Xenharmonic Wiki

List of edo-distinct 53et rank two temperaments

Revision as of 17:35, 5 May 2012 by Wikispaces>genewardsmith (**Imported revision 330519772 - Original comment: **)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-05-05 17:35:17 UTC.
The original revision id was 330519772.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The temperaments listed are 53edo-distinct, meaning that they are all different even if tuned in 53edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity was chosen as the representative for each class of edo-distinctness.

=5-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 -8 -15]] || Helmholtz || 3.103 || 32805/32768 ||
|| 2 || <<2 37 54]] || Monzismic || 12.528 || |54 -37 2> ||
|| 3 || <<3 29 39]] || Tricot || 9.520 || 68719476736000/68630377364883 ||
|| 4 || <<4 21 24]] || Vulture || 6.600 || 10485760000/10460353203 ||
|| 5 || <<5 13 9]] || Amity || 3.970 || 1600000/1594323 ||
|| 6 || <<6 5 -6]] || Hanson || 2.685 || 15625/15552 ||
|| 7 || <<7 -3 -21]] || Orson || 4.232 || 2109375/2097152 ||
|| 8 || <<8 -11 -36]] || Submajor || 6.919 || 69198046875/68719476736 ||
|| 9 || <<9 -19 -51]] || Aufo || 9.853 || 2270041927734375/2251799813685248 ||
|| 10 || <<10 -27 -66]] || || 12.867 || 74468725439326171875/73786976294838206464 ||
|| 11 || <<11 18 3]] || Quartonic || 6.026 || 390625000/387420489 ||
|| 12 || <<41 43 -27]] || || 18.85 || |-27 -43 41> ||
|| 13 || <<13 2 -27]] || Ditonic || 6.373 || 1220703125/1207959552 ||
|| 14 || <<14 47 42]] || || 14.353 || |42 -47 14> ||
|| 15 || <<15 -14 -57]] || Misneb || 11.043 || 145964630126953125/144115188075855872 ||
|| 16 || <<16 31 12]] || || 9.845 || 625000000000000/617673396283947 ||
|| 17 || <<17 23 -3]] || Maja || 8.443 || 762939453125/753145430616 ||
|| 18 || <<35 38 -21]] || || 16.207 || |-21 -38 35> ||
|| 19 || <<19 7 -33]] || Semaja || 8.817 || 19073486328125/18786186952704 ||
|| 20 || <<20 -1 -48]] || || 10.481 || 286102294921875/281474976710656 ||
|| 21 || <<21 44 21]] || || 13.75 || 1000000000000000000000/984770902183611232881 ||
|| 22 || <<31 17 -45]] || || 13.972 || 4656612873077392578125/4543715546604414959616 ||
|| 23 || <<23 28 -9]] || || 10.985 || 11920928955078125/11712917736940032 ||
|| 24 || <<29 33 -15]] || || 13.582 || 186264514923095703125/182159296644891377664 ||
|| 25 || <<25 12 -39]] || || 11.37 || 298023223876953125/292162779488452608 ||
|| 26 || <<27 -4 -69]] || || 14.659 || 603497028350830078125/590295810358705651712 ||

=7-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 -8 -14 -15 -25 -10]] || Garibaldi || 3.823 || 225/224 3125/3087 ||
|| 2 || <<2 -16 25 -30 34 103]] || Hemischis || 9.155 || 6144/6125 19683/19600 ||
|| 3 || <<3 29 11 39 9 -56]] || Tricot || 7.801 || 2430/2401 5120/5103 ||
|| 4 || <<4 21 -3 24 -16 -66]] || Buzzard || 6.420 || 1728/1715 5120/5103 ||
|| 5 || <<5 13 -17 9 -41 -76]] || Amity || 7.127 || 4375/4374 5120/5103 ||
|| 6 || <<6 5 22 -6 18 37]] || Catakleismic || 4.684 || 225/224 4375/4374 ||
|| 7 || <<7 -3 8 -21 -7 27]] || Orwell || 3.685 || 225/224 1728/1715 ||
|| 8 || <<8 -11 -6 -36 -32 17]] || Submajor || 5.869 || 225/224 51200/50421 ||
|| 9 || <<9 -19 -20 -51 -57 7]] || Untriton || 9.195 || 225/224 125000000/121060821 ||
|| 10 || <<10 26 19 18 2 -29]] || Hamity || 6.518 || 2430/2401 4000/3969 ||
|| 11 || <<11 18 5 3 -23 -39]] || Quartonic || 5.395 || 1728/1715 4000/3969 ||
|| 12 || <<12 10 -9 -12 -48 -49]] || Hemikleismic || 6.704 || 4000/3969 6144/6125 ||
|| 13 || <<13 2 30 -27 11 64]] || Coditone || 7.512 || 225/224 2125764/2100875 ||
