Ragismic microtemperaments: Difference between revisions

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[[toc]]
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.

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: [[27edo|27]], [[45edo|45]], [[72edo|72]], [[99edo|99]], [[171edo|171]], [[270edo|270]], [[441edo|441]], [[612edo|612]], [[3600edo|3600]]
Badness: 0.00361

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

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

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

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

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

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

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

POTE generator:

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

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

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

=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

=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

=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 tuning|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 tuning|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 tuning|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

=Nearly Micro= 

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

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

POTE generator: ~7/5 = 583.692

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

=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|]
EDOs: 7, 39, 46, 53, 99, 251, 350
Badness: 0.0236

==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

==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

=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

Original HTML content:

<html><head><title>Ragismic microtemperaments</title></head><body><!-- ws:start:WikiTextTocRule:72:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><div style="margin-left: 1em;"><a href="#Ennealimmal">Ennealimmal</a></div>
<!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><div style="margin-left: 2em;"><a href="#Ennealimmal-11 limit hemiennealimmal">11 limit hemiennealimmal</a></div>
<!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 2em;"><a href="#Ennealimmal-13 limit hemiennealimmal">13 limit hemiennealimmal</a></div>
<!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Semiennealimmal">Semiennealimmal</a></div>
<!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 3em;"><a href="#Ennealimmal-Semiennealimmal-13 limit semiennealimmal">13 limit semiennealimmal</a></div>
<!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Ennealimmic">Ennealimmic</a></div>
<!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 3em;"><a href="#Ennealimmal-Ennealimmic-13 limit ennealimmic">13 limit ennealimmic</a></div>
<!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Semihemiennealimmal">Semihemiennealimmal</a></div>
<!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 3em;"><a href="#Ennealimmal-Semihemiennealimmal-17 limit ennealimmic">17 limit ennealimmic</a></div>
<!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 1em;"><a href="#Gamera">Gamera</a></div>
<!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 1em;"><a href="#Supermajor">Supermajor</a></div>
<!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 1em;"><a href="#Enneadecal">Enneadecal</a></div>
<!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 1em;"><a href="#Deca">Deca</a></div>
<!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Deca-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Deca-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Mitonic">Mitonic</a></div>
<!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 1em;"><a href="#Abigail">Abigail</a></div>
<!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Abigail-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Abigail-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 1em;"><a href="#Nearly Micro">Nearly Micro</a></div>
<!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 1em;"><a href="#Octoid">Octoid</a></div>
<!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Octoid-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#Octoid-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 1em;"><a href="#Amity">Amity</a></div>
<!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Amity-5-limit">5-limit</a></div>
<!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Amity-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Amity-Hitchcock">Hitchcock</a></div>
<!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 2em;"><a href="#Amity-Hemiamity">Hemiamity</a></div>
<!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 1em;"><a href="#Parakleismic">Parakleismic</a></div>
<!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Parakleismic-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Parakleismic-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 1em;"><a href="#Quincy">Quincy</a></div>
<!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Quincy-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Quincy-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Quincy-17-limit">17-limit</a></div>
<!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Quincy-19-limit">19-limit</a></div>
