24edo: Difference between revisions

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<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:~~JosephRuhf~~|~~JosephRuhf~~]] and made on <tt>2016-12-05 14:50:46 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 05:28:42 UTC</tt>.

: The original revision id was <tt>~~601447262~~</tt>.

: The original revision id was <tt>602740098</tt>.

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

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The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate.

|| Degree || Cents ~~coarse/fine~~

||= Degree ||= Cents ||= Approximate Ratios* ||||||= [[Ups and Downs Notation|ups and downs notation]] ||

~~DMS~~ ||= Approximate Ratios* ||||= [[Ups and Downs Notation|ups and downs notation]] ||

||= 0 ||= 0 ||= 1/1 ||= P1 ||= unison ||= C ||

|| 0 || 0 ||= 1/1 || unison || P1 ||

||= 1 ||= 50 ||= 33/32, 34/33 ||= ^P1, vm2 ||= up-unison, downminor 2nd ||= C^, Dbv ||

|| 1 || 50~~, 60~~

||= 2 ||= 100 ||= 17/16, 18/17 ||= A1, m2 ||= aug unison, minor 2nd ||= C#, Db ||

~~15°~~ ||= 33/32, 34/33 || up-unison,

||= 3 ||= 150 ||= 12/11 ||= ~2 ||= mid 2nd ||= Dv ||

downminor 2nd || ^P1, ~~vm2~~ ||

||= 4 ||= 200 ||= 9/8 ||= M2 ||= major 2nd ||= D ||

|| 2 || 100~~, 120~~

||= 5 ||= 250 ||= 22/19 ||= ^M2, vm3 ||= upmajor 2nd, downminor 3rd ||= D^, Ebv ||

~~30°~~ ||= 17/16, 18/17 || aug unison,

||= 6 ||= 300 ||= 19/16 ||= m3 ||= minor 3rd ||= Eb ||

minor 2nd || A1, m2 ||

||= 7 ||= 350 ||= 11/9 ||= ~3 ||= mid 3rd ||= Ev ||

|| 3 || 150~~, 180~~

||= 8 ||= 400 ||= 24/19 ||= M3 ||= major 3rd ||= E ||

~~45°~~ ||= 12/11 || mid 2nd || ~2 ||

||= 9 ||= 450 ||= 22/17 ||= ^M3, vP4 ||= upmajor 3rd, down-fourth ||= E^, Fv ||

|| 4 || 200~~, 240~~

||= 10 ||= 500 ||= 4/3 ||= P4 ||= fourth ||= F ||

~~60°~~ ||= 9/8 || major 2nd || M2 ||

||= 11 ||= 550 ||= 11/8 ||= ^P4 ||= up-fourth ||= F^ ||

|| 5 || 250~~, 300~~

||= 12 ||= 600 ||= 17/12 ||= A4, d5 ||= aug 4th, dim 5th ||= F#, Gb ||

~~75°~~ ||= 22/19 || upmajor 2nd,

||= 13 ||= 650 ||= 16/11 ||= vP5 ||= down-fifth ||= Gv ||

downminor 3rd || ^M2, ~~vm3~~ ||

||= 14 ||= 700 ||= 3/2 ||= P5 ||= fifth ||= G ||

|| 6 || 300~~, 360~~

||= 15 ||= 750 ||= 17/11 ||= ^P5, vm6 ||= up-fifth, downminor 6th ||= G^, Abv ||

~~90°~~ ||= 19/16 || minor 3rd || m3 ||

||= 16 ||= 800 ||= 19/12 ||= m6 ||= minor 6th ||= Ab ||

|| 7 || 350~~, 420~~

||= 17 ||= 850 ||= 18/11 ||= ~6 ||= mid 6th ||= Av ||

~~105°~~ ||= 11/9 || mid 3rd || ~3 ||

||= 18 ||= 900 ||= 32/19 ||= M6 ||= major 6th ||= A ||

|| 8 || 400~~, 480~~

||= 19 ||= 950 ||= 19/11 ||= ^M6, vm7 ||= upmajor 6th, downminor 7th ||= A^, Bbv ||