|| 14 || <<14 47 16 42 -14 -95]] || || 12.061 || 19683/19600 51200/50421 ||
|| 15 || <<15 -14 2 -57 -39 44]] || Misneb || 9.025 || 225/224 4194304/4117715 ||
|| 16 || <<16 31 41 12 20 8]] || || 9.361 || 3125/3087 19683/19600 ||
|| 17 || <<17 23 27 -3 -5 -2]] || Maja || 7.161 || 2430/2401 3125/3087 ||
|| 18 || <<18 15 13 -18 -30 -12]] || Kleiboh || 6.645 || 1728/1715 3125/3087 ||
|| 19 || <<19 7 -1 -33 -55 -22]] || Semaja || 8.139 || 3125/3087 6144/6125 ||
|| 20 || <<20 -1 -15 -48 -80 -32]] || || 10.843 || 3125/3087 65536/64827 ||
|| 21 || <<21 44 24 21 -21 -68]] || || 11.339 || 4000/3969 839808/823543 ||
|| 22 || <<31 17 43 -45 -19 52]] || || 12.262 || 2430/2401 390625/387072 ||
|| 23 || <<23 28 49 -9 13 35]] || || 10.832 || 4375/4374 78125/76832 ||
|| 24 || <<24 20 35 -24 -12 25]] || || 9.340 || 2430/2401 15625/15552 ||
|| 25 || <<25 12 21 -39 -37 15]] || || 9.293 || 1728/1715 78125/76832 ||
|| 26 || <<26 4 7 -54 -62 5]] || || 10.711 || 6144/6125 78125/76832 ||

=11-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 -8 -14 -15 -25 -10]] || Garibaldi || 3.823 || 225/224 3125/3087 ||
|| 2 || <<2 -16 25 -30 34 103]] || Hemischis || 9.155 || 6144/6125 19683/19600 ||
|| 3 || <<3 29 11 39 9 -56]] || Tricot || 7.801 || 2430/2401 5120/5103 ||
|| 4 || <<4 21 -3 24 -16 -66]] || Buzzard || 6.420 || 1728/1715 5120/5103 ||
|| 5 || <<5 13 -17 9 -41 -76]] || Amity || 7.127 || 4375/4374 5120/5103 ||
|| 6 || <<6 5 22 -6 18 37]] || Catakleismic || 4.684 || 225/224 4375/4374 ||
|| 7 || <<7 -3 8 -21 -7 27]] || Orwell || 3.685 || 225/224 1728/1715 ||
|| 8 || <<8 -11 -6 -36 -32 17]] || Submajor || 5.869 || 225/224 51200/50421 ||
|| 9 || <<9 -19 -20 -51 -57 7]] || Untriton || 9.195 || 225/224 125000000/121060821 ||
|| 10 || <<10 26 19 18 2 -29]] || Hamity || 6.518 || 2430/2401 4000/3969 ||
|| 11 || <<11 18 5 3 -23 -39]] || Quartonic || 5.395 || 1728/1715 4000/3969 ||
|| 12 || <<12 10 -9 -12 -48 -49]] || Hemikleismic || 6.704 || 4000/3969 6144/6125 ||
|| 13 || <<13 2 30 -27 11 64]] || Coditone || 7.512 || 225/224 2125764/2100875 ||
|| 14 || <<14 47 16 42 -14 -95]] || || 12.061 || 19683/19600 51200/50421 ||
|| 15 || <<15 -14 2 -57 -39 44]] || Misneb || 9.025 || 225/224 4194304/4117715 ||
|| 16 || <<16 31 41 12 20 8]] || || 9.361 || 3125/3087 19683/19600 ||
|| 17 || <<17 23 27 -3 -5 -2]] || Maja || 7.161 || 2430/2401 3125/3087 ||
|| 18 || <<18 15 13 -18 -30 -12]] || Kleiboh || 6.645 || 1728/1715 3125/3087 ||
|| 19 || <<19 7 -1 -33 -55 -22]] || Semaja || 8.139 || 3125/3087 6144/6125 ||
|| 20 || <<20 -1 -15 -48 -80 -32]] || || 10.843 || 3125/3087 65536/64827 ||
|| 21 || <<21 44 24 21 -21 -68]] || || 11.339 || 4000/3969 839808/823543 ||
|| 22 || <<31 17 43 -45 -19 52]] || || 12.262 || 2430/2401 390625/387072 ||
|| 23 || <<23 28 49 -9 13 35]] || || 10.832 || 4375/4374 78125/76832 ||
|| 24 || <<24 20 35 -24 -12 25]] || || 9.340 || 2430/2401 15625/15552 ||
|| 25 || <<25 12 21 -39 -37 15]] || || 9.293 || 1728/1715 78125/76832 ||
|| 26 || <<26 4 7 -54 -62 5]] || || 10.711 || 6144/6125 78125/76832 ||

=13-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 -8 -14 -30 -33 -15 -25 -51 -56 -10 -42 -47 -36 -41 -3]] || Helenus || 5.812 || 99/98 176/175 275/273 847/845 ||
|| 2 || <<2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19]] || Hemigari || 6.013 || 121/120 169/168 225/224 275/273 ||
|| 3 || <<3 29 11 16 7 39 9 15 0 -56 -63 -91 7 -21 -35]] || Tricot || 6.236 || 99/98 121/120 169/168 352/351 ||
|| 4 || <<4 21 -3 -14 27 24 -16 -36 28 -66 -105 -15 -29 87 145]] || Buteo || 7.137 || 99/98 275/273 385/384 572/567 ||