<!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --></div>
<!-- ws:end:WikiTextTocRule:109 -->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 &quot;relatively&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<br />
4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h1>
 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||.<br />
<br />
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.<br />
<br />
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 &quot;tritaves&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 &quot;tritave&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.<br />
<br />
Commas: 2401/2400, 4375/4374<br />
<br />
POTE generators: 36/35: 49.0205; 10/9: 182.354; 6/5: 315.687; 49/40: 350.980<br />
<br />
Map: [&lt;9 1 1 2|, &lt;0 2 3 2|]<br />
Wedgie: &lt;&lt;18 27 18 1 -22 -34||<br />
EDOs: <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/45edo">45</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/270edo">270</a>, <a class="wiki_link" href="/441edo">441</a>, <a class="wiki_link" href="/612edo">612</a>, <a class="wiki_link" href="/3600edo">3600</a><br />
Badness: 0.00361<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Ennealimmal-11 limit hemiennealimmal"></a><!-- ws:end:WikiTextHeadingRule:2 -->11 limit hemiennealimmal</h2>
 Commas: 2401/2400, 4375/4374, 3025/3024<br />
<br />
POTE generator: 99/98: 17.6219 or 6/5: 315.7114<br />
<br />
Map: [&lt;18 0 -1 22 48|, &lt;0 2 3 2 1|]<br />
EDOs: 72, 198, 270, 342, 612, 954, 1566<br />
Badness: 0.00628<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Ennealimmal-13 limit hemiennealimmal"></a><!-- ws:end:WikiTextHeadingRule:4 -->13 limit hemiennealimmal</h2>
 Commas: 676/675, 1001/1000, 1716/1715, 3025/3024<br />
<br />
POTE generator ~99/98 = 17.7504<br />
<br />
Map: [&lt;18 0 -1 22 48 -19|, &lt;0 2 3 2 1 6|]<br />
EDOs: 72, 198, 270<br />
Badness: 0.0125<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Ennealimmal-Semiennealimmal"></a><!-- ws:end:WikiTextHeadingRule:6 -->Semiennealimmal</h2>
 Commas: 2401/2400, 4375/4374, 4000/3993<br />
<br />
POTE generator: ~140/121 = 250.3367<br />
<br />
Map: [&lt;9 3 4 14 18|, &lt;0 6 9 6 7|]<br />
EDOs: 72, 369, 441<br />
Badness: 0.0342<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Ennealimmal-Semiennealimmal-13 limit semiennealimmal"></a><!-- ws:end:WikiTextHeadingRule:8 -->13 limit semiennealimmal</h3>
 Commas: 1575/1573, 2080/2079, 2401/2400, 4375/4374<br />
<br />
POTE generator: ~140/121 = 250.3375<br />
<br />
Map: [&lt;9 3 4 14 18 -8|, &lt;0 6 9 6 7 22|]<br />
EDOs: 72, 441<br />
Badness: 0.0261<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Ennealimmal-Ennealimmic"></a><!-- ws:end:WikiTextHeadingRule:10 -->Ennealimmic</h2>
 Commas: 243/242, 441/440, 4375/4356<br />
<br />
POTE generator: ~36/35 = 49.395<br />
<br />
Map: [&lt;9 1 1 12 -2|, &lt;0 2 3 2 5|]<br />
EDOs: 72, 171, 243<br />
Badness: 0.0203<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Ennealimmal-Ennealimmic-13 limit ennealimmic"></a><!-- ws:end:WikiTextHeadingRule:12 -->13 limit ennealimmic</h3>
 Commas: 243/242, 364/363, 441/440, 625/624<br />
<br />
POTE generator: ~36/35 = 49.341<br />
<br />
Map: [&lt;9 1 1 12 -2 -33|, &lt;0 2 3 2 5 10|]<br />
EDOs: 72, 171, 243<br />
Badness: 0.0233<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Ennealimmal-Semihemiennealimmal"></a><!-- ws:end:WikiTextHeadingRule:14 -->Semihemiennealimmal</h2>
 Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224<br />
<br />
POTE generator:<br />
<br />
Map: [&lt;18 0 -1 22 48 88|, &lt;0 4 6 4 2 -3|]<br />
EDOs: 126, 144, 270, 684, 954<br />
Badness: 0.0131<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Ennealimmal-Semihemiennealimmal-17 limit ennealimmic"></a><!-- ws:end:WikiTextHeadingRule:16 -->17 limit ennealimmic</h3>
 Commas: 243/242, 364/363, 375/374, 441/440, 595/594<br />
<br />
POTE generator: ~36/35 = 49.335<br />
<br />
Map: [&lt;9 1 1 12 -2 -33 -3|, &lt;0 2 3 2 5 10 6|]<br />
EDOs: 72, 171, 243<br />
Badness: 0.0146<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Gamera"></a><!-- ws:end:WikiTextHeadingRule:18 -->Gamera</h1>
 Commas: 4375/4374, 589824/588245<br />
<br />
POTE generator ~8/7 = 230.336<br />
<br />
Map: [&lt;1 6 10 3|, &lt;0 -23 -40 -1|]<br />
EDOs: 26, 73, 99, 224, 323, 422, 735<br />
Badness: 0.0376<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Supermajor"></a><!-- ws:end:WikiTextHeadingRule:20 -->Supermajor</h1>
 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.<br />
<br />
Commas: 4375/4374, 52734375/52706752<br />
<br />
POTE generator: ~9/7 = 435.082<br />
<br />
Map: [&lt;1 15 19 30|, &lt;0 -37 -46 -75|]<br />
EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214<br />
Badness: 0.0108<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Enneadecal"></a><!-- ws:end:WikiTextHeadingRule:22 -->Enneadecal</h1>
 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 <a class="wiki_link" href="/19edo">19edo</a> up to just ones. <a class="wiki_link" href="/171edo">171edo</a> is a good tuning for either the 5 or 7 limits, and <a class="wiki_link" href="/494edo">494edo</a> 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 <a class="wiki_link" href="/665edo">665edo</a> for a tuning.<br />
<br />
Commas: 4375/4374, 703125/702464<br />
