Ragismic microtemperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-22 17:59:38 UTC</tt>.<br>
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<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]
The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.
The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.


=Ennealimmal=  
=Ennealimmal=
Ennealimmal temperament tempers out the two smallest 7-limit superparticular commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the ennealimma comma, |1 -27 18&gt;, which leads to the identification of (27/25)^9 with the octave, and gives ennealimmal a period of 1/9 octave. While 27/25 is a 5-limit interval, two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit. Its wedgie is &lt;&lt;18 27 18 1 -22 -34||.
Ennealimmal temperament tempers out the two smallest 7-limit superparticular commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the ennealimma comma, |1 -27 18&gt;, which leads to the identification of (27/25)^9 with the octave, and gives ennealimmal a period of 1/9 octave. While 27/25 is a 5-limit interval, two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit. Its wedgie is &lt;&lt;18 27 18 1 -22 -34||.


Line 16: Line 9:
If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example.) In particular, people fond of the idea of "tritaves" as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a "tritave". Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS.
If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example.) In particular, people fond of the idea of "tritaves" as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a "tritave". Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS.


[[Tuning Ranges of Regular Temperaments|valid range]]: [26.667, 66.667] (45bcd to 18bcd)
[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [26.667, 66.667] (45bcd to 18bcd)
 
nice range: [48.920, 49.179]
nice range: [48.920, 49.179]
strict range: [48.920, 49.179]
strict range: [48.920, 49.179]


Line 25: Line 20:


Map: [&lt;9 1 1 2|, &lt;0 2 3 2|]
Map: [&lt;9 1 1 2|, &lt;0 2 3 2|]
Wedgie: &lt;&lt;18 27 18 1 -22 -34||
Wedgie: &lt;&lt;18 27 18 1 -22 -34||
EDOs: [[27edo|27]], [[45edo|45]], [[72edo|72]], [[99edo|99]], [[171edo|171]], [[270edo|270]], [[441edo|441]], [[612edo|612]], [[3600edo|3600]]
EDOs: [[27edo|27]], [[45edo|45]], [[72edo|72]], [[99edo|99]], [[171edo|171]], [[270edo|270]], [[441edo|441]], [[612edo|612]], [[3600edo|3600]]
Badness: 0.00361
Badness: 0.00361


==11 limit hemiennealimmal==  
==11 limit hemiennealimmal==
Commas: 2401/2400, 4375/4374, 3025/3024
Commas: 2401/2400, 4375/4374, 3025/3024


valid range: [13.333, 22.222] (90bcd, 54c)
valid range: [13.333, 22.222] (90bcd, 54c)
nice range: [17.304, 17.985]
nice range: [17.304, 17.985]
strict range:  [17.304, 17.985]
strict range:  [17.304, 17.985]


Line 39: Line 39:


Map: [&lt;18 0 -1 22 48|, &lt;0 2 3 2 1|]
Map: [&lt;18 0 -1 22 48|, &lt;0 2 3 2 1|]
EDOs: 72, 198, 270, 342, 612, 954, 1566
EDOs: 72, 198, 270, 342, 612, 954, 1566
Badness: 0.00628
Badness: 0.00628


==13 limit hemiennealimmal==  
==13 limit hemiennealimmal==
Commas: 676/675, 1001/1000, 1716/1715, 3025/3024
Commas: 676/675, 1001/1000, 1716/1715, 3025/3024


valid range: [16.667, 22.222] (72 to 54cf)
valid range: [16.667, 22.222] (72 to 54cf)
nice range: [17.304, 18.309]
nice range: [17.304, 18.309]
strict range: [17.304, 18.309]
strict range: [17.304, 18.309]


Line 52: Line 56:


Map: [&lt;18 0 -1 22 48 -19|, &lt;0 2 3 2 1 6|]
Map: [&lt;18 0 -1 22 48 -19|, &lt;0 2 3 2 1 6|]
EDOs: 72, 198, 270
EDOs: 72, 198, 270
Badness: 0.0125
Badness: 0.0125


==Semiennealimmal==  
==Semiennealimmal==
Commas: 2401/2400, 4375/4374, 4000/3993
Commas: 2401/2400, 4375/4374, 4000/3993


Line 61: Line 67:


Map: [&lt;9 3 4 14 18|, &lt;0 6 9 6 7|]
Map: [&lt;9 3 4 14 18|, &lt;0 6 9 6 7|]
EDOs: 72, 369, 441
EDOs: 72, 369, 441
Badness: 0.0342
Badness: 0.0342


===13 limit semiennealimmal===  
===13 limit semiennealimmal===
Commas: 1575/1573, 2080/2079, 2401/2400, 4375/4374
Commas: 1575/1573, 2080/2079, 2401/2400, 4375/4374


Line 70: Line 78:


Map: [&lt;9 3 4 14 18 -8|, &lt;0 6 9 6 7 22|]
Map: [&lt;9 3 4 14 18 -8|, &lt;0 6 9 6 7 22|]
EDOs: 72, 441
EDOs: 72, 441
Badness: 0.0261
Badness: 0.0261


Line 79: Line 89:


Map: [&lt;9 1 1 12 -7|, [0 8 12 8 23]]
Map: [&lt;9 1 1 12 -7|, [0 8 12 8 23]]
EDOs: 342, 1053, 1395, 1737, 4869d, 6606cd
EDOs: 342, 1053, 1395, 1737, 4869d, 6606cd
Badness: 0.0213
Badness: 0.0213


==Ennealimnic==  
==Ennealimnic==
Commas: 243/242, 441/440, 4375/4356
Commas: 243/242, 441/440, 4375/4356


valid range: [44.444, 53.333] (27e to 45e)
valid range: [44.444, 53.333] (27e to 45e)
nice range: [48.920, 52.592]
nice range: [48.920, 52.592]
strict range: [48.920, 52.592]
strict range: [48.920, 52.592]


Line 92: Line 106:


Map: [&lt;9 1 1 12 -2|, &lt;0 2 3 2 5|]
Map: [&lt;9 1 1 12 -2|, &lt;0 2 3 2 5|]
EDOs: 72, 171, 243
EDOs: 72, 171, 243
Badness: 0.0203
Badness: 0.0203


===13 limit ennealimnic===  
===13 limit ennealimnic===
Commas: 243/242, 364/363, 441/440, 625/624
Commas: 243/242, 364/363, 441/440, 625/624


valid range: [48.485, 50.000] (99ef to 72)
valid range: [48.485, 50.000] (99ef to 72)
nice range: [48.825, 52.592]
nice range: [48.825, 52.592]
strict range: [48.825, 50.000]
strict range: [48.825, 50.000]


Line 105: Line 123:


Map: [&lt;9 1 1 12 -2 -33|, &lt;0 2 3 2 5 10|]
Map: [&lt;9 1 1 12 -2 -33|, &lt;0 2 3 2 5 10|]
EDOs: 72, 171, 243
EDOs: 72, 171, 243
Badness: 0.0233
Badness: 0.0233


====17 limit ennealimnic====  
====17 limit ennealimnic====
Commas: 243/242, 364/363, 375/374, 441/440, 595/594
Commas: 243/242, 364/363, 375/374, 441/440, 595/594


valid range: [48.485, 50.000] (99ef to 72)
valid range: [48.485, 50.000] (99ef to 72)
nice range: [46.363, 52.592]
nice range: [46.363, 52.592]
strict range: [48.485, 50.000]
strict range: [48.485, 50.000]


Line 118: Line 140:


Map: [&lt;9 1 1 12 -2 -33 -3|, &lt;0 2 3 2 5 10 6|]
Map: [&lt;9 1 1 12 -2 -33 -3|, &lt;0 2 3 2 5 10 6|]
EDOs: 72, 171, 243
EDOs: 72, 171, 243
Badness: 0.0146
Badness: 0.0146


===Ennealim===  
===Ennealim===
Commas: 169/168, 243/242, 325/324, 441/440
Commas: 169/168, 243/242, 325/324, 441/440


Line 127: Line 151:


Map: [&lt;9 1 1 12 -2 20|, &lt;0 2 3 2 5 2|]
Map: [&lt;9 1 1 12 -2 20|, &lt;0 2 3 2 5 2|]
EDOs: 27e, 45f, 72, 315ff, 387cff, 459cdfff
EDOs: 27e, 45f, 72, 315ff, 387cff, 459cdfff
Badness: 0.0207
Badness: 0.0207


==Ennealiminal==  
==Ennealiminal==
Commas: 385/384, 1375/1372, 4375/4374
Commas: 385/384, 1375/1372, 4375/4374


Line 136: Line 162:


Map: [&lt;9 1 1 12 51|, &lt;0 2 3 2 -3|]
Map: [&lt;9 1 1 12 51|, &lt;0 2 3 2 -3|]
EDOs: 27, 45, 72, 171e, 243e, 315e
EDOs: 27, 45, 72, 171e, 243e, 315e
Badness: 0.0311
Badness: 0.0311


Line 145: Line 173:


Map: [&lt;9 1 1 12 51 20|, &lt;0 2 3 2 -3 2|]
Map: [&lt;9 1 1 12 51 20|, &lt;0 2 3 2 -3 2|]
EDOs: 27, 45f, 72, 171ef, 243ef
EDOs: 27, 45f, 72, 171ef, 243ef
Badness: 0.0303
Badness: 0.0303


Line 154: Line 184:


Map: [&lt;27 1 0 34 177|, &lt;0 2 3 2 -4|]
Map: [&lt;27 1 0 34 177|, &lt;0 2 3 2 -4|]
EDOs: 27, 243, 270, 783, 1053, 1323, 10854bcde
EDOs: 27, 243, 270, 783, 1053, 1323, 10854bcde
Badness: 0.0298
Badness: 0.0298


==Semihemiennealimmal==  
==Semihemiennealimmal==
Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224
Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224


Line 163: Line 195:


Map: [&lt;18 0 -1 22 48 88|, &lt;0 4 6 4 2 -3|]
Map: [&lt;18 0 -1 22 48 88|, &lt;0 4 6 4 2 -3|]
EDOs: 126, 144, 270, 684, 954
EDOs: 126, 144, 270, 684, 954
Badness: 0.0131
Badness: 0.0131


=Gamera=  
=Gamera=
Commas: 4375/4374, 589824/588245
Commas: 4375/4374, 589824/588245


Line 172: Line 206:


Map: [&lt;1 6 10 3|, &lt;0 -23 -40 -1|]
Map: [&lt;1 6 10 3|, &lt;0 -23 -40 -1|]
EDOs: 26, 73, 99, 224, 323, 422, 735
EDOs: 26, 73, 99, 224, 323, 422, 735
Badness: 0.0376
Badness: 0.0376


Line 181: Line 217:


Map: [&lt;2 12 20 6 5|, &lt;0 -23 -40 -1 5|]
Map: [&lt;2 12 20 6 5|, &lt;0 -23 -40 -1 5|]
EDOs: 26, 198, 224, 422, 646, 1068d
EDOs: 26, 198, 224, 422, 646, 1068d
Badness: 0.0410
Badness: 0.0410


Line 188: Line 226:


Map: [&lt;2 12 20 6 5 17|, &lt;0 -23 -40 -1 5 -25|]
Map: [&lt;2 12 20 6 5 17|, &lt;0 -23 -40 -1 5 -25|]
EDOs: 26, 198, 224, 422, 646f, 1068df
EDOs: 26, 198, 224, 422, 646f, 1068df
Badness: 0.0204
Badness: 0.0204


=Supermajor=  
=Supermajor=
The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.0002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of &lt;&lt;37 46 75 -13 15 45||. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.
The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.0002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of &lt;&lt;37 46 75 -13 15 45||. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.


Line 199: Line 239:


Map: [&lt;1 15 19 30|, &lt;0 -37 -46 -75|]
Map: [&lt;1 15 19 30|, &lt;0 -37 -46 -75|]
EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214
EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214
Badness: 0.0108
Badness: 0.0108


==Semisupermajor==  
==Semisupermajor==
Commas: 3025/3024, 4375/4374, 35156250/35153041
Commas: 3025/3024, 4375/4374, 35156250/35153041


Line 208: Line 250:


Map: [&lt;2 30 38 60 41|, &lt;0 -37 -46 -75 -47|]
Map: [&lt;2 30 38 60 41|, &lt;0 -37 -46 -75 -47|]
EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf
EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf
Badness: 0.0128
Badness: 0.0128


=Enneadecal=  
=Enneadecal=
Enndedecal temperament tempers out the enneadeca, |-14 -19 19&gt;, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of [[19edo]] up to just ones. [[171edo]] is a good tuning for either the 5 or 7 limits, and [[494edo]] shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use [[665edo]] for a tuning.
Enndedecal temperament tempers out the enneadeca, |-14 -19 19&gt;, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of [[19edo|19edo]] up to just ones. [[171edo|171edo]] is a good tuning for either the 5 or 7 limits, and [[494edo|494edo]] shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use [[665edo|665edo]] for a tuning.