|| 5 || <<5 13 -17 9 -6 9 -41 -3 -28 -76 -24 -62 84 46 -54]] || Hitchcock || 5.834 || 121/120 169/168 176/175 325/324 ||
|| 6 || <<6 5 22 32 14 -6 18 30 0 37 57 14 14 -42 -70]] || Cataclysmic || 4.918 || 99/98 169/168 176/175 275/273 ||
|| 7 || <<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]] || Orwell || 4.717 || 99/98 121/120 176/175 275/273 ||
|| 8 || <<8 -11 -6 25 1 -36 -32 12 -28 17 96 43 91 25 -89]] || Submajor || 6.305 || 169/168 225/224 275/273 385/384 ||
|| 9 || <<9 -19 -20 -5 -32 -51 -57 -39 -84 7 54 -4 55 -16 -92]] || Untriton || 8.047 || 121/120 225/224 275/273 1040/1029 ||
|| 10 || <<10 26 19 18 41 18 2 -6 28 -29 -48 -1 -15 45 75]] || Hamity || 5.887 || 99/98 121/120 275/273 572/567 ||
|| 11 || <<11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72]] || Quartz || 5.990 || 99/98 169/168 275/273 385/384 ||
|| 12 || <<12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56]] || Hemikleismic || 6.023 || 121/120 176/175 275/273 325/324 ||
|| 13 || <<13 2 30 34 48 -27 11 9 28 64 72 104 -8 24 40]] || Coditone || 7.622 || 99/98 176/175 325/324 847/845 ||
|| 14 || <<14 -6 16 4 15 -42 -14 -42 -28 54 30 57 -44 -17 37]] || Doublethink || 5.858 || 99/98 121/120 169/168 176/175 ||
|| 15 || <<15 -14 2 -26 -18 -57 -39 -93 -84 44 -12 10 -80 -58 34]] || Misneb || 8.837 || 99/98 176/175 640/637 847/845 ||
|| 16 || <<16 -22 -12 -3 2 -72 -64 -60 -56 34 69 86 33 50 18]] || || 9.127 || 121/120 169/168 225/224 640/637 ||
|| 17 || <<17 23 27 20 22 -3 -5 -27 -28 -2 -33 -34 -37 -38 2]] || Maja || 5.680 || 99/98 121/120 169/168 275/273 ||
|| 18 || <<18 15 13 43 42 -18 -30 6 0 -12 48 42 76 70 -14]] || Kleiboh || 6.913 || 176/175 275/273 325/324 540/539 ||
|| 19 || <<19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]] || Semaja || 6.343 || 121/120 169/168 176/175 275/273 ||
|| 20 || <<20 -1 38 36 29 -48 4 -12 -28 91 87 71 -30 -59 -33]] || || 8.717 || 99/98 169/168 176/175 4235/4212 ||
|| 21 || <<21 -9 24 6 -4 -63 -21 -63 -84 81 45 24 -66 -100 -36]] || || 9.168 || 99/98 121/120 176/175 2200/2197 ||
|| 22 || <<22 36 10 29 16 6 -46 -30 -56 -78 -57 -96 47 8 -52]] || || 8.657 || 121/120 169/168 325/324 640/637 ||
|| 23 || <<23 28 49 52 36 -9 13 3 -28 35 24 -20 -23 -80 -68]] || || 8.776 || 99/98 169/168 275/273 2662/2625 ||
|| 24 || <<24 20 35 22 3 -24 -12 -48 -84 25 -18 -67 -59 -121 -71]] || || 8.623 || 99/98 121/120 275/273 4225/4224 ||
|| 25 || <<25 12 21 45 23 -39 -37 -15 -56 15 63 9 54 -13 -87]] || || 8.025 || 169/168 176/175 275/273 540/539 ||
|| 26 || <<26 4 7 15 43 -54 -62 -66 -28 5 21 85 18 95 93]] || || 9.145 || 121/120 176/175 676/675 1040/1029 ||

Original HTML content:

<html><head><title>List of edo-distinct 53et rank two temperaments</title></head><body>The temperaments listed are 53edo-distinct, meaning that they are all different even if tuned in 53edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity was chosen as the representative for each class of edo-distinctness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Wedgie<br />
</td>
        <td>Name<br />
</td>
        <td>Complexity<br />
</td>
        <td>Commas<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>&lt;&lt;1 -8 -15]]<br />
</td>
        <td>Helmholtz<br />
</td>
        <td>3.103<br />
</td>
        <td>32805/32768<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 37 54]]<br />
</td>
        <td>Monzismic<br />
</td>
        <td>12.528<br />
</td>
        <td>|54 -37 2&gt;<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 29 39]]<br />