<br />
POTE generator: ~3/2 = 701.880<br />
<br />
Map: [&lt;19 0 14 -37|, &lt;0 1 1 3|]<br />
Generators: 28/27, 3<br />
EDOs: 19, 152, 171, 665, 836, 1007, 2185<br />
Badness: 0.0110<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Deca"></a><!-- ws:end:WikiTextHeadingRule:24 -->Deca</h1>
 Commas: 4375/4374, 165288374272/164794921875<br />
<br />
POTE generator: ~460992/390625 = 284.423<br />
<br />
Map: [&lt;10 4 2 9|, &lt;0 5 6 11|]<br />
EDOs: 80, 190, 270, 1270, 1540, 1810, 2080<br />
Badness: 0.0806<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Deca-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2>
 Commas: 3025/3024, 4375/4374, 422576/421875<br />
<br />
POTE generator: ~33/28 = 284.418<br />
<br />
Map: [&lt;10 4 2 9 18|, &lt;0 5 6 11 7|]<br />
EDOs: 80, 190, 270, 1000, 1270<br />
Badness: 0.0243<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Deca-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2>
 Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374<br />
<br />
POTE generator: ~33/28 = 284.398<br />
<br />
Map: [&lt;10 4 2 9 18 37|, &lt;0 5 6 11 7 0|]<br />
EDOs: 80, 190, 270, 730, 1000<br />
Badness: 0.0168<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Mitonic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Mitonic</h1>
 Commas: 4375/4374, 2100875/2097152<br />
<br />
POTE generator: ~10/9 = 182.458<br />
<br />
Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]<br />
EDOs: 46, 125, 171<br />
Badness: 0.0252<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Abigail"></a><!-- ws:end:WikiTextHeadingRule:32 -->Abigail</h1>
 Commas: 4375/4374, 2147483648/2144153025<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.899<br />
<br />
Map: [&lt;2 7 13 -1|, &lt;0 -11 -24 19|]<br />
Wedgie: &lt;&lt;22 48 -38 25 -122 -223||<br />
EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798<br />
Badness: 0.0370<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Abigail-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2>
 Comma: 3025/3024, 4375/4374, 20614528/20588575<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.901<br />
<br />
Map: [&lt;2 7 13 -1 1|, &lt;0 -11 -24 19 17|]<br />
EDOs: 46, 132, 178, 224, 270, 494, 764<br />
Badness: 0.0129<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Abigail-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2>
 Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 208.903<br />
<br />
Map: [&lt;2 7 13 -1 1 -2|, &lt;0 -11 -24 19 17 27|]<br />
EDOs: 46, 178, 224, 270, 494, 764, 1258<br />
Badness: 0.00886<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Nearly Micro"></a><!-- ws:end:WikiTextHeadingRule:38 -->Nearly Micro</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Octoid"></a><!-- ws:end:WikiTextHeadingRule:40 -->Octoid</h1>
 Commas: 4375/4374, 16875/16807<br />
<br />
POTE generator: ~7/5 = 583.940<br />
<br />
Map: [&lt;8 1 3 3|, &lt;0 3 4 5|]<br />
Generators: 49/45, 7/5<br />
EDOs: 72, 152, 224<br />
Badness: 0.0427<br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Octoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2>
 Commas: 540/539, 1375/1372, 4000/3993<br />
<br />
POTE generator: ~7/5 = 583.692<br />
<br />
Map: Map: [&lt;8 1 3 3 16|, &lt;0 3 4 5 3|]<br />
EDOs: 72, 152, 224<br />
Badness: 0.0141<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Octoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2>
 Commas: 540/539, 1375/1372, 4000/3993, 625/624<br />
<br />
POTE generator: ~7/5 = 583.905<br />
<br />
Map: Map: [&lt;8 1 3 3 16 -21|, &lt;0 3 4 5 3 13|]<br />
EDOs: 72, 224<br />
Badness: 0.0153<br />
<br />
<!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Amity"></a><!-- ws:end:WikiTextHeadingRule:46 -->Amity</h1>
 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||. <a class="wiki_link" href="/99edo">99edo</a> 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.<br />
<br />
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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Amity-5-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->5-limit</h2>
 Comma: 1600000/1594323<br />
<br />
POTE generator: ~243/200 = 339.519<br />
<br />
Map: [&lt;1 3 6|, &lt;0 -5 -13|]<br />
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873<br />
Badness: 0.0220<br />
<br />
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Amity-7-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->7-limit</h2>
 Commas: 4375/4374, 5120/5103<br />
<br />
POTE generator: ~243/200 = 339.432<br />
<br />
Map: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]<br />
EDOs: 7, 39, 46, 53, 99, 251, 350<br />
Badness: 0.0236<br />
<br />
<!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Amity-Hitchcock"></a><!-- ws:end:WikiTextHeadingRule:52 -->Hitchcock</h2>
 Commas: 121/120, 176/175, 2200/2187<br />
<br />
POTE generator: ~11/9 = 339.340<br />
<br />
Map: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]<br />
EDOs: 7, 39, 46, 53, 99<br />
Badness: 0.0352<br />
<br />
<!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Amity-Hemiamity"></a><!-- ws:end:WikiTextHeadingRule:54 -->Hemiamity</h2>
 Commas: 4375/4374, 5120/5103, 3025/3024<br />
<br />
POTE generator: ~ 243/200 = 339.493<br />
<br />
Map: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]<br />