Commas: 4375/4374, 703125/702464
Commas: 4375/4374, 703125/702464
Line 219: Line 263:


Map: [&lt;19 0 14 -37|, &lt;0 1 1 3|]
Map: [&lt;19 0 14 -37|, &lt;0 1 1 3|]
Generators: 28/27, 3
Generators: 28/27, 3
EDOs: 19, 152, 171, 665, 836, 1007, 2185
EDOs: 19, 152, 171, 665, 836, 1007, 2185
Badness: 0.0110
Badness: 0.0110


=Deca=  
=Deca=
Commas: 4375/4374, 165288374272/164794921875
Commas: 4375/4374, 165288374272/164794921875


Line 229: Line 276:


Map: [&lt;10 4 2 9|, &lt;0 5 6 11|]
Map: [&lt;10 4 2 9|, &lt;0 5 6 11|]
EDOs: 80, 190, 270, 1270, 1540, 1810, 2080
EDOs: 80, 190, 270, 1270, 1540, 1810, 2080
Badness: 0.0806
Badness: 0.0806


==11-limit==  
==11-limit==
Commas: 3025/3024, 4375/4374, 422576/421875
Commas: 3025/3024, 4375/4374, 422576/421875


Line 238: Line 287:


Map: [&lt;10 4 2 9 18|, &lt;0 5 6 11 7|]
Map: [&lt;10 4 2 9 18|, &lt;0 5 6 11 7|]
EDOs: 80, 190, 270, 1000, 1270
EDOs: 80, 190, 270, 1000, 1270
Badness: 0.0243
Badness: 0.0243


==13-limit==  
==13-limit==
Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374
Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374


Line 247: Line 298:


Map: [&lt;10 4 2 9 18 37|, &lt;0 5 6 11 7 0|]
Map: [&lt;10 4 2 9 18 37|, &lt;0 5 6 11 7 0|]
EDOs: 80, 190, 270, 730, 1000
EDOs: 80, 190, 270, 730, 1000
Badness: 0.0168
Badness: 0.0168


=Mitonic=  
=Mitonic=
Commas: 4375/4374, 2100875/2097152
Commas: 4375/4374, 2100875/2097152


Line 256: Line 309:


Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
EDOs: 46, 125, 171
EDOs: 46, 125, 171
Badness: 0.0252
Badness: 0.0252


=Abigail=  
=Abigail=
Commas: 4375/4374, 2147483648/2144153025
Commas: 4375/4374, 2147483648/2144153025


[[POTE tuning|POTE generator]]: 208.899
[[POTE_tuning|POTE generator]]: 208.899


Map: [&lt;2 7 13 -1|, &lt;0 -11 -24 19|]
Map: [&lt;2 7 13 -1|, &lt;0 -11 -24 19|]
Wedgie: &lt;&lt;22 48 -38 25 -122 -223||
Wedgie: &lt;&lt;22 48 -38 25 -122 -223||
EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798
EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798
Badness: 0.0370
Badness: 0.0370


==11-limit==  
==11-limit==
Comma: 3025/3024, 4375/4374, 20614528/20588575
Comma: 3025/3024, 4375/4374, 20614528/20588575


[[POTE tuning|POTE generator]]: 208.901
[[POTE_tuning|POTE generator]]: 208.901


Map: [&lt;2 7 13 -1 1|, &lt;0 -11 -24 19 17|]
Map: [&lt;2 7 13 -1 1|, &lt;0 -11 -24 19 17|]
EDOs: 46, 132, 178, 224, 270, 494, 764
EDOs: 46, 132, 178, 224, 270, 494, 764
Badness: 0.0129
Badness: 0.0129


==13-limit==  
==13-limit==
Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095
Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095


[[POTE tuning|POTE generator]]: 208.903
[[POTE_tuning|POTE generator]]: 208.903


Map: [&lt;2 7 13 -1 1 -2|, &lt;0 -11 -24 19 17 27|]
Map: [&lt;2 7 13 -1 1 -2|, &lt;0 -11 -24 19 17 27|]
EDOs: 46, 178, 224, 270, 494, 764, 1258
EDOs: 46, 178, 224, 270, 494, 764, 1258
Badness: 0.00886
Badness: 0.00886


=Semidimi=  
=Semidimi=
Commas: 4375/4374, 3955078125/3954653486
Commas: 4375/4374, 3955078125/3954653486


Line 293: Line 355:


Map: [&lt;1 36 48 61|, &lt;0 -55 -73 -93|]
Map: [&lt;1 36 48 61|, &lt;0 -55 -73 -93|]
Wedgie: &lt;&lt;55 73 93 -12 -7 11||
Wedgie: &lt;&lt;55 73 93 -12 -7 11||
EDOs: 171, 863, 8419, 1205, 1376, 1547, 1718, 4983, 6701, 8419
EDOs: 171, 863, 8419, 1205, 1376, 1547, 1718, 4983, 6701, 8419
Badness: 0.0151
Badness: 0.0151


=Brahmagupta=  
=Brahmagupta=
Commas: 4375/4374, 70368744177664/70338939985125
Commas: 4375/4374, 70368744177664/70338939985125


Line 303: Line 368:


Map: [&lt;7 2 -8 53|, &lt;0 3 8 -11|]
Map: [&lt;7 2 -8 53|, &lt;0 3 8 -11|]
Wedgie: &lt;&lt;21 56 -77 40 -181 -336||
Wedgie: &lt;&lt;21 56 -77 40 -181 -336||
EDOs: 217, 224, 441, 1106, 1547
EDOs: 217, 224, 441, 1106, 1547
Badness: 0.0291
Badness: 0.0291


==11-limit==  
==11-limit==
Commas: 4000/3993, 4375/4374, 131072/130977
Commas: 4000/3993, 4375/4374, 131072/130977


Line 313: Line 381:


Map: [&lt;7 2 -8 53 3|, &lt;0 3 8 -11 7|]
Map: [&lt;7 2 -8 53 3|, &lt;0 3 8 -11 7|]
EDOs: 217, 224, 441, 665, 1771e
EDOs: 217, 224, 441, 665, 1771e
Badness: 0.0522
Badness: 0.0522


=Neusec=  
=Neusec=
Commas: 3025/3024, 4375/4374, 235298/234375
Commas: 3025/3024, 4375/4374, 235298/234375


Line 322: Line 392:


Map: [&lt;2 11 15 19 15|, &lt;0 -31 -41 -53 -32|]
Map: [&lt;2 11 15 19 15|, &lt;0 -31 -41 -53 -32|]
EDOs: 190, 388
EDOs: 190, 388
Badness: 0.0591
Badness: 0.0591


==13-limit==  
==13-limit==
Commas: 847/845, 1001/1000, 3025/3024, 4375/4374
Commas: 847/845, 1001/1000, 3025/3024, 4375/4374


Line 331: Line 403:


Map: [&lt;2 11 15 19 15 17|, &lt;0 -31 -41 -53 -32 -38|]
Map: [&lt;2 11 15 19 15 17|, &lt;0 -31 -41 -53 -32 -38|]
EDOs: 190, 198, 388
EDOs: 190, 198, 388
Badness: 0.0309
Badness: 0.0309


=Quasithird=  
=Quasithird=
Commas: 4375/4374, 1153470752371588581/1152921504606846976
Commas: 4375/4374, 1153470752371588581/1152921504606846976


Line 340: Line 414:


Map: [&lt;4 0 -11 48|, &lt;0 5 16 -29|]
Map: [&lt;4 0 -11 48|, &lt;0 5 16 -29|]
Wedgie: &lt;&lt;20 64 -116 55 -240 -449||
Wedgie: &lt;&lt;20 64 -116 55 -240 -449||
EDOs: 164, 224, 388, 612, 1448, 2060
EDOs: 164, 224, 388, 612, 1448, 2060
Badness: 0.0618
Badness: 0.0618


==11-limit==  
==11-limit==
Commas: 3025/3024, 4375/4374, 4296700485/4294967296
Commas: 3025/3024, 4375/4374, 4296700485/4294967296


Line 350: Line 427:


Map: [&lt;4 0 -11 48 43|, &lt;0 5 16 -29 -23|]
Map: [&lt;4 0 -11 48 43|, &lt;0 5 16 -29 -23|]
EDOs: 164, 224, 388, 612, 836, 1448
EDOs: 164, 224, 388, 612, 836, 1448
Badness: 0.0211
Badness: 0.0211


==13-limit==  
==13-limit==
Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195
Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195


Line 359: Line 438:


Map: [&lt;4 0 -11 48 43 11|, &lt;0 5 16 -29 -23 3|]
Map: [&lt;4 0 -11 48 43 11|, &lt;0 5 16 -29 -23 3|]
EDOs: 164, 224, 388, 612, 836, 1448f, 2284f
EDOs: 164, 224, 388, 612, 836, 1448f, 2284f
Badness: 0.0295
Badness: 0.0295


=Semidimfourth=  
=Semidimfourth=
Commas: 4375/4374, 235298/234375
Commas: 4375/4374, 235298/234375


Line 368: Line 449:


Map: [&lt;1 21 28 36|, &lt;0 -31 -41 -53|]
Map: [&lt;1 21 28 36|, &lt;0 -31 -41 -53|]
Wedgie: &lt;&lt;31 41 53 -7 -3 8||
Wedgie: &lt;&lt;31 41 53 -7 -3 8||
EDOs: 91, 99, 289, 388, 875, 1263d, 1651d
EDOs: 91, 99, 289, 388, 875, 1263d, 1651d
Badness: 0.0552
Badness: 0.0552


=Acrokleismic=  
=Acrokleismic=
Commas: 4375/4374, 2202927104/2197265625
Commas: 4375/4374, 2202927104/2197265625


Line 378: Line 462:


Map: [&lt;1 10 11 27|, &lt;0 -32 -33 -92|]
Map: [&lt;1 10 11 27|, &lt;0 -32 -33 -92|]
Wedgie: &lt;&lt;32 33 92 -22 56 121||
Wedgie: &lt;&lt;32 33 92 -22 56 121||
EDOs: 19, 251, 270
EDOs: 19, 251, 270
Badness: 0.0562
Badness: 0.0562


==11-limit==  
==11-limit==
Commas: 4375/4374, 41503/41472, 172032/171875
Commas: 4375/4374, 41503/41472, 172032/171875


Line 388: Line 475:


Map: [&lt;1 10 11 27 -16|, &lt;0 -32 -33 -92 74|]
Map: [&lt;1 10 11 27 -16|, &lt;0 -32 -33 -92 74|]
EDOs: 19, 251, 270, 829, 1099, 1369, 1639
EDOs: 19, 251, 270, 829, 1099, 1369, 1639
Badness: 0.0369
Badness: 0.0369


==13-limit==  
==13-limit==
Commas: 676/675, 1001/1000, 4375/4374, 10985/10976
Commas: 676/675, 1001/1000, 4375/4374, 10985/10976


Line 397: Line 486:


Map: [&lt;1 10 11 27 -16 25|, &lt;0 -32 -33 -92 74 -81|]
Map: [&lt;1 10 11 27 -16 25|, &lt;0 -32 -33 -92 74 -81|]
EDOs: 19, 251, 270
EDOs: 19, 251, 270
Badness: 0.0268
Badness: 0.0268


==Counteracro==  
==Counteracro==
Commas: 4375/4374, 5632/5625, 117649/117612
Commas: 4375/4374, 5632/5625, 117649/117612


Line 406: Line 497:


Map: [&lt;1 10 11 27 55|, &lt;0 -32 -33 -92 -196|]
Map: [&lt;1 10 11 27 55|, &lt;0 -32 -33 -92 -196|]
EDOs: 270, 1061e, 1331c, 1601c, 1871bc, 4012bcde
EDOs: 270, 1061e, 1331c, 1601c, 1871bc, 4012bcde
Badness: 0.0426
Badness: 0.0426


===13-limit===  
===13-limit===
Commas: 676/675, 1716/1715, 4225/4224, 4375/4374
Commas: 676/675, 1716/1715, 4225/4224, 4375/4374


Line 415: Line 508:


Map: [&lt;1 10 11 27 55 25|, &lt;0 -32 -33 -92 -196 -81|]
Map: [&lt;1 10 11 27 55 25|, &lt;0 -32 -33 -92 -196 -81|]
EDOs: 270, 1331c, 1601c, 1871bcf, 2141bcf
EDOs: 270, 1331c, 1601c, 1871bcf, 2141bcf
Badness: 0.0260
Badness: 0.0260


Line 424: Line 519:


Map: [&lt;1 11 19 2|, &lt;0 -35 -62 3|]
Map: [&lt;1 11 19 2|, &lt;0 -35 -62 3|]
Wedgie: &lt;&lt;35 62 -3 17 -103 -181||
Wedgie: &lt;&lt;35 62 -3 17 -103 -181||
EDOs: 26, 145, 171, 2710d
EDOs: 26, 145, 171, 2710d
Badness: 0.0449
Badness: 0.0449


Line 434: Line 532:


Map: [&lt;2 21 36 5|, &lt;0 -29 -51 1|]
Map: [&lt;2 21 36 5|, &lt;0 -29 -51 1|]
Wedgie: &lt;&lt;58 102 -2 27 -166 -291||
Wedgie: &lt;&lt;58 102 -2 27 -166 -291||
EDOs: 26, 244, 270, 836, 1106, 1376, 2482, 19856bd, 23714bd
EDOs: 26, 244, 270, 836, 1106, 1376, 2482, 19856bd, 23714bd
Badness: 0.0402
Badness: 0.0402


Line 444: Line 545:


Map: [&lt;2 21 36 5 2|, &lt;0 -29 -51 1 8|]
Map: [&lt;2 21 36 5 2|, &lt;0 -29 -51 1 8|]
EDOs: 26, 244, 270, 566, 836, 1106, 7472e, 8578de, 9684cde, 10790cde, 11896cde
EDOs: 26, 244, 270, 566, 836, 1106, 7472e, 8578de, 9684cde, 10790cde, 11896cde
Badness: 0.0162
Badness: 0.0162


Line 453: Line 556:


Map: [&lt;2 7 7 23|, &lt;0 -13 -8 -59|]
Map: [&lt;2 7 7 23|, &lt;0 -13 -8 -59|]
Wedgie: &lt;&lt;26 16 118 -35 114 229||
Wedgie: &lt;&lt;26 16 118 -35 114 229||
EDOs: 190, 224, 414, 638, 1052c, 1690bc
EDOs: 190, 224, 414, 638, 1052c, 1690bc
Badness: 0.1760
Badness: 0.1760


Line 463: Line 569:


Map: [&lt;2 7 7 23 19|, &lt;0 -13 -8 -59 -41|]
Map: [&lt;2 7 7 23 19|, &lt;0 -13 -8 -59 -41|]
EDOs: 190, 224, 414, 638, 1052c
EDOs: 190, 224, 414, 638, 1052c
Badness: 0.0410
Badness: 0.0410


Line 472: Line 580:


Map: [&lt;2 7 7 23 19 13|, &lt;0 -13 -8 -59 -41 -19|]
Map: [&lt;2 7 7 23 19 13|, &lt;0 -13 -8 -59 -41 -19|]
EDOs: 190, 224, 414, 638, 1690bc, 2328bcde
EDOs: 190, 224, 414, 638, 1690bc, 2328bcde
Badness: 0.0226
Badness: 0.0226


=Nearly Micro=  
=Nearly Micro=


=Octoid=  
=Octoid=
Commas: 4375/4374, 16875/16807
Commas: 4375/4374, 16875/16807


valid range: [578.571, 600.000] (56bcd to 8d)
valid range: [578.571, 600.000] (56bcd to 8d)
nice range: [582.512, 584.359]
nice range: [582.512, 584.359]
strict range:  [582.512, 584.359]
strict range:  [582.512, 584.359]


Line 487: Line 599:


Map: [&lt;8 1 3 3|, &lt;0 3 4 5|]
Map: [&lt;8 1 3 3|, &lt;0 3 4 5|]
Generators: 49/45, 7/5
Generators: 49/45, 7/5
EDOs: 72, 152, 224
EDOs: 72, 152, 224
Badness: 0.0427
Badness: 0.0427


==11-limit==  
==11-limit==
Commas: 540/539, 1375/1372, 4000/3993
Commas: 540/539, 1375/1372, 4000/3993


valid range: [581.250, 586.364] (64cd, 88bcde)
valid range: [581.250, 586.364] (64cd, 88bcde)
nice range: [582.512, 585.084]
nice range: [582.512, 585.084]
strict range: [582.512, 585.084]
strict range: [582.512, 585.084]


Line 501: Line 618:


Map: [&lt;8 1 3 3 16|, &lt;0 3 4 5 3|]
Map: [&lt;8 1 3 3 16|, &lt;0 3 4 5 3|]
EDOs: 72, 152, 224
EDOs: 72, 152, 224
Badness: 0.0141
Badness: 0.0141


==13-limit==  
==13-limit==
Commas: 540/539, 1375/1372, 4000/3993, 625/624
Commas: 540/539, 1375/1372, 4000/3993, 625/624


Line 510: Line 629:


Map: [&lt;8 1 3 3 16 -21|, &lt;0 3 4 5 3 13|]
Map: [&lt;8 1 3 3 16 -21|, &lt;0 3 4 5 3 13|]
EDOs: 72, 224
EDOs: 72, 224
Badness: 0.0153
Badness: 0.0153


==Music==  
==Music==
http://www.archive.org/details/Dreyfus
[http://www.archive.org/details/Dreyfus http://www.archive.org/details/Dreyfus]
[[http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3|play]]
 
[http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play]


==Octopus==  
==Octopus==
Commas: 169/168, 325/324, 364/363, 540/539
Commas: 169/168, 325/324, 364/363, 540/539


Line 523: Line 645:


Map: [&lt;8 1 3 3 16 14|, &lt;0 3 4 5 3 4|]
Map: [&lt;8 1 3 3 16 14|, &lt;0 3 4 5 3 4|]
EDOs: 72, 152, 224f
EDOs: 72, 152, 224f
Badness: 0.0217
Badness: 0.0217


=Amity=  
=Amity=
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. [[99edo]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. [[99edo|99edo]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.


In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.


==5-limit==  
==5-limit==
Comma: 1600000/1594323
Comma: 1600000/1594323


Line 537: Line 661:


Map: [&lt;1 3 6|, &lt;0 -5 -13|]
Map: [&lt;1 3 6|, &lt;0 -5 -13|]
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873
Badness: 0.0220
Badness: 0.0220


==7-limit==  
==7-limit==
Commas: 4375/4374, 5120/5103
Commas: 4375/4374, 5120/5103


Line 546: Line 672:


Map: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]
Map: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]
Wedgie: &lt;&lt;5 13 -17 9 -41 -76||
Wedgie: &lt;&lt;5 13 -17 9 -41 -76||
EDOs: 7, 39, 46, 53, 99, 251, 350
EDOs: 7, 39, 46, 53, 99, 251, 350
Badness: 0.0236
Badness: 0.0236


==11-limit==  
==11-limit==
Commas: 540/539, 4375/4374, 5120/5103
Commas: 540/539, 4375/4374, 5120/5103


Line 556: Line 685:


Map: [&lt;1 3 6 -2 21|, &lt;0 -5 -13 17 -62|]
Map: [&lt;1 3 6 -2 21|, &lt;0 -5 -13 17 -62|]
EDOs: 53, 99e, 152, 555de, 707de, 859bde
EDOs: 53, 99e, 152, 555de, 707de, 859bde
Badness: 0.0315
Badness: 0.0315


Line 565: Line 696:


Map: [&lt;1 3 6 -2 21 17|, &lt;0 -5 -13 17 -62 -47|]
Map: [&lt;1 3 6 -2 21 17|, &lt;0 -5 -13 17 -62 -47|]
EDOS: 53, 99ef, 152f, 205
EDOS: 53, 99ef, 152f, 205
Badness: 0.0280
Badness: 0.0280


Line 574: Line 707:


Map: [&lt;1 3 6 11|, &lt;0 -5 -13 -29|]
Map: [&lt;1 3 6 11|, &lt;0 -5 -13 -29|]
Wedgie: &lt;&lt;5 13 29 9 32 31||
Wedgie: &lt;&lt;5 13 29 9 32 31||
EDOs: 46, 131c, 177c
EDOs: 46, 131c, 177c
Badness: 0.0956
Badness: 0.0956


Line 584: Line 720:


Map: [&lt;1 3 6 11 6|, &lt;0 -5 -13 -29 -9|]
Map: [&lt;1 3 6 11 6|, &lt;0 -5 -13 -29 -9|]
EDOs: 46, 177c, 223bc, 269bce
EDOs: 46, 177c, 223bc, 269bce
Badness: 0.0425
Badness: 0.0425


==Hitchcock==  
==Hitchcock==
Commas: 121/120, 176/175, 2200/2187
Commas: 121/120, 176/175, 2200/2187


Line 593: Line 731:


Map: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]
Map: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]
EDOs: 7, 39, 46, 53, 99
EDOs: 7, 39, 46, 53, 99
Badness: 0.0352
Badness: 0.0352


Line 602: Line 742:


Map: [&lt;1 3 6 -2 6 2|, &lt;0 -5 -13 17 -9 6|]
Map: [&lt;1 3 6 -2 6 2|, &lt;0 -5 -13 17 -9 6|]
EDOs: 7, 39, 46, 53, 99
EDOs: 7, 39, 46, 53, 99
Badness: 0.0224
Badness: 0.0224


==Hemiamity==  
==Hemiamity==
Commas: 4375/4374, 5120/5103, 3025/3024
Commas: 4375/4374, 5120/5103, 3025/3024


Line 611: Line 753:


Map: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]
Map: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]
EDOs: 14, 46, 106, 152, 350
EDOs: 14, 46, 106, 152, 350


=Parakleismic=  
=Parakleismic=
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the [[118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit [[99edo]] may be preferred, but in the 11-limit it is best to stick with 118.
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the [[118edo|118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit [[99edo|99edo]] may be preferred, but in the 11-limit it is best to stick with 118.


Comma: 124440064/1220703125
Comma: 124440064/1220703125
Line 621: Line 764:


Map: [&lt;1 5 6|, &lt;0 -13 -14|]
Map: [&lt;1 5 6|, &lt;0 -13 -14|]
EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496
EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496
Badness: 0.0433
Badness: 0.0433


==7-limit==  
==7-limit==
Commas: 3136/3125, 4375/4374
Commas: 3136/3125, 4375/4374


Line 630: Line 775:


Map: [&lt;1 5 6 12|, &lt;0 -13 -14 -35|]
Map: [&lt;1 5 6 12|, &lt;0 -13 -14 -35|]
EDOs: 19, 80, 99, 217, 316, 415
EDOs: 19, 80, 99, 217, 316, 415
Badness: 0.0274
Badness: 0.0274


==11-limit==  
==11-limit==
Commas: 385/384, 3136/3125, 4375/4374
Commas: 385/384, 3136/3125, 4375/4374


Line 639: Line 786:


Map: [&lt;1 5 6 12 -6|, &lt;0 -13 -14 -35 36|]
Map: [&lt;1 5 6 12 -6|, &lt;0 -13 -14 -35 36|]
EDOs: 19, 99, 118
EDOs: 19, 99, 118
Badness: 0.0497
Badness: 0.0497


==Parkleismic==  
==Parkleismic==
Commas: 176/175, 1375/1372, 2200/2187
Commas: 176/175, 1375/1372, 2200/2187


Line 648: Line 797:


Map: [&lt;1 5 6 12 20|, &lt;0 -13 -14 -35 -63|]
Map: [&lt;1 5 6 12 20|, &lt;0 -13 -14 -35 -63|]
EDOs: 80, 179, 259cd
EDOs: 80, 179, 259cd
Badness: 0.0559
Badness: 0.0559


===13-limit===  
===13-limit===
Commas: 169/168, 176/175, 325/324, 1375/1372
Commas: 169/168, 176/175, 325/324, 1375/1372


Line 657: Line 808:


Map: [&lt;1 5 6 12 20 10|, &lt;0 -13 -14 -35 -63 -24|]
Map: [&lt;1 5 6 12 20 10|, &lt;0 -13 -14 -35 -63 -24|]
EDOs: 15, 19, 80, 179
EDOs: 15, 19, 80, 179
Badness: 0.0366
Badness: 0.0366


==Paradigmic==  
==Paradigmic==
Commas: 540/539, 896/891, 3136/3125
Commas: 540/539, 896/891, 3136/3125


Line 666: Line 819:


Map: [&lt;1 5 6 12 -1|, &lt;0 -13 -14 -35 17|]
Map: [&lt;1 5 6 12 -1|, &lt;0 -13 -14 -35 17|]
EDOs: 19, 80, 99e, 179e
EDOs: 19, 80, 99e, 179e
Badness: 0.0417
Badness: 0.0417


===13-limit===  
===13-limit===
Commas: 169/168, 325/324, 540/539, 832/825
Commas: 169/168, 325/324, 540/539, 832/825


Line 675: Line 830:


Map: [&lt;1 5 6 12 -1 10|, &lt;0 -13 -14 -35 17 -24|]
Map: [&lt;1 5 6 12 -1 10|, &lt;0 -13 -14 -35 17 -24|]
EDOs: 19, 80, 99e, 179e
EDOs: 19, 80, 99e, 179e
Badness: 0.0358
Badness: 0.0358


=Semiparakleismic=  
=Semiparakleismic=
Commas: 3025/3024, 3136/3125, 4375/4374
Commas: 3025/3024, 3136/3125, 4375/4374


Line 684: Line 841:


Map: [&lt;2 10 12 24 19|, &lt;0 -13 -14 -35 -23|]
Map: [&lt;2 10 12 24 19|, &lt;0 -13 -14 -35 -23|]
EDOs: 80, 118, 198, 316, 514c, 830c
EDOs: 80, 118, 198, 316, 514c, 830c
Badness: 0.0342
Badness: 0.0342