</td>
        <td>Tricot<br />
</td>
        <td>9.520<br />
</td>
        <td>68719476736000/68630377364883<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 21 24]]<br />
</td>
        <td>Vulture<br />
</td>
        <td>6.600<br />
</td>
        <td>10485760000/10460353203<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 13 9]]<br />
</td>
        <td>Amity<br />
</td>
        <td>3.970<br />
</td>
        <td>1600000/1594323<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 5 -6]]<br />
</td>
        <td>Hanson<br />
</td>
        <td>2.685<br />
</td>
        <td>15625/15552<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;7 -3 -21]]<br />
</td>
        <td>Orson<br />
</td>
        <td>4.232<br />
</td>
        <td>2109375/2097152<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;8 -11 -36]]<br />
</td>
        <td>Submajor<br />
</td>
        <td>6.919<br />
</td>
        <td>69198046875/68719476736<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;9 -19 -51]]<br />
</td>
        <td>Aufo<br />
</td>
        <td>9.853<br />
</td>
        <td>2270041927734375/2251799813685248<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;10 -27 -66]]<br />
</td>
        <td><br />
</td>
        <td>12.867<br />
</td>
        <td>74468725439326171875/73786976294838206464<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;11 18 3]]<br />
</td>
        <td>Quartonic<br />
</td>
        <td>6.026<br />
</td>
        <td>390625000/387420489<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;41 43 -27]]<br />
</td>
        <td><br />
</td>
        <td>18.85<br />
</td>
        <td>|-27 -43 41&gt;<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;13 2 -27]]<br />
</td>
        <td>Ditonic<br />
</td>
        <td>6.373<br />
</td>
        <td>1220703125/1207959552<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;14 47 42]]<br />
</td>
        <td><br />
</td>
        <td>14.353<br />
</td>
        <td>|42 -47 14&gt;<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;15 -14 -57]]<br />
</td>
        <td>Misneb<br />
</td>
        <td>11.043<br />
</td>
        <td>145964630126953125/144115188075855872<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;16 31 12]]<br />
</td>
        <td><br />
</td>
        <td>9.845<br />
</td>
        <td>625000000000000/617673396283947<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;17 23 -3]]<br />
</td>
        <td>Maja<br />
</td>
        <td>8.443<br />
</td>
        <td>762939453125/753145430616<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;35 38 -21]]<br />
</td>
        <td><br />
</td>
        <td>16.207<br />
</td>
        <td>|-21 -38 35&gt;<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;19 7 -33]]<br />
</td>
        <td>Semaja<br />
</td>
        <td>8.817<br />
</td>
        <td>19073486328125/18786186952704<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;20 -1 -48]]<br />
</td>
        <td><br />
</td>
        <td>10.481<br />
</td>
        <td>286102294921875/281474976710656<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;21 44 21]]<br />
</td>
        <td><br />
</td>
        <td>13.75<br />
</td>
        <td>1000000000000000000000/984770902183611232881<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;31 17 -45]]<br />
</td>
        <td><br />
</td>
        <td>13.972<br />
</td>
        <td>4656612873077392578125/4543715546604414959616<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;23 28 -9]]<br />