EDOs: 14, 46, 106, 152, 350<br />
<br />
<!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="Parakleismic"></a><!-- ws:end:WikiTextHeadingRule:56 -->Parakleismic</h1>
 In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> 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 <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.<br />
<br />
Comma: 124440064/1220703125<br />
<br />
POTE generator: ~6/5 = 315.240<br />
<br />
Map: [&lt;1 5 6|, &lt;0 -13 -14|]<br />
EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496<br />
Badness: 0.0433<br />
<br />
<!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Parakleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->7-limit</h2>
 Commas: 3136/3125, 4375/4374<br />
<br />
POTE generator: ~6/5 = 315.181<br />
<br />
Map: [&lt;1 5 6 12|, &lt;0 -13 -14 -35|]<br />
EDOs: 19, 80, 99, 217, 316, 415<br />
Badness: 0.0274<br />
<br />
<!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Parakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2>
 Commas: 385/384, 3136/3125, 4375/4374<br />
<br />
POTE generator: ~6/5 = 315.251<br />
<br />
Map: [&lt;1 5 6 12 -6|, &lt;0 -13 -14 -35 36|]<br />
EDOs: 19, 99, 118<br />
Badness: 0.0497<br />
<br />
<!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Quincy"></a><!-- ws:end:WikiTextHeadingRule:62 -->Quincy</h1>
 Commas: 4375/4374, 823543/819200<br />
<br />
POTE generator: ~1728/1715 = 16.613<br />
<br />
Map: [&lt;1 2 2 3|, &lt;0 -30 -49 -14|]<br />
EDOs: 72, 217, 289<br />
Badness: 0.0797<br />
<br />
<!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Quincy-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2>
 Commas: 441/440, 4000/3993, 41503/41472<br />
<br />
POTE generator: ~100/99 = 16.613<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -30 -49 -14 -39|]<br />
EDOs: 72, 217, 289<br />
Badness: 0.0309<br />
<br />
<!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Quincy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->13-limit</h2>
 Commas: 364/363, 441/440, 676/675, 4375/4374<br />
<br />
POTE generator: ~100/99 = 16.602<br />
<br />
Map: [&lt;1 2 2 3 4 5|, &lt;0 -30 -49 -14 -39 -94|]<br />
EDOs: 72, 145, 217, 289<br />
Badness: 0.0239<br />
<br />
<!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Quincy-17-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->17-limit</h2>
 Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155<br />
<br />
POTE generator: ~100/99 = 16.602<br />
<br />
Map: [&lt;1 2 2 3 4 5 5|, &lt;0 -30 -49 -14 -39 -94 -66|]<br />
EDOs: 72, 145, 217, 289<br />
Badness: 0.0147<br />
<br />
<!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Quincy-19-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->19-limit</h2>
 Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600<br />
<br />
POTE generator: ~100/99 = 16.594<br />
<br />
Map: [&lt;1 2 2 3 4 5 5 4|, &lt;0 -30 -49 -14 -39 -94 -66 18|]<br />
EDOs: 72, 145, 217<br />
Badness: 0.0152</body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Natebedell|Natebedell]] and made on <tt>2011-09-06 16:57:42 UTC</tt>.<br>
+: This revision was by author [[User:Natebedell|Natebedell]] and made on <tt>2011-09-06 16:59:13 UTC</tt>.<br>
-: The original revision id was <tt>251318402</tt>.<br>
+: The original revision id was <tt>251318866</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
 <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 |-1 -7 4 1&gt; = 4375/4374, 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
+/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=
@@ Line 337: / Line 338: @@
 Badness: 0.0152</pre></div>
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-<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:74:&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:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#x4375/4374, 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"&gt; 4375/4374, 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 &lt;/a&gt;&lt;/div&gt;
+<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:72:&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:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ennealimmal"&gt;Ennealimmal&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ennealimmal"&gt;Ennealimmal&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&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;
-&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&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;
+&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&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;
-&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&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;
+&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Semiennealimmal"&gt;Semiennealimmal&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Semiennealimmal"&gt;Semiennealimmal&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&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;
-&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&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;