=Quincy=  
=Quincy=
Commas: 4375/4374, 823543/819200
Commas: 4375/4374, 823543/819200


Line 693: Line 852:


Map: [&lt;1 2 2 3|, &lt;0 -30 -49 -14|]
Map: [&lt;1 2 2 3|, &lt;0 -30 -49 -14|]
EDOs: 72, 217, 289
EDOs: 72, 217, 289
Badness: 0.0797
Badness: 0.0797


==11-limit==  
==11-limit==
Commas: 441/440, 4000/3993, 41503/41472
Commas: 441/440, 4000/3993, 41503/41472


Line 702: Line 863:


Map: [&lt;1 2 2 3 4|, &lt;0 -30 -49 -14 -39|]
Map: [&lt;1 2 2 3 4|, &lt;0 -30 -49 -14 -39|]
EDOs: 72, 217, 289
EDOs: 72, 217, 289
Badness: 0.0309
Badness: 0.0309


==13-limit==  
==13-limit==
Commas: 364/363, 441/440, 676/675, 4375/4374
Commas: 364/363, 441/440, 676/675, 4375/4374


Line 711: Line 874:


Map: [&lt;1 2 2 3 4 5|, &lt;0 -30 -49 -14 -39 -94|]
Map: [&lt;1 2 2 3 4 5|, &lt;0 -30 -49 -14 -39 -94|]
EDOs: 72, 145, 217, 289
EDOs: 72, 145, 217, 289
Badness: 0.0239
Badness: 0.0239


==17-limit==  
==17-limit==
Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155
Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155


Line 720: Line 885:


Map: [&lt;1 2 2 3 4 5 5|, &lt;0 -30 -49 -14 -39 -94 -66|]
Map: [&lt;1 2 2 3 4 5 5|, &lt;0 -30 -49 -14 -39 -94 -66|]
EDOs: 72, 145, 217, 289
EDOs: 72, 145, 217, 289
Badness: 0.0147
Badness: 0.0147


==19-limit==  
==19-limit==
Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600
Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600


Line 729: Line 896:


Map: [&lt;1 2 2 3 4 5 5 4|, &lt;0 -30 -49 -14 -39 -94 -66 18|]
Map: [&lt;1 2 2 3 4 5 5 4|, &lt;0 -30 -49 -14 -39 -94 -66 18|]
EDOs: 72, 145, 217
EDOs: 72, 145, 217
Badness: 0.0152</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0152
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ragismic microtemperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:152:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ennealimmal"&gt;Ennealimmal&lt;/a&gt;&lt;/div&gt;
[[Category:abigail]]
&lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-11 limit hemiennealimmal"&gt;11 limit hemiennealimmal&lt;/a&gt;&lt;/div&gt;
[[Category:amity]]
&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;!-- ws:start:WikiTextTocRule:155: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-13 limit hemiennealimmal"&gt;13 limit hemiennealimmal&lt;/a&gt;&lt;/div&gt;
[[Category:deca]]
&lt;!-- ws:end:WikiTextTocRule:155 --&gt;&lt;!-- ws:start:WikiTextTocRule:156: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Semiennealimmal"&gt;Semiennealimmal&lt;/a&gt;&lt;/div&gt;
[[Category:enneadecal]]
&lt;!-- ws:end:WikiTextTocRule:156 --&gt;&lt;!-- ws:start:WikiTextTocRule:157: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Semiennealimmal-13 limit semiennealimmal"&gt;13 limit semiennealimmal&lt;/a&gt;&lt;/div&gt;
[[Category:ennealimmal]]
&lt;!-- ws:end:WikiTextTocRule:157 --&gt;&lt;!-- ws:start:WikiTextTocRule:158: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Quadraennealimmal"&gt;Quadraennealimmal&lt;/a&gt;&lt;/div&gt;
[[Category:gamera]]
&lt;!-- ws:end:WikiTextTocRule:158 --&gt;&lt;!-- ws:start:WikiTextTocRule:159: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Ennealimnic"&gt;Ennealimnic&lt;/a&gt;&lt;/div&gt;
[[Category:mitonic]]
&lt;!-- ws:end:WikiTextTocRule:159 --&gt;&lt;!-- ws:start:WikiTextTocRule:160: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Ennealimnic-13 limit ennealimnic"&gt;13 limit ennealimnic&lt;/a&gt;&lt;/div&gt;
[[Category:octoid]]
&lt;!-- ws:end:WikiTextTocRule:160 --&gt;&lt;!-- ws:start:WikiTextTocRule:161: --&gt;&lt;div style="margin-left: 4em;"&gt;&lt;a href="#Ennealimmal-Ennealimnic-13 limit ennealimnic-17 limit ennealimnic"&gt;17 limit ennealimnic&lt;/a&gt;&lt;/div&gt;
[[Category:parakleismic]]
&lt;!-- ws:end:WikiTextTocRule:161 --&gt;&lt;!-- ws:start:WikiTextTocRule:162: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Ennealimnic-Ennealim"&gt;Ennealim&lt;/a&gt;&lt;/div&gt;
[[Category:supermajor]]
&lt;!-- ws:end:WikiTextTocRule:162 --&gt;&lt;!-- ws:start:WikiTextTocRule:163: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Ennealiminal"&gt;Ennealiminal&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:163 --&gt;&lt;!-- ws:start:WikiTextTocRule:164: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Ennealiminal-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:164 --&gt;&lt;!-- ws:start:WikiTextTocRule:165: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Trinealimmal"&gt;Trinealimmal&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:165 --&gt;&lt;!-- ws:start:WikiTextTocRule:166: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Semihemiennealimmal"&gt;Semihemiennealimmal&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:166 --&gt;&lt;!-- ws:start:WikiTextTocRule:167: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Gamera"&gt;Gamera&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Gamera-Hemigamera"&gt;Hemigamera&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Gamera-Hemigamera-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;!-- ws:start:WikiTextTocRule:170: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Supermajor"&gt;Supermajor&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:170 --&gt;&lt;!-- ws:start:WikiTextTocRule:171: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Supermajor-Semisupermajor"&gt;Semisupermajor&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:171 --&gt;&lt;!-- ws:start:WikiTextTocRule:172: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Enneadecal"&gt;Enneadecal&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:172 --&gt;&lt;!-- ws:start:WikiTextTocRule:173: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Deca"&gt;Deca&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:173 --&gt;&lt;!-- ws:start:WikiTextTocRule:174: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Deca-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:174 --&gt;&lt;!-- ws:start:WikiTextTocRule:175: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Deca-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:175 --&gt;&lt;!-- ws:start:WikiTextTocRule:176: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mitonic"&gt;Mitonic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:176 --&gt;&lt;!-- ws:start:WikiTextTocRule:177: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Abigail"&gt;Abigail&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:177 --&gt;&lt;!-- ws:start:WikiTextTocRule:178: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Abigail-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:178 --&gt;&lt;!-- ws:start:WikiTextTocRule:179: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Abigail-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:179 --&gt;&lt;!-- ws:start:WikiTextTocRule:180: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Semidimi"&gt;Semidimi&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:180 --&gt;&lt;!-- ws:start:WikiTextTocRule:181: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Brahmagupta"&gt;Brahmagupta&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:181 --&gt;&lt;!-- ws:start:WikiTextTocRule:182: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Brahmagupta-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:182 --&gt;&lt;!-- ws:start:WikiTextTocRule:183: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Neusec"&gt;Neusec&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:183 --&gt;&lt;!-- ws:start:WikiTextTocRule:184: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Neusec-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:184 --&gt;&lt;!-- ws:start:WikiTextTocRule:185: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quasithird"&gt;Quasithird&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:185 --&gt;&lt;!-- ws:start:WikiTextTocRule:186: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quasithird-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:186 --&gt;&lt;!-- ws:start:WikiTextTocRule:187: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quasithird-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:187 --&gt;&lt;!-- ws:start:WikiTextTocRule:188: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Semidimfourth"&gt;Semidimfourth&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:188 --&gt;&lt;!-- ws:start:WikiTextTocRule:189: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Acrokleismic"&gt;Acrokleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:189 --&gt;&lt;!-- ws:start:WikiTextTocRule:190: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Acrokleismic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:190 --&gt;&lt;!-- ws:start:WikiTextTocRule:191: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Acrokleismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:191 --&gt;&lt;!-- ws:start:WikiTextTocRule:192: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Acrokleismic-Counteracro"&gt;Counteracro&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:192 --&gt;&lt;!-- ws:start:WikiTextTocRule:193: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Acrokleismic-Counteracro-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:193 --&gt;&lt;!-- ws:start:WikiTextTocRule:194: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Seniority"&gt;Seniority&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:194 --&gt;&lt;!-- ws:start:WikiTextTocRule:195: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Orga"&gt;Orga&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:195 --&gt;&lt;!-- ws:start:WikiTextTocRule:196: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Orga-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:196 --&gt;&lt;!-- ws:start:WikiTextTocRule:197: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quatracot"&gt;Quatracot&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:197 --&gt;&lt;!-- ws:start:WikiTextTocRule:198: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quatracot-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:198 --&gt;&lt;!-- ws:start:WikiTextTocRule:199: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quatracot-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:199 --&gt;&lt;!-- ws:start:WikiTextTocRule:200: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Nearly Micro"&gt;Nearly Micro&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:200 --&gt;&lt;!-- ws:start:WikiTextTocRule:201: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Octoid"&gt;Octoid&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:201 --&gt;&lt;!-- ws:start:WikiTextTocRule:202: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:202 --&gt;&lt;!-- ws:start:WikiTextTocRule:203: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:203 --&gt;&lt;!-- ws:start:WikiTextTocRule:204: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:204 --&gt;&lt;!-- ws:start:WikiTextTocRule:205: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-Octopus"&gt;Octopus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:205 --&gt;&lt;!-- ws:start:WikiTextTocRule:206: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Amity"&gt;Amity&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:206 --&gt;&lt;!-- ws:start:WikiTextTocRule:207: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-5-limit"&gt;5-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:207 --&gt;&lt;!-- ws:start:WikiTextTocRule:208: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:208 --&gt;&lt;!-- ws:start:WikiTextTocRule:209: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:209 --&gt;&lt;!-- ws:start:WikiTextTocRule:210: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:210 --&gt;&lt;!-- ws:start:WikiTextTocRule:211: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-Accord"&gt;Accord&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:211 --&gt;&lt;!-- ws:start:WikiTextTocRule:212: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Amity-Accord-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:212 --&gt;&lt;!-- ws:start:WikiTextTocRule:213: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-Hitchcock"&gt;Hitchcock&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:213 --&gt;&lt;!-- ws:start:WikiTextTocRule:214: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Amity-Hitchcock-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:214 --&gt;&lt;!-- ws:start:WikiTextTocRule:215: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-Hemiamity"&gt;Hemiamity&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:215 --&gt;&lt;!-- ws:start:WikiTextTocRule:216: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Parakleismic"&gt;Parakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:216 --&gt;&lt;!-- ws:start:WikiTextTocRule:217: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:217 --&gt;&lt;!-- ws:start:WikiTextTocRule:218: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:218 --&gt;&lt;!-- ws:start:WikiTextTocRule:219: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-Parkleismic"&gt;Parkleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:219 --&gt;&lt;!-- ws:start:WikiTextTocRule:220: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Parakleismic-Parkleismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:220 --&gt;&lt;!-- ws:start:WikiTextTocRule:221: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-Paradigmic"&gt;Paradigmic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:221 --&gt;&lt;!-- ws:start:WikiTextTocRule:222: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Parakleismic-Paradigmic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:222 --&gt;&lt;!-- ws:start:WikiTextTocRule:223: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Semiparakleismic"&gt;Semiparakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:223 --&gt;&lt;!-- ws:start:WikiTextTocRule:224: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quincy"&gt;Quincy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:224 --&gt;&lt;!-- ws:start:WikiTextTocRule:225: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:225 --&gt;&lt;!-- ws:start:WikiTextTocRule:226: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:226 --&gt;&lt;!-- ws:start:WikiTextTocRule:227: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:227 --&gt;&lt;!-- ws:start:WikiTextTocRule:228: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:228 --&gt;&lt;!-- ws:start:WikiTextTocRule:229: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:229 --&gt;The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&amp;gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &amp;quot;relatively&amp;quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &amp;quot;relatively&amp;quot;; however 27/25 is the period for ennealimmal.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ennealimmal&lt;/h1&gt;
Ennealimmal temperament tempers out the two smallest 7-limit superparticular commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the ennealimma comma, |1 -27 18&amp;gt;, which leads to the identification of (27/25)^9 with the octave, and gives ennealimmal a period of 1/9 octave. While 27/25 is a 5-limit interval, two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit. Its wedgie is &amp;lt;&amp;lt;18 27 18 1 -22 -34||.&lt;br /&gt;
&lt;br /&gt;
Aside from 10/9 which has already been mentioned, possible generators include 36/35, 21/20, 6/5, 7/5 and the neutral thirds pair 49/40 and 60/49, all of which have their own interesting advantages. Possible tunings are 441, 612, or 3600 equal, though its hardly likely anyone could tell the difference.&lt;br /&gt;
&lt;br /&gt;
If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example.) In particular, people fond of the idea of &amp;quot;tritaves&amp;quot; as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a &amp;quot;tritave&amp;quot;. Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments"&gt;valid range&lt;/a&gt;: [26.667, 66.667] (45bcd to 18bcd)&lt;br /&gt;
nice range: [48.920, 49.179]&lt;br /&gt;
strict range: [48.920, 49.179]&lt;br /&gt;
&lt;br /&gt;
Commas: 2401/2400, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generators: 36/35: 49.0205; 10/9: 182.354; 6/5: 315.687; 49/40: 350.980&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 2|, &amp;lt;0 2 3 2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;18 27 18 1 -22 -34||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;, &lt;a class="wiki_link" href="/270edo"&gt;270&lt;/a&gt;, &lt;a class="wiki_link" href="/441edo"&gt;441&lt;/a&gt;, &lt;a class="wiki_link" href="/612edo"&gt;612&lt;/a&gt;, &lt;a class="wiki_link" href="/3600edo"&gt;3600&lt;/a&gt;&lt;br /&gt;
Badness: 0.00361&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Ennealimmal-11 limit hemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11 limit hemiennealimmal&lt;/h2&gt;
Commas: 2401/2400, 4375/4374, 3025/3024&lt;br /&gt;
&lt;br /&gt;
valid range: [13.333, 22.222] (90bcd, 54c)&lt;br /&gt;
nice range: [17.304, 17.985]&lt;br /&gt;
strict range:  [17.304, 17.985]&lt;br /&gt;
&lt;br /&gt;
POTE generator: 99/98: 17.6219 or 6/5: 315.7114&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;18 0 -1 22 48|, &amp;lt;0 2 3 2 1|]&lt;br /&gt;
EDOs: 72, 198, 270, 342, 612, 954, 1566&lt;br /&gt;
Badness: 0.00628&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Ennealimmal-13 limit hemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13 limit hemiennealimmal&lt;/h2&gt;
Commas: 676/675, 1001/1000, 1716/1715, 3025/3024&lt;br /&gt;
&lt;br /&gt;
valid range: [16.667, 22.222] (72 to 54cf)&lt;br /&gt;
nice range: [17.304, 18.309]&lt;br /&gt;
strict range: [17.304, 18.309]&lt;br /&gt;
&lt;br /&gt;
POTE generator ~99/98 = 17.7504&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;18 0 -1 22 48 -19|, &amp;lt;0 2 3 2 1 6|]&lt;br /&gt;
EDOs: 72, 198, 270&lt;br /&gt;
Badness: 0.0125&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Ennealimmal-Semiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Semiennealimmal&lt;/h2&gt;
Commas: 2401/2400, 4375/4374, 4000/3993&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~140/121 = 250.3367&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 3 4 14 18|, &amp;lt;0 6 9 6 7|]&lt;br /&gt;
EDOs: 72, 369, 441&lt;br /&gt;
Badness: 0.0342&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Ennealimmal-Semiennealimmal-13 limit semiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13 limit semiennealimmal&lt;/h3&gt;
Commas: 1575/1573, 2080/2079, 2401/2400, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~140/121 = 250.3375&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 3 4 14 18 -8|, &amp;lt;0 6 9 6 7 22|]&lt;br /&gt;
EDOs: 72, 441&lt;br /&gt;
Badness: 0.0261&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Ennealimmal-Quadraennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Quadraennealimmal&lt;/h2&gt;
Commas: 2401/2400 4375/4374 234375/234256&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~77/75 = 45.595&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 -7|, [0 8 12 8 23]]&lt;br /&gt;
EDOs: 342, 1053, 1395, 1737, 4869d, 6606cd&lt;br /&gt;
Badness: 0.0213&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Ennealimmal-Ennealimnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Ennealimnic&lt;/h2&gt;
Commas: 243/242, 441/440, 4375/4356&lt;br /&gt;
&lt;br /&gt;
valid range: [44.444, 53.333] (27e to 45e)&lt;br /&gt;
nice range: [48.920, 52.592]&lt;br /&gt;
strict range: [48.920, 52.592]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 49.395&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 -2|, &amp;lt;0 2 3 2 5|]&lt;br /&gt;
EDOs: 72, 171, 243&lt;br /&gt;
Badness: 0.0203&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Ennealimmal-Ennealimnic-13 limit ennealimnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13 limit ennealimnic&lt;/h3&gt;
Commas: 243/242, 364/363, 441/440, 625/624&lt;br /&gt;
&lt;br /&gt;
valid range: [48.485, 50.000] (99ef to 72)&lt;br /&gt;
nice range: [48.825, 52.592]&lt;br /&gt;
strict range: [48.825, 50.000]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 49.341&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 -2 -33|, &amp;lt;0 2 3 2 5 10|]&lt;br /&gt;
EDOs: 72, 171, 243&lt;br /&gt;
Badness: 0.0233&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc8"&gt;&lt;a name="Ennealimmal-Ennealimnic-13 limit ennealimnic-17 limit ennealimnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;17 limit ennealimnic&lt;/h4&gt;
Commas: 243/242, 364/363, 375/374, 441/440, 595/594&lt;br /&gt;
&lt;br /&gt;
valid range: [48.485, 50.000] (99ef to 72)&lt;br /&gt;
nice range: [46.363, 52.592]&lt;br /&gt;
strict range: [48.485, 50.000]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 49.335&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 -2 -33 -3|, &amp;lt;0 2 3 2 5 10 6|]&lt;br /&gt;
EDOs: 72, 171, 243&lt;br /&gt;
Badness: 0.0146&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Ennealimmal-Ennealimnic-Ennealim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Ennealim&lt;/h3&gt;
Commas: 169/168, 243/242, 325/324, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 49.708&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 -2 20|, &amp;lt;0 2 3 2 5 2|]&lt;br /&gt;
EDOs: 27e, 45f, 72, 315ff, 387cff, 459cdfff&lt;br /&gt;
Badness: 0.0207&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Ennealimmal-Ennealiminal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Ennealiminal&lt;/h2&gt;
Commas: 385/384, 1375/1372, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 49.504&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 51|, &amp;lt;0 2 3 2 -3|]&lt;br /&gt;
EDOs: 27, 45, 72, 171e, 243e, 315e&lt;br /&gt;
Badness: 0.0311&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Ennealimmal-Ennealiminal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h3&gt;
Commas: 169/168, 325/324, 385/384, 1375/1372&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 49.486&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 1 1 12 51 20|, &amp;lt;0 2 3 2 -3 2|]&lt;br /&gt;
EDOs: 27, 45f, 72, 171ef, 243ef&lt;br /&gt;
Badness: 0.0303&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Ennealimmal-Trinealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Trinealimmal&lt;/h2&gt;
Commas: 2401/2400, 4375/4374, 2097152/2096325&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.644&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;27 1 0 34 177|, &amp;lt;0 2 3 2 -4|]&lt;br /&gt;
EDOs: 27, 243, 270, 783, 1053, 1323, 10854bcde&lt;br /&gt;
Badness: 0.0298&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Ennealimmal-Semihemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Semihemiennealimmal&lt;/h2&gt;
Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~39/32 = 342.139&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;18 0 -1 22 48 88|, &amp;lt;0 4 6 4 2 -3|]&lt;br /&gt;
EDOs: 126, 144, 270, 684, 954&lt;br /&gt;
Badness: 0.0131&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Gamera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Gamera&lt;/h1&gt;
Commas: 4375/4374, 589824/588245&lt;br /&gt;
&lt;br /&gt;
POTE generator ~8/7 = 230.336&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 10 3|, &amp;lt;0 -23 -40 -1|]&lt;br /&gt;
EDOs: 26, 73, 99, 224, 323, 422, 735&lt;br /&gt;
Badness: 0.0376&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Gamera-Hemigamera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Hemigamera&lt;/h2&gt;
Commas: 3025/3024, 4375/4374, 202397184/201768035&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 230.337&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 12 20 6 5|, &amp;lt;0 -23 -40 -1 5|]&lt;br /&gt;
EDOs: 26, 198, 224, 422, 646, 1068d&lt;br /&gt;
Badness: 0.0410&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Gamera-Hemigamera-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h3&gt;
Commas: 1716/1715 2080/2079 2200/2197 3025/3024&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 12 20 6 5 17|, &amp;lt;0 -23 -40 -1 5 -25|]&lt;br /&gt;
EDOs: 26, 198, 224, 422, 646f, 1068df&lt;br /&gt;
Badness: 0.0204&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Supermajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Supermajor&lt;/h1&gt;
The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.0002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of &amp;lt;&amp;lt;37 46 75 -13 15 45||. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.&lt;br /&gt;
&lt;br /&gt;
Commas: 4375/4374, 52734375/52706752&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 435.082&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 15 19 30|, &amp;lt;0 -37 -46 -75|]&lt;br /&gt;
EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214&lt;br /&gt;
Badness: 0.0108&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Supermajor-Semisupermajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Semisupermajor&lt;/h2&gt;
Commas: 3025/3024, 4375/4374, 35156250/35153041&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 435.082&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 30 38 60 41|, &amp;lt;0 -37 -46 -75 -47|]&lt;br /&gt;
EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf&lt;br /&gt;
Badness: 0.0128&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Enneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Enneadecal&lt;/h1&gt;
Enndedecal temperament tempers out the enneadeca, |-14 -19 19&amp;gt;, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; up to just ones. &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; is a good tuning for either the 5 or 7 limits, and &lt;a class="wiki_link" href="/494edo"&gt;494edo&lt;/a&gt; shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use &lt;a class="wiki_link" href="/665edo"&gt;665edo&lt;/a&gt; for a tuning.&lt;br /&gt;
