27edo: 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:~~MasonGreen1~~|~~MasonGreen1~~]] and made on <tt>2016-05-~~15 02~~:06:38 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-31 16:51:10 UTC</tt>.

: The original revision id was <tt>~~583137091~~</tt>.

: The original revision id was <tt>597593470</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.

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Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.

The 27 note system ~~ore~~ one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila

The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila

==Intervals==

|| Degrees of 27-EDO || Cents value

|| Degrees of 27-EDO || Cents value coarse/fine

DMS value ||= Approximate

Ratios* ||= Solfege ||

|| 0 || 0 ||= 1/1 ||= do ||

|| 1 || 44.44

|| 1 || 44.44, 53.33

13°20' ||= 36/35, 49/48, 50/49 ||= di ||

|| 2 || 88.89

|| 2 || 88.89, 106.67

26°40' ||= 16/15, 21/20, 25/24 ||= ra ||

|| 3 || 133.33

|| 3 || 133.33, 160

40° ||= 14/13, 13/12 ||= ru ||

|| 4 || 177.78

|| 4 || 177.78, 213.33

53°20' ||= 10/9 ||= reh ||

|| 5 || 222.22

|| 5 || 222.22, 266.67

66°40' ||= 8/7, 9/8 ||= re ||

|| 6 || 266.67

|| 6 || 266.67, 320

80° ||= 7/6 ||= ma ||

|| 7 || 311.11

|| 7 || 311.11, 373.33

93°20' ||= 6/5 ||= me ||

|| 8 || 355.56

|| 8 || 355.56, 426.67

106°40' ||= 16/13 ||= mu ||

|| 9 || 400

|| 9 || 400, 480

120° ||= 5/4 ||= mi ||

|| 10 || 444.44

|| 10 || 444.44, 513.33

133°20' ||= 9/7, 13/10 ||= mo ||

|| 11 || 488.89

|| 11 || 488.89, 566.67

146°40' ||= 4/3 ||= fa ||

|| 12 || 533.33

|| 12 || 533.33, 640

160° ||= 49/36, 48/35 ||= fih ||

|| 13 || 577.78

|| 13 || 577.78, 693.33

173°20' ||= 7/5, 18/13 ||= fi ||

|| 14 || 622.22

|| 14 || 622.22, 746.67

186°40' ||= 10/7, 13/9 ||= se ||

|| 15 || 666.67

|| 15 || 666.67, 800

200° ||= 72/49, 35/24 ||= sih ||

|| 16 || 711.11

|| 16 || 711.11, 853.33

213°20' ||= 3/2 ||= so/sol ||

|| 17 || 755.56

|| 17 || 755.56, 906.67

226°40' ||= 14/9, 20/13 ||= lo ||

|| 18 || 800

|| 18 || 800, 960

240° ||= 8/5 ||= le ||

|| 19 || 844.44

|| 19 || 844.44, 1013.33

253°20' ||= 13/8 ||= lu ||

|| 20 || 888.89

|| 20 || 888.89, 1066.67

266°40' ||= 5/3 ||= la ||

|| 21 || 933.33

|| 21 || 933.33, 1120

280° ||= 12/7 ||= li ||

|| 22 || 977.78

|| 22 || 977.78, 1173.33

293°20' ||= 7/4, 16/9 ||= ta ||

|| 23 || 1022.22

|| 23 || 1022.22, 1226.67

306°40' ||= 9/5 ||= te ||

|| 24 || 1066,67

|| 24 || 1066,67, 1280

320° ||= 13/7, 24/13 ||= tu ||

|| 25 || 1111.11

|| 25 || 1111.11, 1333.33

333°20' ||= 40/21 ||= ti ||

|| 26 || 1155.56

|| 26 || 1155.56, 1386.67

346°40' ||= 35/18, 96/49, 49/25 ||= da ||

|| 27 || 1200

|| 27 || 1200, 1440

360° ||= 2/1 ||= do ||

*based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.

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/ Niner ||

==Commas==

27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.)