+&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Ennealimmic"&gt;Ennealimmic&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-Ennealimmic"&gt;Ennealimmic&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Ennealimmic-13 limit ennealimmic"&gt;13 limit ennealimmic&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Ennealimmic-13 limit ennealimmic"&gt;13 limit ennealimmic&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&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:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&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:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Semihemiennealimmal-17 limit ennealimmic"&gt;17 limit ennealimmic&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Semihemiennealimmal-17 limit ennealimmic"&gt;17 limit ennealimmic&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Gamera"&gt;Gamera&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Gamera"&gt;Gamera&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Supermajor"&gt;Supermajor&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Supermajor"&gt;Supermajor&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Enneadecal"&gt;Enneadecal&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Enneadecal"&gt;Enneadecal&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Deca"&gt;Deca&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Deca"&gt;Deca&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&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:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&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:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Deca-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
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+&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mitonic"&gt;Mitonic&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mitonic"&gt;Mitonic&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Abigail"&gt;Abigail&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Abigail"&gt;Abigail&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&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:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&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:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Abigail-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
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+&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&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:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&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:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Octoid"&gt;Octoid&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Octoid"&gt;Octoid&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
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+&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&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:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&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:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Amity"&gt;Amity&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Amity"&gt;Amity&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&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:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&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:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&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:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&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:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&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:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&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:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&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:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&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:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Parakleismic"&gt;Parakleismic&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Parakleismic"&gt;Parakleismic&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&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:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&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:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&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:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&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:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quincy"&gt;Quincy&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quincy"&gt;Quincy&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&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:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&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:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&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:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&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:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&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:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&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:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&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:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&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:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:109 --&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&lt;br /&gt;