&lt;br /&gt;
Commas: 4375/4374, 703125/702464&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.880&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;19 0 14 -37|, &amp;lt;0 1 1 3|]&lt;br /&gt;
Generators: 28/27, 3&lt;br /&gt;
EDOs: 19, 152, 171, 665, 836, 1007, 2185&lt;br /&gt;
Badness: 0.0110&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Deca"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Deca&lt;/h1&gt;
Commas: 4375/4374, 165288374272/164794921875&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~460992/390625 = 284.423&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;10 4 2 9|, &amp;lt;0 5 6 11|]&lt;br /&gt;
EDOs: 80, 190, 270, 1270, 1540, 1810, 2080&lt;br /&gt;
Badness: 0.0806&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Deca-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
Commas: 3025/3024, 4375/4374, 422576/421875&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~33/28 = 284.418&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;10 4 2 9 18|, &amp;lt;0 5 6 11 7|]&lt;br /&gt;
EDOs: 80, 190, 270, 1000, 1270&lt;br /&gt;
Badness: 0.0243&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Deca-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~33/28 = 284.398&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;10 4 2 9 18 37|, &amp;lt;0 5 6 11 7 0|]&lt;br /&gt;
EDOs: 80, 190, 270, 730, 1000&lt;br /&gt;
Badness: 0.0168&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Mitonic&lt;/h1&gt;
Commas: 4375/4374, 2100875/2097152&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 182.458&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 16 32 -15|, &amp;lt;0 -17 -35 21|]&lt;br /&gt;
EDOs: 46, 125, 171&lt;br /&gt;
Badness: 0.0252&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Abigail&lt;/h1&gt;
Commas: 4375/4374, 2147483648/2144153025&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 208.899&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 7 13 -1|, &amp;lt;0 -11 -24 19|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;22 48 -38 25 -122 -223||&lt;br /&gt;
EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798&lt;br /&gt;
Badness: 0.0370&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
Comma: 3025/3024, 4375/4374, 20614528/20588575&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 208.901&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 7 13 -1 1|, &amp;lt;0 -11 -24 19 17|]&lt;br /&gt;
EDOs: 46, 132, 178, 224, 270, 494, 764&lt;br /&gt;
Badness: 0.0129&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 208.903&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 7 13 -1 1 -2|, &amp;lt;0 -11 -24 19 17 27|]&lt;br /&gt;
EDOs: 46, 178, 224, 270, 494, 764, 1258&lt;br /&gt;
Badness: 0.00886&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Semidimi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Semidimi&lt;/h1&gt;
Commas: 4375/4374, 3955078125/3954653486&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~35/27 = 449.127&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 36 48 61|, &amp;lt;0 -55 -73 -93|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;55 73 93 -12 -7 11||&lt;br /&gt;
EDOs: 171, 863, 8419, 1205, 1376, 1547, 1718, 4983, 6701, 8419&lt;br /&gt;
Badness: 0.0151&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="Brahmagupta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Brahmagupta&lt;/h1&gt;
Commas: 4375/4374, 70368744177664/70338939985125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 519.716&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 2 -8 53|, &amp;lt;0 3 8 -11|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;21 56 -77 40 -181 -336||&lt;br /&gt;
EDOs: 217, 224, 441, 1106, 1547&lt;br /&gt;
Badness: 0.0291&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Brahmagupta-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;11-limit&lt;/h2&gt;
Commas: 4000/3993, 4375/4374, 131072/130977&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 519.704&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;7 2 -8 53 3|, &amp;lt;0 3 8 -11 7|]&lt;br /&gt;
EDOs: 217, 224, 441, 665, 1771e&lt;br /&gt;
Badness: 0.0522&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Neusec"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Neusec&lt;/h1&gt;
Commas: 3025/3024, 4375/4374, 235298/234375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~12/11 = 151.547&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 11 15 19 15|, &amp;lt;0 -31 -41 -53 -32|]&lt;br /&gt;
EDOs: 190, 388&lt;br /&gt;
Badness: 0.0591&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Neusec-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;13-limit&lt;/h2&gt;
Commas: 847/845, 1001/1000, 3025/3024, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~12/11 = 151.545&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 11 15 19 15 17|, &amp;lt;0 -31 -41 -53 -32 -38|]&lt;br /&gt;
EDOs: 190, 198, 388&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Quasithird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Quasithird&lt;/h1&gt;
Commas: 4375/4374, 1153470752371588581/1152921504606846976&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5103/4096 = 380.388&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;4 0 -11 48|, &amp;lt;0 5 16 -29|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;20 64 -116 55 -240 -449||&lt;br /&gt;
EDOs: 164, 224, 388, 612, 1448, 2060&lt;br /&gt;
Badness: 0.0618&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Quasithird-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;11-limit&lt;/h2&gt;
Commas: 3025/3024, 4375/4374, 4296700485/4294967296&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5103/4096 = 380.387&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;4 0 -11 48 43|, &amp;lt;0 5 16 -29 -23|]&lt;br /&gt;
EDOs: 164, 224, 388, 612, 836, 1448&lt;br /&gt;
Badness: 0.0211&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Quasithird-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;13-limit&lt;/h2&gt;
Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5103/4096 = 380.385&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;4 0 -11 48 43 11|, &amp;lt;0 5 16 -29 -23 3|]&lt;br /&gt;
EDOs: 164, 224, 388, 612, 836, 1448f, 2284f&lt;br /&gt;
Badness: 0.0295&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Semidimfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Semidimfourth&lt;/h1&gt;
Commas: 4375/4374, 235298/234375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~35/27 = 448.457&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 21 28 36|, &amp;lt;0 -31 -41 -53|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;31 41 53 -7 -3 8||&lt;br /&gt;
EDOs: 91, 99, 289, 388, 875, 1263d, 1651d&lt;br /&gt;
Badness: 0.0552&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc36"&gt;&lt;a name="Acrokleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Acrokleismic&lt;/h1&gt;
Commas: 4375/4374, 2202927104/2197265625&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.557&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 10 11 27|, &amp;lt;0 -32 -33 -92|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;32 33 92 -22 56 121||&lt;br /&gt;
EDOs: 19, 251, 270&lt;br /&gt;
Badness: 0.0562&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Acrokleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;11-limit&lt;/h2&gt;
Commas: 4375/4374, 41503/41472, 172032/171875&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.558&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 10 11 27 -16|, &amp;lt;0 -32 -33 -92 74|]&lt;br /&gt;
EDOs: 19, 251, 270, 829, 1099, 1369, 1639&lt;br /&gt;
Badness: 0.0369&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Acrokleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;13-limit&lt;/h2&gt;
Commas: 676/675, 1001/1000, 4375/4374, 10985/10976&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.557&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 10 11 27 -16 25|, &amp;lt;0 -32 -33 -92 74 -81|]&lt;br /&gt;
EDOs: 19, 251, 270&lt;br /&gt;
Badness: 0.0268&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Acrokleismic-Counteracro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;Counteracro&lt;/h2&gt;
Commas: 4375/4374, 5632/5625, 117649/117612&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.553&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 10 11 27 55|, &amp;lt;0 -32 -33 -92 -196|]&lt;br /&gt;
EDOs: 270, 1061e, 1331c, 1601c, 1871bc, 4012bcde&lt;br /&gt;
Badness: 0.0426&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc40"&gt;&lt;a name="Acrokleismic-Counteracro-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;13-limit&lt;/h3&gt;
Commas: 676/675, 1716/1715, 4225/4224, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.554&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 10 11 27 55 25|, &amp;lt;0 -32 -33 -92 -196 -81|]&lt;br /&gt;
EDOs: 270, 1331c, 1601c, 1871bcf, 2141bcf&lt;br /&gt;
Badness: 0.0260&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc41"&gt;&lt;a name="Seniority"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;Seniority&lt;/h1&gt;
Commas: 4375/4374 201768035/201326592&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3087/2560 = 322.804&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 11 19 2|, &amp;lt;0 -35 -62 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;35 62 -3 17 -103 -181||&lt;br /&gt;
EDOs: 26, 145, 171, 2710d&lt;br /&gt;
Badness: 0.0449&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc42"&gt;&lt;a name="Orga"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;Orga&lt;/h1&gt;
Commas: 4375/4374 54975581388800/54936068900769&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 231.104&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 21 36 5|, &amp;lt;0 -29 -51 1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;58 102 -2 27 -166 -291||&lt;br /&gt;
EDOs: 26, 244, 270, 836, 1106, 1376, 2482, 19856bd, 23714bd&lt;br /&gt;
Badness: 0.0402&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc43"&gt;&lt;a name="Orga-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;11-limit&lt;/h2&gt;
Commas: 3025/3024 4375/4374 5767168/5764801&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 231.103&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 21 36 5 2|, &amp;lt;0 -29 -51 1 8|]&lt;br /&gt;
EDOs: 26, 244, 270, 566, 836, 1106, 7472e, 8578de, 9684cde, 10790cde, 11896cde&lt;br /&gt;
Badness: 0.0162&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc44"&gt;&lt;a name="Quatracot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;Quatracot&lt;/h1&gt;
Commas: 4375/4374, 1483154296875/1473173782528&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~448/405 = 176.805&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 7 7 23|, &amp;lt;0 -13 -8 -59|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;26 16 118 -35 114 229||&lt;br /&gt;
EDOs: 190, 224, 414, 638, 1052c, 1690bc&lt;br /&gt;
Badness: 0.1760&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Quatracot-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;11-limit&lt;/h2&gt;
Commas: 3025/3024, 4375/4374, 1265625/1261568&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~448/405 = 176.806&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 7 7 23 19|, &amp;lt;0 -13 -8 -59 -41|]&lt;br /&gt;
EDOs: 190, 224, 414, 638, 1052c&lt;br /&gt;
Badness: 0.0410&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc46"&gt;&lt;a name="Quatracot-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;13-limit&lt;/h2&gt;
Commas: 625/624, 729/728, 1575/1573, 2200/2197&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~448/405 = 176.804&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 7 7 23 19 13|, &amp;lt;0 -13 -8 -59 -41 -19|]&lt;br /&gt;
EDOs: 190, 224, 414, 638, 1690bc, 2328bcde&lt;br /&gt;
Badness: 0.0226&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc47"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;Nearly Micro&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc48"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Octoid&lt;/h1&gt;
Commas: 4375/4374, 16875/16807&lt;br /&gt;
&lt;br /&gt;
valid range: [578.571, 600.000] (56bcd to 8d)&lt;br /&gt;
nice range: [582.512, 584.359]&lt;br /&gt;
strict range:  [582.512, 584.359]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 583.940&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 1 3 3|, &amp;lt;0 3 4 5|]&lt;br /&gt;
Generators: 49/45, 7/5&lt;br /&gt;
EDOs: 72, 152, 224&lt;br /&gt;
Badness: 0.0427&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
&lt;br /&gt;
valid range: [581.250, 586.364] (64cd, 88bcde)&lt;br /&gt;
nice range: [582.512, 585.084]&lt;br /&gt;
strict range: [582.512, 585.084]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 583.692&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 1 3 3 16|, &amp;lt;0 3 4 5 3|]&lt;br /&gt;
EDOs: 72, 152, 224&lt;br /&gt;
Badness: 0.0141&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;13-limit&lt;/h2&gt;
Commas: 540/539, 1375/1372, 4000/3993, 625/624&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 583.905&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 1 3 3 16 -21|, &amp;lt;0 3 4 5 3 13|]&lt;br /&gt;
EDOs: 72, 224&lt;br /&gt;
Badness: 0.0153&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;Music&lt;/h2&gt;
&lt;!-- ws:start:WikiTextUrlRule:898:http://www.archive.org/details/Dreyfus --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow"&gt;http://www.archive.org/details/Dreyfus&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:898 --&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Octoid-Octopus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;Octopus&lt;/h2&gt;
Commas: 169/168, 325/324, 364/363, 540/539&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 583.892&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 1 3 3 16 14|, &amp;lt;0 3 4 5 3 4|]&lt;br /&gt;
EDOs: 72, 152, 224f&lt;br /&gt;
Badness: 0.0217&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc53"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Amity&lt;/h1&gt;
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;amp;53 temperament, or by its wedgie, &amp;lt;&amp;lt;5 13 -17 9 -41 -76||. &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.&lt;br /&gt;
&lt;br /&gt;
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc54"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;5-limit&lt;/h2&gt;
Comma: 1600000/1594323&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.519&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6|, &amp;lt;0 -5 -13|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873&lt;br /&gt;
Badness: 0.0220&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;7-limit&lt;/h2&gt;
Commas: 4375/4374, 5120/5103&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.432&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2|, &amp;lt;0 -5 -13 17|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 13 -17 9 -41 -76||&lt;br /&gt;
EDOs: 7, 39, 46, 53, 99, 251, 350&lt;br /&gt;
Badness: 0.0236&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc56"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.464&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2 21|, &amp;lt;0 -5 -13 17 -62|]&lt;br /&gt;
EDOs: 53, 99e, 152, 555de, 707de, 859bde&lt;br /&gt;
Badness: 0.0315&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:114:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc57"&gt;&lt;a name="Amity-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:114 --&gt;13-limit&lt;/h2&gt;
Commas: 352/351, 540/539, 625/624, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.481&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2 21 17|, &amp;lt;0 -5 -13 17 -62 -47|]&lt;br /&gt;
EDOS: 53, 99ef, 152f, 205&lt;br /&gt;
Badness: 0.0280&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:116:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc58"&gt;&lt;a name="Amity-Accord"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:116 --&gt;Accord&lt;/h2&gt;
Commas: 126/125, 100352/98415&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 338.993&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 11|, &amp;lt;0 -5 -13 -29|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 13 29 9 32 31||&lt;br /&gt;
EDOs: 46, 131c, 177c&lt;br /&gt;
Badness: 0.0956&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:118:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc59"&gt;&lt;a name="Amity-Accord-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:118 --&gt;11-limit&lt;/h3&gt;
Commas: 121/120, 126/125, 896/891&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 339.047&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 11 6|, &amp;lt;0 -5 -13 -29 -9|]&lt;br /&gt;
EDOs: 46, 177c, 223bc, 269bce&lt;br /&gt;
Badness: 0.0425&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc60"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;Hitchcock&lt;/h2&gt;
Commas: 121/120, 176/175, 2200/2187&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 339.340&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2 6|, &amp;lt;0 -5 -13 17 -9|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 99&lt;br /&gt;
Badness: 0.0352&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc61"&gt;&lt;a name="Amity-Hitchcock-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;13-limit&lt;/h3&gt;
Commas: 121/120, 169/168, 176/175, 325/324&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 339.419&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2 6 2|, &amp;lt;0 -5 -13 17 -9 6|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 99&lt;br /&gt;
Badness: 0.0224&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:124:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc62"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:124 --&gt;Hemiamity&lt;/h2&gt;
Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~ 243/200 = 339.493&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 -1 13 13|, &amp;lt;0 5 13 -17 -14|]&lt;br /&gt;
EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:126:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc63"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:126 --&gt;Parakleismic&lt;/h1&gt;
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&amp;gt;, with the &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &amp;lt;&amp;lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &amp;lt;&amp;lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; may be preferred, but in the 11-limit it is best to stick with 118.&lt;br /&gt;
&lt;br /&gt;
Comma: 124440064/1220703125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.240&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6|, &amp;lt;0 -13 -14|]&lt;br /&gt;
EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496&lt;br /&gt;
Badness: 0.0433&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:128:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc64"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:128 --&gt;7-limit&lt;/h2&gt;
Commas: 3136/3125, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.181&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12|, &amp;lt;0 -13 -14 -35|]&lt;br /&gt;
EDOs: 19, 80, 99, 217, 316, 415&lt;br /&gt;
Badness: 0.0274&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc65"&gt;&lt;a name="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;11-limit&lt;/h2&gt;
Commas: 385/384, 3136/3125, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.251&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 -6|, &amp;lt;0 -13 -14 -35 36|]&lt;br /&gt;
EDOs: 19, 99, 118&lt;br /&gt;
Badness: 0.0497&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc66"&gt;&lt;a name="Parakleismic-Parkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;Parkleismic&lt;/h2&gt;
Commas: 176/175, 1375/1372, 2200/2187&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.060&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 20|, &amp;lt;0 -13 -14 -35 -63|]&lt;br /&gt;
EDOs: 80, 179, 259cd&lt;br /&gt;
Badness: 0.0559&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:134:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc67"&gt;&lt;a name="Parakleismic-Parkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:134 --&gt;13-limit&lt;/h3&gt;
Commas: 169/168, 176/175, 325/324, 1375/1372&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.075&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 20 10|, &amp;lt;0 -13 -14 -35 -63 -24|]&lt;br /&gt;
EDOs: 15, 19, 80, 179&lt;br /&gt;
Badness: 0.0366&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:136:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc68"&gt;&lt;a name="Parakleismic-Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:136 --&gt;Paradigmic&lt;/h2&gt;
Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.096&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 -1|, &amp;lt;0 -13 -14 -35 17|]&lt;br /&gt;
EDOs: 19, 80, 99e, 179e&lt;br /&gt;
Badness: 0.0417&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:138:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc69"&gt;&lt;a name="Parakleismic-Paradigmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:138 --&gt;13-limit&lt;/h3&gt;
Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.080&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 -1 10|, &amp;lt;0 -13 -14 -35 17 -24|]&lt;br /&gt;
EDOs: 19, 80, 99e, 179e&lt;br /&gt;
Badness: 0.0358&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:140:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc70"&gt;&lt;a name="Semiparakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:140 --&gt;Semiparakleismic&lt;/h1&gt;
Commas: 3025/3024, 3136/3125, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: 315.181&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 10 12 24 19|, &amp;lt;0 -13 -14 -35 -23|]&lt;br /&gt;
EDOs: 80, 118, 198, 316, 514c, 830c&lt;br /&gt;
Badness: 0.0342&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:142:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc71"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:142 --&gt;Quincy&lt;/h1&gt;
Commas: 4375/4374, 823543/819200&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~1728/1715 = 16.613&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -30 -49 -14|]&lt;br /&gt;
EDOs: 72, 217, 289&lt;br /&gt;
Badness: 0.0797&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:144:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc72"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:144 --&gt;11-limit&lt;/h2&gt;
Commas: 441/440, 4000/3993, 41503/41472&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~100/99 = 16.613&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -30 -49 -14 -39|]&lt;br /&gt;
EDOs: 72, 217, 289&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:146:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc73"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:146 --&gt;13-limit&lt;/h2&gt;
Commas: 364/363, 441/440, 676/675, 4375/4374&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~100/99 = 16.602&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 5|, &amp;lt;0 -30 -49 -14 -39 -94|]&lt;br /&gt;
EDOs: 72, 145, 217, 289&lt;br /&gt;
Badness: 0.0239&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:148:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc74"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:148 --&gt;17-limit&lt;/h2&gt;
Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~100/99 = 16.602&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 5 5|, &amp;lt;0 -30 -49 -14 -39 -94 -66|]&lt;br /&gt;
EDOs: 72, 145, 217, 289&lt;br /&gt;
Badness: 0.0147&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:150:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc75"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:150 --&gt;19-limit&lt;/h2&gt;
Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~100/99 = 16.594&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 5 5 4|, &amp;lt;0 -30 -49 -14 -39 -94 -66 18|]&lt;br /&gt;
EDOs: 72, 145, 217&lt;br /&gt;
Badness: 0.0152&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The ragisma is 4375/4374 with a monzo of |-1 -7 4 1>, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.