27 EDO tempers out the following commas. (Note: This assumes the val < [[tel:27 43 63 76 93 100|27 43 63 76 93 100]] |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

||= 128/125 ||< | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma ||= ||

||= 20000/19683 ||< | 5 -9 4 > ||> 27.66 ||= Minimal Diesis ||= Tetracot Comma ||= ||

||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||= ||

||= 4711802/4709457 ||< | 1 -27 18 > ||> 0.86 ||= Ennealimma ||= ||= ||

||= [[tel:4711802/4709457|4711802/4709457]] ||< | 1 -27 18 > ||> 0.86 ||= Ennealimma ||= ||= ||

||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= ||

||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||

Line 113:

||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||= ||= ||

||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||= ||

||= 420175/419904 ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||= ||= ||

||= [[tel:420175/419904|420175/419904]] ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||= ||= ||

||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= ||= ||

||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma ||= ||= ||

||= 250047/250000 ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||= ||= ||

||= [[tel:250047/250000|250047/250000]] ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||= ||= ||

||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||= ||

||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.69 ||= Pentacircle ||= ||= ||

Line 147:

Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less &quot;tension&quot; and thus are also more consonant.

The 27 note system ~~ore~~ one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila

The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila

<h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a>Intervals</h2>

Line 156:

<td>Degrees of 27-EDO

</td>

<td>Cents value

<td>Cents value coarse/fine

DMS value

</td>

Line 178:

<td>1

</td>

<td>44.44

<td>44.44, 53.33

13°20'

</td>

Line 189:

<td>2

</td>

<td>88.89

<td>88.89, 106.67

26°40'

</td>

Line 200:

<td>3

</td>

<td>133.33

<td>133.33, 160

40°

</td>

Line 211:

<td>4

</td>

<td>177.78

<td>177.78, 213.33

53°20'

</td>

Line 222:

<td>5

</td>

<td>222.22

<td>222.22, 266.67

66°40'

</td>

Line 233:

<td>6

</td>

<td>266.67

<td>266.67, 320

80°

</td>

Line 244:

<td>7

</td>

<td>311.11

<td>311.11, 373.33

93°20'

</td>

Line 255:

<td>8

</td>

<td>355.56

<td>355.56, 426.67

106°40'

</td>

Line 266:

<td>9

</td>

<td>400

<td>400, 480

120°

</td>

Line 277:

<td>10

</td>

<td>444.44

<td>444.44, 513.33

133°20'

</td>

Line 288:

<td>11

</td>

<td>488.89

<td>488.89, 566.67

146°40'

</td>

Line 299:

<td>12

</td>

<td>533.33

<td>533.33, 640

160°

</td>

Line 310:

<td>13

</td>

<td>577.78

<td>577.78, 693.33

173°20'

</td>

Line 321:

<td>14

</td>

<td>622.22

<td>622.22, 746.67

186°40'

</td>

Line 332:

<td>15

</td>

<td>666.67

<td>666.67, 800

200°

</td>

Line 343:

<td>16

</td>

<td>711.11

<td>711.11, 853.33

213°20'

</td>

Line 354:

<td>17

</td>

<td>755.56

<td>755.56, 906.67

226°40'

</td>

Line 365:

<td>18

</td>

<td>800

<td>800, 960

240°

</td>

Line 376:

<td>19

</td>

<td>844.44

<td>844.44, 1013.33

253°20'

</td>

Line 387:

<td>20

</td>

<td>888.89

<td>888.89, 1066.67

266°40'

</td>

Line 398:

<td>21

</td>

<td>933.33

<td>933.33, 1120

280°

</td>

Line 409:

<td>22

</td>

<td>977.78

<td>977.78, 1173.33

293°20'

</td>

Line 420:

<td>23

</td>

<td>1022.22

<td>1022.22, 1226.67

306°40'

</td>

Line 431:

<td>24

</td>

<td>1066,67

<td>1066,67, 1280

320°

</td>

Line 442:

<td>25

</td>

<td>1111.11

<td>1111.11, 1333.33

333°20'

</td>

Line 453:

<td>26

</td>

<td>1155.56

<td>1155.56, 1386.67

346°40'

</td>

Line 464:

<td>27

</td>

<td>1200

<td>1200, 1440

360°

</td>

Line 598:

<h2 id="toc3"><a name="x27 tone equal tempertament-Commas"></a>Commas</h2>

27 EDO tempers out the following commas. (Note: This assumes the val &lt; 27 43 63 76 93 100 |.)

27 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/27%2043%2063%2076%2093%20100">27 43 63 76 93 100</a> |.)