~~120°~~ ||= 24/19 || major 3rd || M3 ||

||= 20 ||= 1000 ||= 16/9 ||= m7 ||= minor 7th ||= Bb ||

|| 9 || 450~~, 540~~

||= 21 ||= 1050 ||= 11/6 ||= ~7 ||= mid 7th ||= Bv ||

~~135°~~ ||= 22/17 || upmajor 3rd,

||= 22 ||= 1100 ||= 17/9, 32/17 ||= M7 ||= major 7th ||= B ||

down-fourth || ^M3, ~~vP4~~ ||

||= 23 ||= 1150 ||= 33/17, 64/33 ||= ^M7, vP8 ||= upmajor 7th, down-8ve ||= B^, Cv ||

|| 10 || 500~~, 600~~

||= 24 ||= 1200 ||= 2/1 ||= P8 ||= perfect 8ve ||= C ||

~~150°~~ ||= 4/3 || fourth || P4 ||

|| 11 || 550~~, 660~~

~~165°~~ ||= 11/8 || up-fourth || ^P4 ||

|| 12 || 600~~, 720~~

~~180°~~ ||= 17/12 || ~~augmented~~ 4th,

~~diminished~~ 5th || A4, d5 ||

|| 13 || 650~~, 780~~

~~195°~~ ||= 16/11 || down-fifth || ~~vP5~~ ||

|| 14 || 700~~, 840~~

~~210°~~ ||= 3/2 || fifth || P5 ||

|| 15 || 750~~, 900~~

~~225°~~ ||= 17/11 || up-fifth,

downminor 6th || ^P5, ~~vm6~~ ||

|| 16 || 800~~, 960~~

240* ||= 19/12 || minor 6th || m6 ||

|| 17 || 850~~, 1020~~

~~255°~~ ||= 18/11 || mid 6th || ~6 ||

|| 18 || 900~~, 1080~~

~~270°~~ ||= 32/19 || major 6th || M6 ||

|| 19 || 950~~, 1140~~

~~285°~~ ||= 19/11 || upmajor 6th,

downminor 7th || ^M6, ~~vm7~~ ||

|| 20 || 1000~~, 1200~~

~~300°~~ ||= 16/9 || minor 7th || m7 ||

|| 21 || 1050~~, 1260~~

~~315°~~ ||= 11/6 || mid 7th || ~7 ||

|| 22 || 1100~~, 1320~~

~~330°~~ ||= 17/9, 32/17 || major 7th || M7 ||

|| 23 || 1150~~, 1380~~

~~345°~~ ||= 33/17, 64/33 || upmajor 7th,

down-~~octave~~ || ^M7, ~~vP8~~ ||

*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.

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Line 450:

<tr>

<td>Degree

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

</td>

<td>Cents ~~coarse/fine ~~

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

~~DMS~~

</td>

<td style="text-align: center;">Approximate Ratios*

</td>

<td colspan="2" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a>

<td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a>

</td>

</tr>

<tr>

<td>0

<td style="text-align: center;">0

</td>

<td>0

<td style="text-align: center;">0

</td>

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

</td>

<td>~~unison~~

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

</td>

<td>P1

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

</td>

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

</td>

</tr>

<tr>

<td>1

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

</td>

<td>50~~, 60 ~~

<td style="text-align: center;">50

~~15°~~

</td>

<td style="text-align: center;">33/32, 34/33

</td>

<td~~>up~~-~~unison,&lt~~;~~br /~~>

<td style="text-align: center;">^P1, vm2

~~downminor 2nd~~

</td>

<td>^P1, ~~vm2~~

<td style="text-align: center;">up-unison, downminor 2nd

</td>

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

</td>

</tr>

<tr>

<td>2

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

</td>

<td>100~~, 120 ~~

<td style="text-align: center;">100

~~30°~~

</td>

<td style="text-align: center;">17/16, 18/17

</td>

<td>~~aug unison~~,~~ ~~

<td style="text-align: center;">A1, m2

~~minor 2nd~~

</td>

<td>A1, m2

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

</td>

<td style="text-align: center;">C#, Db

</td>

</tr>

<tr>

<td>3

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

</td>

<td>150~~, 180 ~~

<td style="text-align: center;">150

~~45°~~

</td>

<td style="text-align: center;">12/11

</td>

<td>~~mid 2nd~~

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

</td>

<td>~2

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

</td>

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

</td>

</tr>

<tr>

<td>4

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

</td>

<td>200~~, 240 ~~

<td style="text-align: center;">200

~~60°~~

</td>

<td style="text-align: center;">9/8

</td>

<td>major 2nd

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

</td>

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

</td>

<td>M2

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

</td>

</tr>

<tr>

<td>5

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

</td>

<td>250~~, 300 ~~

<td style="text-align: center;">250

~~75°~~

</td>

<td style="text-align: center;">22/19

</td>

<td>~~upmajor 2nd~~,

<td style="text-align: center;">^M2, vm3

downminor 3rd

</td>

<td style="text-align: center;">upmajor 2nd, downminor 3rd

</td>

<td>^M2, ~~vm3~~

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

</td>

</tr>

<tr>

<td>6

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

</td>

<td>300~~, 360 ~~

<td style="text-align: center;">300

~~90°~~

</td>

<td style="text-align: center;">19/16

</td>

<td>minor 3rd

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

</td>

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

</td>

<td>m3

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

</td>

</tr>

<tr>

<td>7

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

</td>

<td>350~~, 420 ~~

<td style="text-align: center;">350

~~105°~~

</td>

<td style="text-align: center;">11/9

</td>

<td>~~mid 3rd~~

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

</td>

<td>~3

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

</td>

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

</td>

</tr>

<tr>

<td>8

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

</td>

<td>400~~, 480 ~~

<td style="text-align: center;">400

~~120°~~

</td>

<td style="text-align: center;">24/19

</td>

<td>~~major 3rd~~

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

</td>

<td>M3

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

</td>

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

</td>

</tr>

<tr>

<td>9

<td style="text-align: center;">9

</td>

<td>450~~, 540 ~~

<td style="text-align: center;">450

~~135°~~

</td>

<td style="text-align: center;">22/17

</td>

<td>~~upmajor 3rd~~,~~ ~~

<td style="text-align: center;">^M3, vP4

~~down-fourth~~

</td>

<td>^M3, ~~vP4~~

<td style="text-align: center;">upmajor 3rd, down-fourth

</td>

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

</td>

</tr>

<tr>

<td>10

<td style="text-align: center;">10

</td>

<td>500~~, 600 ~~

<td style="text-align: center;">500

~~150°~~

</td>

<td style="text-align: center;">4/3

</td>

<td>~~fourth~~

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

</td>

<td>P4

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

</td>

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

</td>

</tr>

<tr>

<td>11

<td style="text-align: center;">11

</td>

<td>550~~, 660 ~~

<td style="text-align: center;">550

~~165°~~

</td>

<td style="text-align: center;">11/8

</td>

<td>up-fourth

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

</td>

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

</td>

<td>^P4

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

</td>

</tr>

<tr>

<td>12

<td style="text-align: center;">12

</td>

<td>600~~, 720 ~~

<td style="text-align: center;">600

~~180°~~

</td>

<td style="text-align: center;">17/12

</td>

<td>~~augmented 4th~~,~~ ~~

<td style="text-align: center;">A4, d5

~~diminished 5th~~

</td>

<td>A4, d5

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

</td>

<td style="text-align: center;">F#, Gb

</td>

</tr>

<tr>

<td>13

<td style="text-align: center;">13