Ennealimmal

Ennealimmal temperament tempers out the two smallest 7-limit superparticular commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the ennealimma comma, |1 -27 18>, which leads to the identification of (27/25)^9 with the octave, and gives ennealimmal a period of 1/9 octave. While 27/25 is a 5-limit interval, two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit. Its wedgie is <<18 27 18 1 -22 -34||.

Aside from 10/9 which has already been mentioned, possible generators include 36/35, 21/20, 6/5, 7/5 and the neutral thirds pair 49/40 and 60/49, all of which have their own interesting advantages. Possible tunings are 441, 612, or 3600 equal, though its hardly likely anyone could tell the difference.

If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example.) In particular, people fond of the idea of "tritaves" as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a "tritave". Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS.

valid range: [26.667, 66.667] (45bcd to 18bcd)

nice range: [48.920, 49.179]

strict range: [48.920, 49.179]

Commas: 2401/2400, 4375/4374

POTE generators: 36/35: 49.0205; 10/9: 182.354; 6/5: 315.687; 49/40: 350.980

Map: [<9 1 1 2|, <0 2 3 2|]

Wedgie: <<18 27 18 1 -22 -34||

EDOs: 27, 45, 72, 99, 171, 270, 441, 612, 3600

Badness: 0.00361

11 limit hemiennealimmal

Commas: 2401/2400, 4375/4374, 3025/3024

valid range: [13.333, 22.222] (90bcd, 54c)

nice range: [17.304, 17.985]

strict range: [17.304, 17.985]

POTE generator: 99/98: 17.6219 or 6/5: 315.7114

Map: [<18 0 -1 22 48|, <0 2 3 2 1|]

EDOs: 72, 198, 270, 342, 612, 954, 1566

Badness: 0.00628

13 limit hemiennealimmal

Commas: 676/675, 1001/1000, 1716/1715, 3025/3024

valid range: [16.667, 22.222] (72 to 54cf)

nice range: [17.304, 18.309]

strict range: [17.304, 18.309]

POTE generator ~99/98 = 17.7504

Map: [<18 0 -1 22 48 -19|, <0 2 3 2 1 6|]

EDOs: 72, 198, 270

Badness: 0.0125

Semiennealimmal

Commas: 2401/2400, 4375/4374, 4000/3993

POTE generator: ~140/121 = 250.3367

Map: [<9 3 4 14 18|, <0 6 9 6 7|]

EDOs: 72, 369, 441

Badness: 0.0342

13 limit semiennealimmal

Commas: 1575/1573, 2080/2079, 2401/2400, 4375/4374

POTE generator: ~140/121 = 250.3375

Map: [<9 3 4 14 18 -8|, <0 6 9 6 7 22|]

EDOs: 72, 441

Badness: 0.0261

Quadraennealimmal

Commas: 2401/2400 4375/4374 234375/234256

POTE generator: ~77/75 = 45.595

Map: [<9 1 1 12 -7|, [0 8 12 8 23]]

EDOs: 342, 1053, 1395, 1737, 4869d, 6606cd

Badness: 0.0213

Ennealimnic

Commas: 243/242, 441/440, 4375/4356

valid range: [44.444, 53.333] (27e to 45e)

nice range: [48.920, 52.592]

strict range: [48.920, 52.592]

POTE generator: ~36/35 = 49.395

Map: [<9 1 1 12 -2|, <0 2 3 2 5|]

EDOs: 72, 171, 243

Badness: 0.0203

13 limit ennealimnic

Commas: 243/242, 364/363, 441/440, 625/624

valid range: [48.485, 50.000] (99ef to 72)

nice range: [48.825, 52.592]

strict range: [48.825, 50.000]

POTE generator: ~36/35 = 49.341

Map: [<9 1 1 12 -2 -33|, <0 2 3 2 5 10|]

EDOs: 72, 171, 243

Badness: 0.0233

17 limit ennealimnic

Commas: 243/242, 364/363, 375/374, 441/440, 595/594

valid range: [48.485, 50.000] (99ef to 72)

nice range: [46.363, 52.592]

strict range: [48.485, 50.000]

POTE generator: ~36/35 = 49.335

Map: [<9 1 1 12 -2 -33 -3|, <0 2 3 2 5 10 6|]

EDOs: 72, 171, 243

Badness: 0.0146

Ennealim

Commas: 169/168, 243/242, 325/324, 441/440

POTE generator: ~36/35 = 49.708

Map: [<9 1 1 12 -2 20|, <0 2 3 2 5 2|]

EDOs: 27e, 45f, 72, 315ff, 387cff, 459cdfff

Badness: 0.0207

Ennealiminal

Commas: 385/384, 1375/1372, 4375/4374

POTE generator: ~36/35 = 49.504

Map: [<9 1 1 12 51|, <0 2 3 2 -3|]

EDOs: 27, 45, 72, 171e, 243e, 315e

Badness: 0.0311

13-limit

Commas: 169/168, 325/324, 385/384, 1375/1372

POTE generator: ~36/35 = 49.486

Map: [<9 1 1 12 51 20|, <0 2 3 2 -3 2|]

EDOs: 27, 45f, 72, 171ef, 243ef

Badness: 0.0303

Trinealimmal

Commas: 2401/2400, 4375/4374, 2097152/2096325

POTE generator: ~6/5 = 315.644

Map: [<27 1 0 34 177|, <0 2 3 2 -4|]

EDOs: 27, 243, 270, 783, 1053, 1323, 10854bcde

Badness: 0.0298

Semihemiennealimmal

Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224

POTE generator: ~39/32 = 342.139

Map: [<18 0 -1 22 48 88|, <0 4 6 4 2 -3|]

EDOs: 126, 144, 270, 684, 954

Badness: 0.0131

Gamera

Commas: 4375/4374, 589824/588245

POTE generator ~8/7 = 230.336

Map: [<1 6 10 3|, <0 -23 -40 -1|]

EDOs: 26, 73, 99, 224, 323, 422, 735

Badness: 0.0376

Hemigamera

Commas: 3025/3024, 4375/4374, 202397184/201768035

POTE generator: ~8/7 = 230.337

Map: [<2 12 20 6 5|, <0 -23 -40 -1 5|]

EDOs: 26, 198, 224, 422, 646, 1068d

Badness: 0.0410

13-limit

Commas: 1716/1715 2080/2079 2200/2197 3025/3024

Map: [<2 12 20 6 5 17|, <0 -23 -40 -1 5 -25|]

EDOs: 26, 198, 224, 422, 646f, 1068df

Badness: 0.0204

Supermajor

The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.0002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of <<37 46 75 -13 15 45||. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.

Commas: 4375/4374, 52734375/52706752

POTE generator: ~9/7 = 435.082

Map: [<1 15 19 30|, <0 -37 -46 -75|]

EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214

Badness: 0.0108

Semisupermajor

Commas: 3025/3024, 4375/4374, 35156250/35153041

POTE generator: ~9/7 = 435.082

Map: [<2 30 38 60 41|, <0 -37 -46 -75 -47|]

EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf

Badness: 0.0128

Enneadecal

Enndedecal temperament tempers out the enneadeca, |-14 -19 19>, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of 19edo up to just ones. 171edo is a good tuning for either the 5 or 7 limits, and 494edo shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use 665edo for a tuning.

Commas: 4375/4374, 703125/702464

POTE generator: ~3/2 = 701.880

Map: [<19 0 14 -37|, <0 1 1 3|]

Generators: 28/27, 3

EDOs: 19, 152, 171, 665, 836, 1007, 2185

Badness: 0.0110

Deca

Commas: 4375/4374, 165288374272/164794921875

POTE generator: ~460992/390625 = 284.423

Map: [<10 4 2 9|, <0 5 6 11|]

EDOs: 80, 190, 270, 1270, 1540, 1810, 2080

Badness: 0.0806

11-limit

Commas: 3025/3024, 4375/4374, 422576/421875

POTE generator: ~33/28 = 284.418

Map: [<10 4 2 9 18|, <0 5 6 11 7|]

EDOs: 80, 190, 270, 1000, 1270

Badness: 0.0243

13-limit

Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374

POTE generator: ~33/28 = 284.398

Map: [<10 4 2 9 18 37|, <0 5 6 11 7 0|]

EDOs: 80, 190, 270, 730, 1000

Badness: 0.0168

Mitonic

Commas: 4375/4374, 2100875/2097152

POTE generator: ~10/9 = 182.458

Map: [<1 16 32 -15|, <0 -17 -35 21|]

EDOs: 46, 125, 171

Badness: 0.0252

Abigail

Commas: 4375/4374, 2147483648/2144153025

POTE generator: 208.899

Map: [<2 7 13 -1|, <0 -11 -24 19|]

Wedgie: <<22 48 -38 25 -122 -223||

EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798

Badness: 0.0370

11-limit

Comma: 3025/3024, 4375/4374, 20614528/20588575

POTE generator: 208.901

Map: [<2 7 13 -1 1|, <0 -11 -24 19 17|]

EDOs: 46, 132, 178, 224, 270, 494, 764

Badness: 0.0129

13-limit

Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095

POTE generator: 208.903

Map: [<2 7 13 -1 1 -2|, <0 -11 -24 19 17 27|]

EDOs: 46, 178, 224, 270, 494, 764, 1258

Badness: 0.00886

Semidimi

Commas: 4375/4374, 3955078125/3954653486

POTE generator: ~35/27 = 449.127

Map: [<1 36 48 61|, <0 -55 -73 -93|]