Line 659:

</tr>

<tr>

<td style="text-align: center;">4711802/4709457

<td style="text-align: center;">[[tel:4711802/4709457|4711802/4709457]]

</td>

<td style="text-align: left;">| 1 -27 18 &gt;

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</tr>

<tr>

<td style="text-align: center;">420175/419904

<td style="text-align: center;">[[tel:420175/419904|420175/419904]]

</td>

<td style="text-align: left;">| -6 -8 2 5 &gt;

Line 813:

</tr>

<tr>

<td style="text-align: center;">250047/250000

<td style="text-align: center;">[[tel:250047/250000|250047/250000]]

</td>

<td style="text-align: left;">| -4 6 -6 3 &gt;

@@ 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-05-15 02:06:38 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-31 16:51:10 UTC</tt>.<br>
-: The original revision id was <tt>583137091</tt>.<br>
+: The original revision id was <tt>597593470</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 18: / Line 18: @@
 Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
-The 27 note system ore one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila
+The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila
 ==Intervals==
-|| Degrees of 27-EDO || Cents value
+|| Degrees of 27-EDO || Cents value coarse/fine
 DMS value ||= Approximate
 Ratios* ||= Solfege ||
 || 0 || 0 ||= 1/1 ||= do ||
-|| 1 || 44.44
+|| 1 || 44.44, 53.33
 °20' ||= 36/35, 49/48, 50/49 ||= di ||
-|| 2 || 88.89
+|| 2 || 88.89, 106.67
 °40' ||= 16/15, 21/20, 25/24 ||= ra ||
-|| 3 || 133.33
+|| 3 || 133.33, 160
 ° ||= 14/13, 13/12 ||= ru ||
-|| 4 || 177.78
+|| 4 || 177.78, 213.33
 °20' ||= 10/9 ||= reh ||
-|| 5 || 222.22
+|| 5 || 222.22, 266.67
 °40' ||= 8/7, 9/8 ||= re ||
-|| 6 || 266.67
+|| 6 || 266.67, 320
 ° ||= 7/6 ||= ma ||
-|| 7 || 311.11
+|| 7 || 311.11, 373.33
 °20' ||= 6/5 ||= me ||
-|| 8 || 355.56
+|| 8 || 355.56, 426.67
 °40' ||= 16/13 ||= mu ||
-|| 9 || 400
+|| 9 || 400, 480
 ° ||= 5/4 ||= mi ||
-|| 10 || 444.44
+|| 10 || 444.44, 513.33
 °20' ||= 9/7, 13/10 ||= mo ||
-|| 11 || 488.89
+|| 11 || 488.89, 566.67
 °40' ||= 4/3 ||= fa ||
-|| 12 || 533.33
+|| 12 || 533.33, 640
 ° ||= 49/36, 48/35 ||= fih ||
-|| 13 || 577.78
+|| 13 || 577.78, 693.33
 °20' ||= 7/5, 18/13 ||= fi ||
-|| 14 || 622.22
+|| 14 || 622.22, 746.67
 °40' ||= 10/7, 13/9 ||= se ||
-|| 15 || 666.67
+|| 15 || 666.67, 800
 ° ||= 72/49, 35/24 ||= sih ||
-|| 16 || 711.11
+|| 16 || 711.11, 853.33
 °20' ||= 3/2 ||= so/sol ||
-|| 17 || 755.56
+|| 17 || 755.56, 906.67
 °40' ||= 14/9, 20/13 ||= lo ||
-|| 18 || 800
+|| 18 || 800, 960
 ° ||= 8/5 ||= le ||
-|| 19 || 844.44
+|| 19 || 844.44, 1013.33
 °20' ||= 13/8 ||= lu ||
-|| 20 || 888.89
+|| 20 || 888.89, 1066.67
 °40' ||= 5/3 ||= la ||
-|| 21 || 933.33
+|| 21 || 933.33, 1120
 ° ||= 12/7 ||= li ||
-|| 22 || 977.78
+|| 22 || 977.78, 1173.33
 °20' ||= 7/4, 16/9 ||= ta ||
-|| 23 || 1022.22
+|| 23 || 1022.22, 1226.67
 °40' ||= 9/5 ||= te ||
-|| 24 || 1066,67
+|| 24 || 1066,67, 1280
 ° ||= 13/7, 24/13 ||= tu ||
-|| 25 || 1111.11
+|| 25 || 1111.11, 1333.33
 °20' ||= 40/21 ||= ti ||
-|| 26 || 1155.56
+|| 26 || 1155.56, 1386.67
 °40' ||= 35/18, 96/49, 49/25 ||= da ||
-|| 27 || 1200
+|| 27 || 1200, 1440
 ° ||= 2/1 ||= do ||
 *based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.
@@ Line 100: / Line 100: @@
 / Niner ||
 ==Commas==
-EDO tempers out the following commas. (Note: This assumes the val &lt; 27 43 63 76 93 100 |.)
+EDO tempers out the following commas. (Note: This assumes the val &lt; [[tel:27 43 63 76 93 100|27 43 63 76 93 100]] |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
 ||= 128/125 ||&lt; | 7 0 -3 &gt; ||&gt; 41.06 ||= Diesis ||= Augmented Comma ||=   ||
 ||= 20000/19683 ||&lt; | 5 -9 4 &gt; ||&gt; 27.66 ||= Minimal Diesis ||= Tetracot Comma ||=   ||
 ||= 78732/78125 ||&lt; | 2 9 -7 &gt; ||&gt; 13.40 ||= Medium Semicomma ||= Sensipent Comma ||=   ||
-||= 4711802/4709457 ||&lt; | 1 -27 18 &gt; ||&gt; 0.86 ||= Ennealimma ||=   ||=   ||
+||= [[tel:4711802/4709457|4711802/4709457]] ||&lt; | 1 -27 18 &gt; ||&gt; 0.86 ||= Ennealimma ||=   ||=   ||