</td>

<td>650~~, 780 ~~

<td style="text-align: center;">650

~~195°~~

</td>

<td style="text-align: center;">16/11

</td>

<td>down-fifth

<td style="text-align: center;">vP5

</td>

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

</td>

<td>~~vP5~~

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

</td>

</tr>

<tr>

<td>14

<td style="text-align: center;">14

</td>

<td>700~~, 840 ~~

<td style="text-align: center;">700

~~210°~~

</td>

<td style="text-align: center;">3/2

</td>

<td>fifth

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

</td>

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

</td>

<td>P5

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

</td>

</tr>

<tr>

<td>15

<td style="text-align: center;">15

</td>

<td>750~~, 900 ~~

<td style="text-align: center;">750

~~225°~~

</td>

<td style="text-align: center;">17/11

</td>

<td~~>up~~-~~fifth,&lt~~;~~br /~~>

<td style="text-align: center;">^P5, vm6

~~downminor 6th~~

</td>

<td>^P5, ~~vm6~~

<td style="text-align: center;">up-fifth, downminor 6th

</td>

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

</td>

</tr>

<tr>

<td>16

<td style="text-align: center;">16

</td>

<td>800~~, 960 ~~

<td style="text-align: center;">800

240*

</td>

<td style="text-align: center;">19/12

</td>

<td>~~minor 6th~~

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

</td>

<td>m6

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

</td>

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

</td>

</tr>

<tr>

<td>17

<td style="text-align: center;">17

</td>

<td>850~~, 1020 ~~

<td style="text-align: center;">850

~~255°~~

</td>

<td style="text-align: center;">18/11

</td>

<td>~~mid 6th~~

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

</td>

<td>~6

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

</td>

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

</td>

</tr>

<tr>

<td>18

<td style="text-align: center;">18

</td>

<td>900~~, 1080 ~~

<td style="text-align: center;">900

~~270°~~

</td>

<td style="text-align: center;">32/19

</td>

<td>~~major 6th~~

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

</td>

<td>M6

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

</td>

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

</td>

</tr>

<tr>

<td>19

<td style="text-align: center;">19

</td>

<td>950~~, 1140 ~~

<td style="text-align: center;">950

~~285°~~

</td>

<td style="text-align: center;">19/11

</td>

<td>~~upmajor 6th~~,

<td style="text-align: center;">^M6, vm7

downminor 7th

</td>

<td style="text-align: center;">upmajor 6th, downminor 7th

</td>

<td>^M6, ~~vm7~~

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

</td>

</tr>

<tr>

<td>20

<td style="text-align: center;">20

</td>

<td>1000~~, 1200 ~~

<td style="text-align: center;">1000

~~300°~~

</td>

<td style="text-align: center;">16/9

</td>

<td>~~minor 7th~~

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

</td>

<td>m7

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

</td>

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

</td>

</tr>

<tr>

<td>21

<td style="text-align: center;">21

</td>

<td>1050~~, 1260 ~~

<td style="text-align: center;">1050

~~315°~~

</td>

<td style="text-align: center;">11/6

</td>

<td>~~mid 7th~~

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

</td>

<td>~7

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

</td>

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

</td>

</tr>

<tr>

<td>22

<td style="text-align: center;">22

</td>

<td>1100~~, 1320 ~~

<td style="text-align: center;">1100

~~330°~~

</td>

<td style="text-align: center;">17/9, 32/17

</td>

<td>~~major 7th~~

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

</td>

<td>M7

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

</td>

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

</td>

</tr>

<tr>

<td>23

<td style="text-align: center;">23

</td>

<td>1150~~, 1380 ~~

<td style="text-align: center;">1150

~~345°~~

</td>

<td style="text-align: center;">33/17, 64/33

</td>

<td>upmajor 7th,

<td style="text-align: center;">^M7, vP8

~~down~~-~~octave~~

</td>

<td style="text-align: center;">upmajor 7th, down-8ve

</td>

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

</td>

</tr>

<tr>

<td style="text-align: center;">24

</td>

<td style="text-align: center;">1200

</td>

<td style="text-align: center;">2/1

</td>

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

</td>

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

</td>

<td>~~^M7, vP8~~

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

</td>

</tr>

Line 1,354:

Line 1,353:

<h2 id="toc5"><a name="Notation-Mainstream Quartertone Notation"></a>Mainstream Quartertone Notation</h2>

<img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /> or ^ = quarter-tone sharp or &quot;Jump&quot; or &quot;up&quot;

<img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /> or ^ = quarter-tone sharp or &quot;Jump&quot; or &quot;up&quot;

<img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /> or #^ or ^# = three-quarter-tone sharp or &quot;Jump-Sharp&quot; or &quot;upsharp&quot;

<img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /> or #^ or ^# = three-quarter-tone sharp or &quot;Jump-Sharp&quot; or &quot;upsharp&quot;

<img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /> or v = quarter-tone flat or &quot;Drop&quot; or &quot;down&quot;

<img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /> or v = quarter-tone flat or &quot;Drop&quot; or &quot;down&quot;

<img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /> or bv or vb = three-quarter-tone flat or &quot;Drop-Flat&quot; or &quot;downflat&quot;