Wedgie: <<55 73 93 -12 -7 11||

EDOs: 171, 863, 8419, 1205, 1376, 1547, 1718, 4983, 6701, 8419

Badness: 0.0151

Brahmagupta

Commas: 4375/4374, 70368744177664/70338939985125

POTE generator: ~27/20 = 519.716

Map: [<7 2 -8 53|, <0 3 8 -11|]

Wedgie: <<21 56 -77 40 -181 -336||

EDOs: 217, 224, 441, 1106, 1547

Badness: 0.0291

11-limit

Commas: 4000/3993, 4375/4374, 131072/130977

POTE generator: ~27/20 = 519.704

Map: [<7 2 -8 53 3|, <0 3 8 -11 7|]

EDOs: 217, 224, 441, 665, 1771e

Badness: 0.0522

Neusec

Commas: 3025/3024, 4375/4374, 235298/234375

POTE generator: ~12/11 = 151.547

Map: [<2 11 15 19 15|, <0 -31 -41 -53 -32|]

EDOs: 190, 388

Badness: 0.0591

13-limit

Commas: 847/845, 1001/1000, 3025/3024, 4375/4374

POTE generator: ~12/11 = 151.545

Map: [<2 11 15 19 15 17|, <0 -31 -41 -53 -32 -38|]

EDOs: 190, 198, 388

Badness: 0.0309

Quasithird

Commas: 4375/4374, 1153470752371588581/1152921504606846976

POTE generator: ~5103/4096 = 380.388

Map: [<4 0 -11 48|, <0 5 16 -29|]

Wedgie: <<20 64 -116 55 -240 -449||

EDOs: 164, 224, 388, 612, 1448, 2060

Badness: 0.0618

11-limit

Commas: 3025/3024, 4375/4374, 4296700485/4294967296

POTE generator: ~5103/4096 = 380.387

Map: [<4 0 -11 48 43|, <0 5 16 -29 -23|]

EDOs: 164, 224, 388, 612, 836, 1448

Badness: 0.0211

13-limit

Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195

POTE generator: ~5103/4096 = 380.385

Map: [<4 0 -11 48 43 11|, <0 5 16 -29 -23 3|]

EDOs: 164, 224, 388, 612, 836, 1448f, 2284f

Badness: 0.0295

Semidimfourth

Commas: 4375/4374, 235298/234375

POTE generator: ~35/27 = 448.457

Map: [<1 21 28 36|, <0 -31 -41 -53|]

Wedgie: <<31 41 53 -7 -3 8||

EDOs: 91, 99, 289, 388, 875, 1263d, 1651d

Badness: 0.0552

Acrokleismic

Commas: 4375/4374, 2202927104/2197265625

POTE generator: ~6/5 = 315.557

Map: [<1 10 11 27|, <0 -32 -33 -92|]

Wedgie: <<32 33 92 -22 56 121||

EDOs: 19, 251, 270

Badness: 0.0562

11-limit

Commas: 4375/4374, 41503/41472, 172032/171875

POTE generator: ~6/5 = 315.558

Map: [<1 10 11 27 -16|, <0 -32 -33 -92 74|]

EDOs: 19, 251, 270, 829, 1099, 1369, 1639

Badness: 0.0369

13-limit

Commas: 676/675, 1001/1000, 4375/4374, 10985/10976

POTE generator: ~6/5 = 315.557

Map: [<1 10 11 27 -16 25|, <0 -32 -33 -92 74 -81|]

EDOs: 19, 251, 270

Badness: 0.0268

Counteracro

Commas: 4375/4374, 5632/5625, 117649/117612

POTE generator: ~6/5 = 315.553

Map: [<1 10 11 27 55|, <0 -32 -33 -92 -196|]

EDOs: 270, 1061e, 1331c, 1601c, 1871bc, 4012bcde

Badness: 0.0426

13-limit

Commas: 676/675, 1716/1715, 4225/4224, 4375/4374

POTE generator: ~6/5 = 315.554

Map: [<1 10 11 27 55 25|, <0 -32 -33 -92 -196 -81|]

EDOs: 270, 1331c, 1601c, 1871bcf, 2141bcf

Badness: 0.0260

Seniority

Commas: 4375/4374 201768035/201326592

POTE generator: ~3087/2560 = 322.804

Map: [<1 11 19 2|, <0 -35 -62 3|]

Wedgie: <<35 62 -3 17 -103 -181||

EDOs: 26, 145, 171, 2710d

Badness: 0.0449

Orga

Commas: 4375/4374 54975581388800/54936068900769

POTE generator: ~8/7 = 231.104

Map: [<2 21 36 5|, <0 -29 -51 1|]

Wedgie: <<58 102 -2 27 -166 -291||

EDOs: 26, 244, 270, 836, 1106, 1376, 2482, 19856bd, 23714bd

Badness: 0.0402

11-limit

Commas: 3025/3024 4375/4374 5767168/5764801

POTE generator: ~8/7 = 231.103

Map: [<2 21 36 5 2|, <0 -29 -51 1 8|]

EDOs: 26, 244, 270, 566, 836, 1106, 7472e, 8578de, 9684cde, 10790cde, 11896cde

Badness: 0.0162

Quatracot

Commas: 4375/4374, 1483154296875/1473173782528

POTE generator: ~448/405 = 176.805

Map: [<2 7 7 23|, <0 -13 -8 -59|]

Wedgie: <<26 16 118 -35 114 229||

EDOs: 190, 224, 414, 638, 1052c, 1690bc

Badness: 0.1760

11-limit

Commas: 3025/3024, 4375/4374, 1265625/1261568

POTE generator: ~448/405 = 176.806

Map: [<2 7 7 23 19|, <0 -13 -8 -59 -41|]

EDOs: 190, 224, 414, 638, 1052c

Badness: 0.0410

13-limit

Commas: 625/624, 729/728, 1575/1573, 2200/2197

POTE generator: ~448/405 = 176.804

Map: [<2 7 7 23 19 13|, <0 -13 -8 -59 -41 -19|]

EDOs: 190, 224, 414, 638, 1690bc, 2328bcde

Badness: 0.0226

Nearly Micro

Octoid

Commas: 4375/4374, 16875/16807

valid range: [578.571, 600.000] (56bcd to 8d)

nice range: [582.512, 584.359]

strict range: [582.512, 584.359]

POTE generator: ~7/5 = 583.940

Map: [<8 1 3 3|, <0 3 4 5|]

Generators: 49/45, 7/5

EDOs: 72, 152, 224

Badness: 0.0427

11-limit

Commas: 540/539, 1375/1372, 4000/3993

valid range: [581.250, 586.364] (64cd, 88bcde)

nice range: [582.512, 585.084]

strict range: [582.512, 585.084]

POTE generator: ~7/5 = 583.692

Map: [<8 1 3 3 16|, <0 3 4 5 3|]

EDOs: 72, 152, 224

Badness: 0.0141

13-limit

Commas: 540/539, 1375/1372, 4000/3993, 625/624

POTE generator: ~7/5 = 583.905

Map: [<8 1 3 3 16 -21|, <0 3 4 5 3 13|]

EDOs: 72, 224

Badness: 0.0153

Music

http://www.archive.org/details/Dreyfus

play

Octopus

Commas: 169/168, 325/324, 364/363, 540/539

POTE generator: ~7/5 = 583.892

Map: [<8 1 3 3 16 14|, <0 3 4 5 3 4|]

EDOs: 72, 152, 224f

Badness: 0.0217

Amity

The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. 99edo is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.

In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.

5-limit

Comma: 1600000/1594323

POTE generator: ~243/200 = 339.519

Map: [<1 3 6|, <0 -5 -13|]

EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873

Badness: 0.0220

7-limit

Commas: 4375/4374, 5120/5103

POTE generator: ~243/200 = 339.432

Map: [<1 3 6 -2|, <0 -5 -13 17|]

Wedgie: <<5 13 -17 9 -41 -76||

EDOs: 7, 39, 46, 53, 99, 251, 350

Badness: 0.0236

11-limit

Commas: 540/539, 4375/4374, 5120/5103

POTE generator: ~243/200 = 339.464

Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]

EDOs: 53, 99e, 152, 555de, 707de, 859bde

Badness: 0.0315

13-limit

Commas: 352/351, 540/539, 625/624, 847/845

POTE generator: ~243/200 = 339.481

Map: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]

EDOS: 53, 99ef, 152f, 205

Badness: 0.0280

Accord

Commas: 126/125, 100352/98415

POTE generator: ~243/200 = 338.993

Map: [<1 3 6 11|, <0 -5 -13 -29|]

Wedgie: <<5 13 29 9 32 31||

EDOs: 46, 131c, 177c

Badness: 0.0956

11-limit

Commas: 121/120, 126/125, 896/891

POTE generator: ~11/9 = 339.047

Map: [<1 3 6 11 6|, <0 -5 -13 -29 -9|]

EDOs: 46, 177c, 223bc, 269bce

Badness: 0.0425

Hitchcock

Commas: 121/120, 176/175, 2200/2187

POTE generator: ~11/9 = 339.340

Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]

EDOs: 7, 39, 46, 53, 99

Badness: 0.0352

13-limit

Commas: 121/120, 169/168, 176/175, 325/324

POTE generator: ~11/9 = 339.419

Map: [<1 3 6 -2 6 2|, <0 -5 -13 17 -9 6|]

EDOs: 7, 39, 46, 53, 99

Badness: 0.0224

Hemiamity

Commas: 4375/4374, 5120/5103, 3025/3024

POTE generator: ~ 243/200 = 339.493

Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|]

EDOs: 14, 46, 106, 152, 350

Parakleismic

In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13>, with the 118edo tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being <<13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie <<13 14 35 -36 ...|| adding 385/384. For the 7-limit 99edo may be preferred, but in the 11-limit it is best to stick with 118.

Comma: 124440064/1220703125

POTE generator: ~6/5 = 315.240

Map: [<1 5 6|, <0 -13 -14|]

EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496

Badness: 0.0433

7-limit

Commas: 3136/3125, 4375/4374

POTE generator: ~6/5 = 315.181

Map: [<1 5 6 12|, <0 -13 -14 -35|]

EDOs: 19, 80, 99, 217, 316, 415

Badness: 0.0274

11-limit

Commas: 385/384, 3136/3125, 4375/4374

POTE generator: ~6/5 = 315.251

Map: [<1 5 6 12 -6|, <0 -13 -14 -35 36|]

EDOs: 19, 99, 118

Badness: 0.0497

Parkleismic

Commas: 176/175, 1375/1372, 2200/2187

POTE generator: ~6/5 = 315.060

Map: [<1 5 6 12 20|, <0 -13 -14 -35 -63|]

EDOs: 80, 179, 259cd

Badness: 0.0559

13-limit

Commas: 169/168, 176/175, 325/324, 1375/1372

POTE generator: ~6/5 = 315.075

Map: [<1 5 6 12 20 10|, <0 -13 -14 -35 -63 -24|]

EDOs: 15, 19, 80, 179

Badness: 0.0366

Paradigmic

Commas: 540/539, 896/891, 3136/3125

POTE generator: ~6/5 = 315.096

Map: [<1 5 6 12 -1|, <0 -13 -14 -35 17|]

EDOs: 19, 80, 99e, 179e

Badness: 0.0417

13-limit

Commas: 169/168, 325/324, 540/539, 832/825

POTE generator: ~6/5 = 315.080

Map: [<1 5 6 12 -1 10|, <0 -13 -14 -35 17 -24|]

EDOs: 19, 80, 99e, 179e

Badness: 0.0358

Semiparakleismic

Commas: 3025/3024, 3136/3125, 4375/4374

POTE generator: 315.181

Map: [<2 10 12 24 19|, <0 -13 -14 -35 -23|]

EDOs: 80, 118, 198, 316, 514c, 830c

Badness: 0.0342

Quincy

Commas: 4375/4374, 823543/819200

POTE generator: ~1728/1715 = 16.613

Map: [<1 2 2 3|, <0 -30 -49 -14|]

EDOs: 72, 217, 289

Badness: 0.0797

11-limit

Commas: 441/440, 4000/3993, 41503/41472

POTE generator: ~100/99 = 16.613

Map: [<1 2 2 3 4|, <0 -30 -49 -14 -39|]

EDOs: 72, 217, 289

Badness: 0.0309

13-limit

Commas: 364/363, 441/440, 676/675, 4375/4374

POTE generator: ~100/99 = 16.602

Map: [<1 2 2 3 4 5|, <0 -30 -49 -14 -39 -94|]

EDOs: 72, 145, 217, 289

Badness: 0.0239

17-limit

Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155

POTE generator: ~100/99 = 16.602

Map: [<1 2 2 3 4 5 5|, <0 -30 -49 -14 -39 -94 -66|]

EDOs: 72, 145, 217, 289

Badness: 0.0147

19-limit

Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600

POTE generator: ~100/99 = 16.594

Map: [<1 2 2 3 4 5 5 4|, <0 -30 -49 -14 -39 -94 -66 18|]

EDOs: 72, 145, 217

Badness: 0.0152

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