</td>
        <td><br />
</td>
        <td>10.985<br />
</td>
        <td>11920928955078125/11712917736940032<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;29 33 -15]]<br />
</td>
        <td><br />
</td>
        <td>13.582<br />
</td>
        <td>186264514923095703125/182159296644891377664<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;25 12 -39]]<br />
</td>
        <td><br />
</td>
        <td>11.37<br />
</td>
        <td>298023223876953125/292162779488452608<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;27 -4 -69]]<br />
</td>
        <td><br />
</td>
        <td>14.659<br />
</td>
        <td>603497028350830078125/590295810358705651712<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Wedgie<br />
</td>
        <td>Name<br />
</td>
        <td>Complexity<br />
</td>
        <td>Commas<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>&lt;&lt;1 -8 -14 -15 -25 -10]]<br />
</td>
        <td>Garibaldi<br />
</td>
        <td>3.823<br />
</td>
        <td>225/224 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 -16 25 -30 34 103]]<br />
</td>
        <td>Hemischis<br />
</td>
        <td>9.155<br />
</td>
        <td>6144/6125 19683/19600<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 29 11 39 9 -56]]<br />
</td>
        <td>Tricot<br />
</td>
        <td>7.801<br />
</td>
        <td>2430/2401 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 21 -3 24 -16 -66]]<br />
</td>
        <td>Buzzard<br />
</td>
        <td>6.420<br />
</td>
        <td>1728/1715 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 13 -17 9 -41 -76]]<br />
</td>
        <td>Amity<br />
</td>
        <td>7.127<br />
</td>
        <td>4375/4374 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 5 22 -6 18 37]]<br />
</td>
        <td>Catakleismic<br />
</td>
        <td>4.684<br />
</td>
        <td>225/224 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;7 -3 8 -21 -7 27]]<br />
</td>
        <td>Orwell<br />
</td>
        <td>3.685<br />
</td>
        <td>225/224 1728/1715<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;8 -11 -6 -36 -32 17]]<br />
</td>
        <td>Submajor<br />
</td>
        <td>5.869<br />
</td>
        <td>225/224 51200/50421<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;9 -19 -20 -51 -57 7]]<br />
</td>
        <td>Untriton<br />
</td>
        <td>9.195<br />
</td>
        <td>225/224 125000000/121060821<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;10 26 19 18 2 -29]]<br />
</td>
        <td>Hamity<br />
</td>
        <td>6.518<br />
</td>
        <td>2430/2401 4000/3969<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;11 18 5 3 -23 -39]]<br />
</td>
        <td>Quartonic<br />
</td>
        <td>5.395<br />
</td>
        <td>1728/1715 4000/3969<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;12 10 -9 -12 -48 -49]]<br />
</td>
        <td>Hemikleismic<br />
</td>
        <td>6.704<br />
</td>
        <td>4000/3969 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;13 2 30 -27 11 64]]<br />
</td>
        <td>Coditone<br />
</td>
        <td>7.512<br />
</td>
        <td>225/224 2125764/2100875<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;14 47 16 42 -14 -95]]<br />
</td>
        <td><br />
</td>
        <td>12.061<br />
</td>
        <td>19683/19600 51200/50421<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;15 -14 2 -57 -39 44]]<br />
</td>
        <td>Misneb<br />
</td>
        <td>9.025<br />
</td>
        <td>225/224 4194304/4117715<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;16 31 41 12 20 8]]<br />