<img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /> or bv or vb = three-quarter-tone flat or &quot;Drop-Flat&quot; or &quot;downflat&quot;

Pros: Familiar, fairly easy to learn

Line 1,363:

Line 1,362:

<h2 id="toc6"><a name="Notation-Alternate Quartertone Accidentals"></a>Alternate Quartertone Accidentals</h2>

<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> = quarter-tone sharp or Jump

<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> = quarter-tone sharp or Jump

††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp

<img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /> = quarter-tone flat or Drop

<img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /> = quarter-tone flat or Drop

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /> = three quarter-tones flat or drop-flat

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /> = three quarter-tones flat or drop-flat

For example, the scale 0-5-10-15-20 is written as C-D<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or E<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" />) F G<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or A<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" />) Bb.

For example, the scale 0-5-10-15-20 is written as C-D<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or E<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" />) F G<img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /> (or A<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" />) Bb.

Pros: Very easy to distinguish accidentals from one another

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<h2 id="toc7"><a name="Notation-And in Persian music"></a>And in Persian music</h2>

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" />Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" />Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" />Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop

<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" />Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop

Pros: Easy to read

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with Sagittal signs for sharp and flat.

<img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" />

<img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" />

<h1 id="toc9"><a name="Interval Alterations"></a>Interval Alterations</h1>

Line 1,408:

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William Lynch considers these as some possible good tetrads:

<img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" />

<img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" />

Line 2,264:

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<h1 id="toc23"><a name="Instruments"></a>Instruments<a name="instruments"></a></h1>

The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This <a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales">&quot;12 note octave scales&quot;</a> approach is used in a wide part of the existing literature - see below.

<img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" />24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars

<img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" />24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars

Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called <a class="wiki_link" href="/Iceface%20Tuning">Iceface tuning</a>.

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<h1 id="toc27"><a name="Practical Theory / Books"></a>Practical Theory / Books</h1>

<img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" />&quot;Icosakaiteraphonic Scales for Guitar&quot; - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.

<img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" />&quot;Icosakaiteraphonic Scales for Guitar&quot; - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.