-&lt;!-- ws:end:WikiTextTocRule:112 --&gt;The ragisma is |-1 -7 4 1&amp;gt;  &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x4375/4374, 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"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; 4375/4374, 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 &lt;/h1&gt;
+/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;
-/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:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Ennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Ennealimmal&lt;/h1&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;
@@ Line 394: / Line 394: @@
 Badness: 0.00361&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-11 limit hemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11 limit hemiennealimmal&lt;/h2&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;
@@ Line 403: / Line 403: @@
 Badness: 0.00628&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-13 limit hemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13 limit hemiennealimmal&lt;/h2&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;
@@ Line 412: / Line 412: @@
 Badness: 0.0125&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Ennealimmal-Semiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Semiennealimmal&lt;/h2&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;
@@ Line 421: / Line 421: @@
 Badness: 0.0342&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Ennealimmal-Semiennealimmal-13 limit semiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13 limit semiennealimmal&lt;/h3&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;
@@ Line 430: / Line 430: @@
 Badness: 0.0261&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-Ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Ennealimmic&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Ennealimmal-Ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Ennealimmic&lt;/h2&gt;
   Commas: 243/242, 441/440, 4375/4356&lt;br /&gt;
 &lt;br /&gt;
@@ Line 439: / Line 439: @@
 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-Ennealimmic-13 limit ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13 limit ennealimmic&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Ennealimmal-Ennealimmic-13 limit ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13 limit ennealimmic&lt;/h3&gt;
   Commas: 243/242, 364/363, 441/440, 625/624&lt;br /&gt;
 &lt;br /&gt;
@@ Line 448: / Line 448: @@
 Badness: 0.0233&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Ennealimmal-Semihemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Semihemiennealimmal&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Ennealimmal-Semihemiennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Semihemiennealimmal&lt;/h2&gt;
   Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224&lt;br /&gt;
 &lt;br /&gt;
@@ Line 457: / Line 457: @@
 Badness: 0.0131&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-Semihemiennealimmal-17 limit ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;17 limit ennealimmic&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Ennealimmal-Semihemiennealimmal-17 limit ennealimmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;17 limit ennealimmic&lt;/h3&gt;
   Commas: 243/242, 364/363, 375/374, 441/440, 595/594&lt;br /&gt;
 &lt;br /&gt;
@@ Line 466: / Line 466: @@
 Badness: 0.0146&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Gamera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Gamera&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Gamera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Gamera&lt;/h1&gt;
   Commas: 4375/4374, 589824/588245&lt;br /&gt;
 &lt;br /&gt;
@@ Line 475: / Line 475: @@
 Badness: 0.0376&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Supermajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Supermajor&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Supermajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&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;
@@ Line 486: / Line 486: @@
 Badness: 0.0108&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Enneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Enneadecal&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Enneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&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;
@@ Line 498: / Line 498: @@
 Badness: 0.0110&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Deca"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Deca&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Deca"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Deca&lt;/h1&gt;
   Commas: 4375/4374, 165288374272/164794921875&lt;br /&gt;
 &lt;br /&gt;
@@ Line 507: / Line 507: @@
 Badness: 0.0806&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Deca-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Deca-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