</td>
        <td><br />
</td>
        <td>9.361<br />
</td>
        <td>3125/3087 19683/19600<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;17 23 27 -3 -5 -2]]<br />
</td>
        <td>Maja<br />
</td>
        <td>7.161<br />
</td>
        <td>2430/2401 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;18 15 13 -18 -30 -12]]<br />
</td>
        <td>Kleiboh<br />
</td>
        <td>6.645<br />
</td>
        <td>1728/1715 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;19 7 -1 -33 -55 -22]]<br />
</td>
        <td>Semaja<br />
</td>
        <td>8.139<br />
</td>
        <td>3125/3087 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;20 -1 -15 -48 -80 -32]]<br />
</td>
        <td><br />
</td>
        <td>10.843<br />
</td>
        <td>3125/3087 65536/64827<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;21 44 24 21 -21 -68]]<br />
</td>
        <td><br />
</td>
        <td>11.339<br />
</td>
        <td>4000/3969 839808/823543<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;31 17 43 -45 -19 52]]<br />
</td>
        <td><br />
</td>
        <td>12.262<br />
</td>
        <td>2430/2401 390625/387072<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;23 28 49 -9 13 35]]<br />
</td>
        <td><br />
</td>
        <td>10.832<br />
</td>
        <td>4375/4374 78125/76832<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;24 20 35 -24 -12 25]]<br />
</td>
        <td><br />
</td>
        <td>9.340<br />
</td>
        <td>2430/2401 15625/15552<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;25 12 21 -39 -37 15]]<br />
</td>
        <td><br />
</td>
        <td>9.293<br />
</td>
        <td>1728/1715 78125/76832<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;26 4 7 -54 -62 5]]<br />
</td>
        <td><br />
</td>
        <td>10.711<br />
</td>
        <td>6144/6125 78125/76832<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x11-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Wedgie<br />
</td>
        <td>Name<br />
</td>
        <td>Complexity<br />
</td>
        <td>Commas<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>&lt;&lt;1 -8 -14 -15 -25 -10]]<br />
</td>
        <td>Garibaldi<br />
</td>
        <td>3.823<br />
</td>
        <td>225/224 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 -16 25 -30 34 103]]<br />
</td>
        <td>Hemischis<br />
</td>
        <td>9.155<br />
</td>
        <td>6144/6125 19683/19600<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 29 11 39 9 -56]]<br />
</td>
        <td>Tricot<br />
</td>
        <td>7.801<br />
</td>
        <td>2430/2401 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 21 -3 24 -16 -66]]<br />
</td>
        <td>Buzzard<br />
</td>
        <td>6.420<br />
</td>
        <td>1728/1715 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 13 -17 9 -41 -76]]<br />
</td>
        <td>Amity<br />
</td>
        <td>7.127<br />
</td>
        <td>4375/4374 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 5 22 -6 18 37]]<br />
</td>
        <td>Catakleismic<br />
</td>
        <td>4.684<br />
</td>
        <td>225/224 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;7 -3 8 -21 -7 27]]<br />
</td>
        <td>Orwell<br />
</td>
        <td>3.685<br />
</td>
        <td>225/224 1728/1715<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;8 -11 -6 -36 -32 17]]<br />
</td>
        <td>Submajor<br />
</td>
        <td>5.869<br />
</td>