 ||= 686/675 ||&lt; | 1 -3 -2 3 &gt; ||&gt; 27.99 ||= Senga ||=   ||=   ||
 ||= 64/63 ||&lt; | 6 -2 0 -1 &gt; ||&gt; 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
@@ Line 113: / Line 113: @@
 ||= 4000/3969 ||&lt; | 5 -4 3 -2 &gt; ||&gt; 13.47 ||= Octagar ||=   ||=   ||
 ||= 1728/1715 ||&lt; | 6 3 -1 -3 &gt; ||&gt; 13.07 ||= Orwellisma ||= Orwell Comma ||=   ||
-||= 420175/419904 ||&lt; | -6 -8 2 5 &gt; ||&gt; 1.12 ||= Wizma ||=   ||=   ||
+||= [[tel:420175/419904|420175/419904]] ||&lt; | -6 -8 2 5 &gt; ||&gt; 1.12 ||= Wizma ||=   ||=   ||
 ||= 2401/2400 ||&lt; | -5 -1 -2 4 &gt; ||&gt; 0.72 ||= Breedsma ||=   ||=   ||
 ||= 4375/4374 ||&lt; | -1 -7 4 1 &gt; ||&gt; 0.40 ||= Ragisma ||=   ||=   ||
-||= 250047/250000 ||&lt; | -4 6 -6 3 &gt; ||&gt; 0.33 ||= Landscape Comma ||=   ||=   ||
+||= [[tel:250047/250000|250047/250000]] ||&lt; | -4 6 -6 3 &gt; ||&gt; 0.33 ||= Landscape Comma ||=   ||=   ||
 ||= 99/98 ||&lt; | -1 2 0 -2 1 &gt; ||&gt; 17.58 ||= Mothwellsma ||=   ||=   ||
 ||= 896/891 ||&lt; | 7 -4 0 1 -1 &gt; ||&gt; 9.69 ||= Pentacircle ||=   ||=   ||
@@ Line 147: / Line 147: @@
 Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less &amp;quot;tension&amp;quot; and thus are also more consonant.&lt;br /&gt;
 &lt;br /&gt;
-The 27 note system ore one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila&lt;br /&gt;
+The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x27 tone equal tempertament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Intervals&lt;/h2&gt;
@@ Line 156: / Line 156: @@
          &lt;td&gt;Degrees of 27-EDO&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents value&lt;br /&gt;
+         &lt;td&gt;Cents value coarse/fine&lt;br /&gt;
 DMS value&lt;br /&gt;
 &lt;/td&gt;
@@ Line 178: / Line 178: @@
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;44.44&lt;br /&gt;
+         &lt;td&gt;44.44, 53.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 189: / Line 189: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;88.89&lt;br /&gt;
+         &lt;td&gt;88.89, 106.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 200: / Line 200: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;133.33&lt;br /&gt;
+         &lt;td&gt;133.33, 160&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 211: / Line 211: @@
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;177.78&lt;br /&gt;
+         &lt;td&gt;177.78, 213.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 222: / Line 222: @@
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;222.22&lt;br /&gt;
+         &lt;td&gt;222.22, 266.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 233: / Line 233: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;266.67&lt;br /&gt;
+         &lt;td&gt;266.67, 320&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 244: / Line 244: @@
          &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;311.11&lt;br /&gt;
+         &lt;td&gt;311.11, 373.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 255: / Line 255: @@
          &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;355.56&lt;br /&gt;
+         &lt;td&gt;355.56, 426.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 266: / Line 266: @@
          &lt;td&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;400&lt;br /&gt;
+         &lt;td&gt;400, 480&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 277: / Line 277: @@
          &lt;td&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;444.44&lt;br /&gt;
+         &lt;td&gt;444.44, 513.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 288: / Line 288: @@
          &lt;td&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;488.89&lt;br /&gt;
+         &lt;td&gt;488.89, 566.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 299: / Line 299: @@
          &lt;td&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;533.33&lt;br /&gt;
+         &lt;td&gt;533.33, 640&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 310: / Line 310: @@
          &lt;td&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;577.78&lt;br /&gt;