<h1 id="toc28"><a name="External links"></a>External links</h1>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 14:50:46 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 05:28:42 UTC</tt>.<br>
-: The original revision id was <tt>601447262</tt>.<br>
+: The original revision id was <tt>602740098</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 17: / Line 17: @@
 The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate.
-|| Degree || Cents coarse/fine
+||= Degree ||= Cents ||= Approximate Ratios* ||||||= [[Ups and Downs Notation|ups and downs notation]] ||
-DMS ||= Approximate Ratios* ||||= [[Ups and Downs Notation|ups and downs notation]] ||
+||= 0 ||= 0 ||= 1/1 ||= P1 ||= unison ||= C ||
-|| 0 || 0 ||= 1/1 || unison || P1 ||
+||= 1 ||= 50 ||= 33/32, 34/33 ||= ^P1, vm2 ||= up-unison, downminor 2nd ||= C^, Dbv ||
-|| 1 || 50, 60
+||= 2 ||= 100 ||= 17/16, 18/17 ||= A1, m2 ||= aug unison, minor 2nd ||= C#, Db ||
-° ||= 33/32, 34/33 || up-unison,
+||= 3 ||= 150 ||= 12/11 ||= ~2 ||= mid 2nd ||= Dv ||
-downminor 2nd || ^P1, vm2 ||
+||= 4 ||= 200 ||= 9/8 ||= M2 ||= major 2nd ||= D ||
-|| 2 || 100, 120
+||= 5 ||= 250 ||= 22/19 ||= ^M2, vm3 ||= upmajor 2nd, downminor 3rd ||= D^, Ebv ||
-° ||= 17/16, 18/17 || aug unison,
+||= 6 ||= 300 ||= 19/16 ||= m3 ||= minor 3rd ||= Eb ||
-minor 2nd || A1, m2 ||
+||= 7 ||= 350 ||= 11/9 ||= ~3 ||= mid 3rd ||= Ev ||
-|| 3 || 150, 180
+||= 8 ||= 400 ||= 24/19 ||= M3 ||= major 3rd ||= E ||
-° ||= 12/11 || mid 2nd || ~2 ||
+||= 9 ||= 450 ||= 22/17 ||= ^M3, vP4 ||= upmajor 3rd, down-fourth ||= E^, Fv ||
-|| 4 || 200, 240
+||= 10 ||= 500 ||= 4/3 ||= P4 ||= fourth ||= F ||
-° ||= 9/8 || major 2nd || M2 ||
+||= 11 ||= 550 ||= 11/8 ||= ^P4 ||= up-fourth ||= F^ ||
-|| 5 || 250, 300
+||= 12 ||= 600 ||= 17/12 ||= A4, d5 ||= aug 4th, dim 5th ||= F#, Gb ||
-° ||= 22/19 || upmajor 2nd,
+||= 13 ||= 650 ||= 16/11 ||= vP5 ||= down-fifth ||= Gv ||
-downminor 3rd || ^M2, vm3 ||
+||= 14 ||= 700 ||= 3/2 ||= P5 ||= fifth ||= G ||
-|| 6 || 300, 360
+||= 15 ||= 750 ||= 17/11 ||= ^P5, vm6 ||= up-fifth, downminor 6th ||= G^, Abv ||
-° ||= 19/16 || minor 3rd || m3 ||
+||= 16 ||= 800 ||= 19/12 ||= m6 ||= minor 6th ||= Ab ||
-|| 7 || 350, 420
+||= 17 ||= 850 ||= 18/11 ||= ~6 ||= mid 6th ||= Av ||
-° ||= 11/9 || mid 3rd || ~3 ||
+||= 18 ||= 900 ||= 32/19 ||= M6 ||= major 6th ||= A ||
-|| 8 || 400, 480
+||= 19 ||= 950 ||= 19/11 ||= ^M6, vm7 ||= upmajor 6th, downminor 7th ||= A^, Bbv ||
-° ||= 24/19 || major 3rd || M3 ||
+||= 20 ||= 1000 ||= 16/9 ||= m7 ||= minor 7th ||= Bb ||
-|| 9 || 450, 540
+||= 21 ||= 1050 ||= 11/6 ||= ~7 ||= mid 7th ||= Bv ||
-° ||= 22/17 || upmajor 3rd,
+||= 22 ||= 1100 ||= 17/9, 32/17 ||= M7 ||= major 7th ||= B ||
-down-fourth || ^M3, vP4 ||
+||= 23 ||= 1150 ||= 33/17, 64/33 ||= ^M7, vP8 ||= upmajor 7th, down-8ve ||= B^, Cv ||
-|| 10 || 500, 600
+||= 24 ||= 1200 ||= 2/1 ||= P8 ||= perfect 8ve ||= C ||
-° ||= 4/3 || fourth || P4 ||
-|| 11 || 550, 660
-° ||= 11/8 || up-fourth || ^P4 ||
-|| 12 || 600, 720
-° ||= 17/12 || augmented 4th,
-diminished 5th || A4, d5 ||
-|| 13 || 650, 780
-° ||= 16/11 || down-fifth || vP5 ||
-|| 14 || 700, 840
-° ||= 3/2 || fifth || P5 ||
-|| 15 || 750, 900
-° ||= 17/11 || up-fifth,
-downminor 6th || ^P5, vm6 ||
-|| 16 || 800, 960
-* ||= 19/12 || minor 6th || m6 ||
-|| 17 || 850, 1020
-° ||= 18/11 || mid 6th || ~6 ||
-|| 18 || 900, 1080
-° ||= 32/19 || major 6th || M6 ||
-|| 19 || 950, 1140
-° ||= 19/11 || upmajor 6th,
-downminor 7th || ^M6, vm7 ||
-|| 20 || 1000, 1200
-° ||= 16/9 || minor 7th || m7 ||
-|| 21 || 1050, 1260
-° ||= 11/6 || mid 7th || ~7 ||
-|| 22 || 1100, 1320
-° ||= 17/9, 32/17 || major 7th || M7 ||
-|| 23 || 1150, 1380
-° ||= 33/17, 64/33 || upmajor 7th,
-down-octave || ^M7, vP8 ||
 *based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.
@@ Line 481: / Line 450: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;Degree&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Degree&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents coarse/fine&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Cents&lt;br /&gt;
-DMS&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Approximate Ratios*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
+         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;unison&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;P1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;50, 60&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;50&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/32, 34/33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;up-unison,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^P1, vm2&lt;br /&gt;
-downminor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;^P1, vm2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-unison, downminor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C^, Dbv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;100, 120&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;100&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/16, 18/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;aug unison,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A1, m2&lt;br /&gt;
-minor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A1, m2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;aug unison, minor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#, Db&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;150, 180&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;150&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;12/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;mid 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;~2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;mid 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;200, 240&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;200&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;major 2nd&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;M2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;250, 300&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;250&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;upmajor 2nd,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M2, vm3&lt;br /&gt;
-downminor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmajor 2nd, downminor 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;^M2, vm3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^, Ebv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;300, 360&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;300&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;minor 3rd&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;m3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;350, 420&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;350&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;mid 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;~3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;mid 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;400, 480&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;400&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;24/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;major 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;450, 540&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;450&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;upmajor 3rd,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M3, vP4&lt;br /&gt;