        <td>225/224 51200/50421<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;9 -19 -20 -51 -57 7]]<br />
</td>
        <td>Untriton<br />
</td>
        <td>9.195<br />
</td>
        <td>225/224 125000000/121060821<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;10 26 19 18 2 -29]]<br />
</td>
        <td>Hamity<br />
</td>
        <td>6.518<br />
</td>
        <td>2430/2401 4000/3969<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;11 18 5 3 -23 -39]]<br />
</td>
        <td>Quartonic<br />
</td>
        <td>5.395<br />
</td>
        <td>1728/1715 4000/3969<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;12 10 -9 -12 -48 -49]]<br />
</td>
        <td>Hemikleismic<br />
</td>
        <td>6.704<br />
</td>
        <td>4000/3969 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;13 2 30 -27 11 64]]<br />
</td>
        <td>Coditone<br />
</td>
        <td>7.512<br />
</td>
        <td>225/224 2125764/2100875<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;14 47 16 42 -14 -95]]<br />
</td>
        <td><br />
</td>
        <td>12.061<br />
</td>
        <td>19683/19600 51200/50421<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;15 -14 2 -57 -39 44]]<br />
</td>
        <td>Misneb<br />
</td>
        <td>9.025<br />
</td>
        <td>225/224 4194304/4117715<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;16 31 41 12 20 8]]<br />
</td>
        <td><br />
</td>
        <td>9.361<br />
</td>
        <td>3125/3087 19683/19600<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;17 23 27 -3 -5 -2]]<br />
</td>
        <td>Maja<br />
</td>
        <td>7.161<br />
</td>
        <td>2430/2401 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;18 15 13 -18 -30 -12]]<br />
</td>
        <td>Kleiboh<br />
</td>
        <td>6.645<br />
</td>
        <td>1728/1715 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;19 7 -1 -33 -55 -22]]<br />
</td>
        <td>Semaja<br />
</td>
        <td>8.139<br />
</td>
        <td>3125/3087 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;20 -1 -15 -48 -80 -32]]<br />
</td>
        <td><br />
</td>
        <td>10.843<br />
</td>
        <td>3125/3087 65536/64827<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;21 44 24 21 -21 -68]]<br />
</td>
        <td><br />
</td>
        <td>11.339<br />
</td>
        <td>4000/3969 839808/823543<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;31 17 43 -45 -19 52]]<br />
</td>
        <td><br />
</td>
        <td>12.262<br />
</td>
        <td>2430/2401 390625/387072<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;23 28 49 -9 13 35]]<br />
</td>
        <td><br />
</td>
        <td>10.832<br />
</td>
        <td>4375/4374 78125/76832<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;24 20 35 -24 -12 25]]<br />
</td>
        <td><br />
</td>
        <td>9.340<br />
</td>
        <td>2430/2401 15625/15552<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;25 12 21 -39 -37 15]]<br />
</td>
        <td><br />
</td>
        <td>9.293<br />
</td>
        <td>1728/1715 78125/76832<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;26 4 7 -54 -62 5]]<br />
</td>
        <td><br />
</td>
        <td>10.711<br />
</td>
        <td>6144/6125 78125/76832<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x13-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Wedgie<br />
</td>
        <td>Name<br />
</td>
        <td>Complexity<br />
</td>
        <td>Commas<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>&lt;&lt;1 -8 -14 -30 -33 -15 -25 -51 -56 -10 -42 -47 -36 -41 -3]]<br />