+         &lt;td&gt;577.78, 693.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 321: / Line 321: @@
          &lt;td&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;622.22&lt;br /&gt;
+         &lt;td&gt;622.22, 746.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 332: / Line 332: @@
          &lt;td&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;666.67&lt;br /&gt;
+         &lt;td&gt;666.67, 800&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 343: / Line 343: @@
          &lt;td&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;711.11&lt;br /&gt;
+         &lt;td&gt;711.11, 853.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 354: / Line 354: @@
          &lt;td&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;755.56&lt;br /&gt;
+         &lt;td&gt;755.56, 906.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 365: / Line 365: @@
          &lt;td&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;800&lt;br /&gt;
+         &lt;td&gt;800, 960&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 376: / Line 376: @@
          &lt;td&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;844.44&lt;br /&gt;
+         &lt;td&gt;844.44, 1013.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 387: / Line 387: @@
          &lt;td&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;888.89&lt;br /&gt;
+         &lt;td&gt;888.89, 1066.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 398: / Line 398: @@
          &lt;td&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.33&lt;br /&gt;
+         &lt;td&gt;933.33, 1120&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 409: / Line 409: @@
          &lt;td&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;977.78&lt;br /&gt;
+         &lt;td&gt;977.78, 1173.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 420: / Line 420: @@
          &lt;td&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1022.22&lt;br /&gt;
+         &lt;td&gt;1022.22, 1226.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 431: / Line 431: @@
          &lt;td&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1066,67&lt;br /&gt;
+         &lt;td&gt;1066,67, 1280&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 442: / Line 442: @@
          &lt;td&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1111.11&lt;br /&gt;
+         &lt;td&gt;1111.11, 1333.33&lt;br /&gt;
 °20'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 453: / Line 453: @@
          &lt;td&gt;26&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1155.56&lt;br /&gt;
+         &lt;td&gt;1155.56, 1386.67&lt;br /&gt;
 °40'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 464: / Line 464: @@
          &lt;td&gt;27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200&lt;br /&gt;
+         &lt;td&gt;1200, 1440&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 598: / Line 598: @@
 &lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x27 tone equal tempertament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Commas&lt;/h2&gt;
-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 27 43 63 76 93 100 |.)&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/27%2043%2063%2076%2093%20100"&gt;27 43 63 76 93 100&lt;/a&gt; |.)&lt;br /&gt;
@@ Line 659: / Line 659: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;4711802/4709457&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;[[tel:4711802/4709457|4711802/4709457]]&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;| 1 -27 18 &amp;gt;&lt;br /&gt;
@@ Line 771: / Line 771: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;420175/419904&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;[[tel:420175/419904|420175/419904]]&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;| -6 -8 2 5 &amp;gt;&lt;br /&gt;
@@ Line 813: / Line 813: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;250047/250000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;[[tel:250047/250000|250047/250000]]&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;| -4 6 -6 3 &amp;gt;&lt;br /&gt;