   Commas: 3025/3024, 4375/4374, 422576/421875&lt;br /&gt;
 &lt;br /&gt;
@@ Line 516: / Line 516: @@
 Badness: 0.0243&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="Deca-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Deca-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
   Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 525: / Line 525: @@
 Badness: 0.0168&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Mitonic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Mitonic&lt;/h1&gt;
   Commas: 4375/4374, 2100875/2097152&lt;br /&gt;
 &lt;br /&gt;
@@ Line 534: / Line 534: @@
 Badness: 0.0252&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="Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Abigail&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Abigail&lt;/h1&gt;
   Commas: 4375/4374, 2147483648/2144153025&lt;br /&gt;
 &lt;br /&gt;
@@ Line 544: / Line 544: @@
 Badness: 0.0370&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="Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
   Comma: 3025/3024, 4375/4374, 20614528/20588575&lt;br /&gt;
 &lt;br /&gt;
@@ Line 553: / Line 553: @@
 Badness: 0.0129&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;13-limit&lt;/h2&gt;
   Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095&lt;br /&gt;
 &lt;br /&gt;
@@ Line 562: / Line 562: @@
 Badness: 0.00886&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="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Nearly Micro&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Nearly Micro&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Octoid&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Octoid&lt;/h1&gt;
   Commas: 4375/4374, 16875/16807&lt;br /&gt;
 &lt;br /&gt;
@@ Line 574: / Line 574: @@
 Badness: 0.0427&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="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
   Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
@@ Line 583: / Line 583: @@
 Badness: 0.0141&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
   Commas: 540/539, 1375/1372, 4000/3993, 625/624&lt;br /&gt;
 &lt;br /&gt;
@@ Line 592: / Line 592: @@
 Badness: 0.0153&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="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Amity&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&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:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;5-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;5-limit&lt;/h2&gt;
   Comma: 1600000/1594323&lt;br /&gt;
 &lt;br /&gt;
@@ Line 606: / Line 606: @@
 Badness: 0.0220&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="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;7-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;7-limit&lt;/h2&gt;
   Commas: 4375/4374, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
@@ Line 615: / Line 615: @@
 Badness: 0.0236&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Hitchcock&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Hitchcock&lt;/h2&gt;
   Commas: 121/120, 176/175, 2200/2187&lt;br /&gt;
 &lt;br /&gt;
@@ Line 624: / Line 624: @@
 Badness: 0.0352&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Hemiamity&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Hemiamity&lt;/h2&gt;
   Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 632: / Line 632: @@
 EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Parakleismic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&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;
@@ Line 643: / Line 643: @@
 Badness: 0.0433&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;7-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;7-limit&lt;/h2&gt;
   Commas: 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 652: / Line 652: @@
 Badness: 0.0274&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="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;11-limit&lt;/h2&gt;
   Commas: 385/384, 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 661: / Line 661: @@
 Badness: 0.0497&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="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Quincy&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Quincy&lt;/h1&gt;
   Commas: 4375/4374, 823543/819200&lt;br /&gt;
 &lt;br /&gt;
@@ Line 670: / Line 670: @@
 Badness: 0.0797&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="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;11-limit&lt;/h2&gt;
   Commas: 441/440, 4000/3993, 41503/41472&lt;br /&gt;
 &lt;br /&gt;
@@ Line 679: / Line 679: @@
 Badness: 0.0309&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="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;13-limit&lt;/h2&gt;
   Commas: 364/363, 441/440, 676/675, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 688: / Line 688: @@
 Badness: 0.0239&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;17-limit&lt;/h2&gt;
   Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155&lt;br /&gt;
 &lt;br /&gt;
@@ Line 697: / Line 697: @@
 Badness: 0.0147&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;19-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&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;

Ragismic microtemperaments: Difference between revisions

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