-down-fourth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;^M3, vP4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmajor 3rd, down-fourth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E^, Fv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;500, 600&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;500&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;fourth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;P4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;fourth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;550, 660&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;550&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;up-fourth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^P4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up-fourth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;^P4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600, 720&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;600&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;augmented 4th,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A4, d5&lt;br /&gt;
-diminished 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A4, d5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;aug 4th, dim 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#, Gb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;650, 780&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;650&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;down-fifth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vP5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down-fifth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;vP5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Gv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;700, 840&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;700&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;fifth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;fifth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;P5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;750, 900&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;750&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;up-fifth,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^P5, vm6&lt;br /&gt;
-downminor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;^P5, vm6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-fifth, downminor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G^, Abv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;800, 960&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;800&lt;br /&gt;
-*&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;minor 6th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;m6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Ab&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;850, 1020&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;850&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;mid 6th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;~6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;mid 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;900, 1080&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;900&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;32/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;major 6th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;950, 1140&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;950&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;upmajor 6th,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M6, vm7&lt;br /&gt;
-downminor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmajor 6th, downminor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;^M6, vm7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^, Bbv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1000, 1200&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1000&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;minor 7th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;m7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1050, 1260&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1050&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;mid 7th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;~7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;mid 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;22&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1100, 1320&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1100&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/9, 32/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;major 7th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;M7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1150, 1380&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1150&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/17, 64/33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;upmajor 7th,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M7, vP8&lt;br /&gt;
-down-octave&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upmajor 7th, down-8ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B^, Cv&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
+&lt;/td&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;^M7, vP8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,354: / Line 1,353: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Notation-Mainstream Quartertone Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Mainstream Quartertone Notation&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:1632:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1632 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot; or &amp;quot;up&amp;quot;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:1694:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1694 --&gt; or ^ = quarter-tone sharp or &amp;quot;Jump&amp;quot; or &amp;quot;up&amp;quot;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1633:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1633 --&gt; or #^ or ^# = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot; or &amp;quot;upsharp&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1695:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/s34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1695 --&gt; or #^ or ^# = three-quarter-tone sharp or &amp;quot;Jump-Sharp&amp;quot; or &amp;quot;upsharp&amp;quot;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1634:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1634 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot; or &amp;quot;down&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1696:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f14_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1696 --&gt; or v = quarter-tone flat or &amp;quot;Drop&amp;quot; or &amp;quot;down&amp;quot;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1635:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1635 --&gt; or bv or vb = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot; or &amp;quot;downflat&amp;quot;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1697:&amp;lt;img src=&amp;quot;http://www.wfg.woodwind.org/n/f34_blue.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1697 --&gt; or bv or vb = three-quarter-tone flat or &amp;quot;Drop-Flat&amp;quot; or &amp;quot;downflat&amp;quot;&lt;br /&gt;
