt;
          &lt;td&gt;29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;892.3077&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;892.3077&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;72/43&lt;br /&gt;
@@ Line 680: / Line 817: @@
      &lt;tr&gt;
          &lt;td&gt;30&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;923.0769&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;923.0769&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;46/27&lt;br /&gt;
@@ Line 696: / Line 837: @@
      &lt;tr&gt;
          &lt;td&gt;31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;953.8462&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;953.8462&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M6,&lt;br /&gt;
+vm7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmajor 6th,&lt;br /&gt;
+downminor 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;26/15&lt;br /&gt;
@@ Line 712: / Line 859: @@
      &lt;tr&gt;
          &lt;td&gt;32&lt;strong&gt;·&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;984.6154&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;984.6154&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;30/17&lt;br /&gt;
@@ Line 728: / Line 879: @@
      &lt;tr&gt;
          &lt;td&gt;33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1015.3846&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1015.3846&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/5&lt;br /&gt;
@@ Line 744: / Line 899: @@
      &lt;tr&gt;
          &lt;td&gt;34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1046.1538&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1046.1538&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmid 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;64/35&lt;br /&gt;
@@ Line 760: / Line 919: @@
      &lt;tr&gt;
          &lt;td&gt;35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1076.9231&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1076.9231&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmid 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;41/22&lt;br /&gt;
@@ Line 776: / Line 939: @@
      &lt;tr&gt;
          &lt;td&gt;36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1107.6923&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9v (1b)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1107.6923&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;74/39&lt;br /&gt;
@@ Line 792: / Line 959: @@
      &lt;tr&gt;
          &lt;td&gt;37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1138.4615&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1138.4615&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;56/29&lt;br /&gt;
@@ Line 808: / Line 979: @@
      &lt;tr&gt;
          &lt;td&gt;38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1169.2308&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9‡ (1v)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1169.2308&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down-8ve&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;112/57&lt;br /&gt;
@@ Line 824: / Line 999: @@
      &lt;tr&gt;
          &lt;td&gt;39&lt;strong&gt;··&lt;/strong&gt;(or 0)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2/1&lt;br /&gt;
@@ Line 840: / Line 1,019: @@
 &lt;/table&gt;
+Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&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="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:704:&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:704 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:866:&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:866 --&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:705:&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:705 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:867:&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:867 --&gt;&lt;br /&gt;
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