 &lt;br /&gt;
 Pros: Familiar, fairly easy to learn&lt;br /&gt;
@@ Line 1,363: / Line 1,362: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Notation-Alternate Quartertone Accidentals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Alternate Quartertone Accidentals&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:1636:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1636 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:1698:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1698 --&gt; = quarter-tone sharp or Jump&lt;br /&gt;
 ††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1637:&amp;lt;img src=&amp;quot;http://www.dolmetsch.com/onequarterflat.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1637 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1699:&amp;lt;img src=&amp;quot;http://www.dolmetsch.com/onequarterflat.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1699 --&gt; = quarter-tone flat or Drop&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1638:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1638 --&gt; = three quarter-tones flat or drop-flat&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1700:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1700 --&gt; = three quarter-tones flat or drop-flat&lt;br /&gt;
-For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1639:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1639 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1640:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1640 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1641:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1641 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1642:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1642 --&gt;) Bb.&lt;br /&gt;
+For example, the scale 0-5-10-15-20 is written as C-D&lt;!-- ws:start:WikiTextRemoteImageRule:1701:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1701 --&gt; (or E&lt;!-- ws:start:WikiTextRemoteImageRule:1702:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1702 --&gt;) F G&lt;!-- ws:start:WikiTextRemoteImageRule:1703:&amp;lt;img src=&amp;quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1703 --&gt; (or A&lt;!-- ws:start:WikiTextRemoteImageRule:1704:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1704 --&gt;) Bb.&lt;br /&gt;
 &lt;br /&gt;
 Pros: Very easy to distinguish accidentals from one another&lt;br /&gt;
@@ Line 1,373: / Line 1,372: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Notation-And in Persian music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;span style="line-height: 1.5;"&gt;And in Persian music&lt;/span&gt;&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:1643:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 12px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1643 --&gt;Koron (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow"&gt;en&lt;/a&gt; | &lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone flat or Jump&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:1705:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 12px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1705 --&gt;Koron (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow"&gt;en&lt;/a&gt; | &lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone flat or Jump&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1644:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 15px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1644 --&gt;Sori (&lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone sharp or Drop&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1706:&amp;lt;img src=&amp;quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 25px; width: 15px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1706 --&gt;Sori (&lt;a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow"&gt;fa&lt;/a&gt;) = quarter-tone sharp or Drop&lt;br /&gt;
 &lt;br /&gt;
 Pros: Easy to read&lt;br /&gt;
@@ Line 1,385: / Line 1,384: @@
 with Sagittal signs for sharp and flat.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1630:&amp;lt;img src=&amp;quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1630 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:1692:&amp;lt;img src=&amp;quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1692 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Interval Alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Interval Alterations&lt;/h1&gt;
@@ Line 1,408: / Line 1,407: @@
 William Lynch considers these as some possible good tetrads:&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1631:&amp;lt;img src=&amp;quot;/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1631 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:1693:&amp;lt;img src=&amp;quot;/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1693 --&gt;&lt;br /&gt;
 &lt;br /&gt;
@@ Line 2,264: / Line 2,263: @@
 &lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Instruments&lt;!-- ws:start:WikiTextAnchorRule:91:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@instruments&amp;quot; title=&amp;quot;Anchor: instruments&amp;quot;/&amp;gt; --&gt;&lt;a name="instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:91 --&gt;&lt;/h1&gt;
   The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This &lt;a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales"&gt;&amp;quot;12 note octave scales&amp;quot;&lt;/a&gt; approach is used in a wide part of the existing literature - see below.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1645:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 195px; width: 406px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1645 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1707:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 195px; width: 406px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1707 --&gt;24-tone &amp;quot;1/4-tone&amp;quot; Guitar by Ron Sword / Sword guitars&lt;br /&gt;
 &lt;br /&gt;
 Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called &lt;a class="wiki_link" href="/Iceface%20Tuning"&gt;Iceface tuning&lt;/a&gt;.&lt;br /&gt;
@@ Line 2,287: / Line 2,286: @@
 &lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Practical Theory / Books&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:1646:&amp;lt;img src=&amp;quot;http://ronsword.com/images/24_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 236px; width: 179px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1646 --&gt;&lt;strong&gt;&amp;quot;Icosakaiteraphonic Scales for Guitar&amp;quot;&lt;/strong&gt; - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1708:&amp;lt;img src=&amp;quot;http://ronsword.com/images/24_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 236px; width: 179px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1708 --&gt;&lt;strong&gt;&amp;quot;Icosakaiteraphonic Scales for Guitar&amp;quot;&lt;/strong&gt; - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;External links&lt;/h1&gt;