</td>
        <td>Helenus<br />
</td>
        <td>5.812<br />
</td>
        <td>99/98 176/175 275/273 847/845<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19]]<br />
</td>
        <td>Hemigari<br />
</td>
        <td>6.013<br />
</td>
        <td>121/120 169/168 225/224 275/273<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 29 11 16 7 39 9 15 0 -56 -63 -91 7 -21 -35]]<br />
</td>
        <td>Tricot<br />
</td>
        <td>6.236<br />
</td>
        <td>99/98 121/120 169/168 352/351<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 21 -3 -14 27 24 -16 -36 28 -66 -105 -15 -29 87 145]]<br />
</td>
        <td>Buteo<br />
</td>
        <td>7.137<br />
</td>
        <td>99/98 275/273 385/384 572/567<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 13 -17 9 -6 9 -41 -3 -28 -76 -24 -62 84 46 -54]]<br />
</td>
        <td>Hitchcock<br />
</td>
        <td>5.834<br />
</td>
        <td>121/120 169/168 176/175 325/324<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 5 22 32 14 -6 18 30 0 37 57 14 14 -42 -70]]<br />
</td>
        <td>Cataclysmic<br />
</td>
        <td>4.918<br />
</td>
        <td>99/98 169/168 176/175 275/273<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]]<br />
</td>
        <td>Orwell<br />
</td>
        <td>4.717<br />
</td>
        <td>99/98 121/120 176/175 275/273<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;8 -11 -6 25 1 -36 -32 12 -28 17 96 43 91 25 -89]]<br />
</td>
        <td>Submajor<br />
</td>
        <td>6.305<br />
</td>
        <td>169/168 225/224 275/273 385/384<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;9 -19 -20 -5 -32 -51 -57 -39 -84 7 54 -4 55 -16 -92]]<br />
</td>
        <td>Untriton<br />
</td>
        <td>8.047<br />
</td>
        <td>121/120 225/224 275/273 1040/1029<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;10 26 19 18 41 18 2 -6 28 -29 -48 -1 -15 45 75]]<br />
</td>
        <td>Hamity<br />
</td>
        <td>5.887<br />
</td>
        <td>99/98 121/120 275/273 572/567<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72]]<br />
</td>
        <td>Quartz<br />
</td>
        <td>5.990<br />
</td>
        <td>99/98 169/168 275/273 385/384<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56]]<br />
</td>
        <td>Hemikleismic<br />
</td>
        <td>6.023<br />
</td>
        <td>121/120 176/175 275/273 325/324<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;13 2 30 34 48 -27 11 9 28 64 72 104 -8 24 40]]<br />
</td>
        <td>Coditone<br />
</td>
        <td>7.622<br />
</td>
        <td>99/98 176/175 325/324 847/845<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;14 -6 16 4 15 -42 -14 -42 -28 54 30 57 -44 -17 37]]<br />
</td>
        <td>Doublethink<br />
</td>
        <td>5.858<br />
</td>
        <td>99/98 121/120 169/168 176/175<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;15 -14 2 -26 -18 -57 -39 -93 -84 44 -12 10 -80 -58 34]]<br />
</td>
        <td>Misneb<br />
</td>
        <td>8.837<br />
</td>
        <td>99/98 176/175 640/637 847/845<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;16 -22 -12 -3 2 -72 -64 -60 -56 34 69 86 33 50 18]]<br />
</td>
        <td><br />
</td>
        <td>9.127<br />
</td>
        <td>121/120 169/168 225/224 640/637<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;17 23 27 20 22 -3 -5 -27 -28 -2 -33 -34 -37 -38 2]]<br />
</td>
        <td>Maja<br />
</td>
        <td>5.680<br />
</td>
        <td>99/98 121/120 169/168 275/273<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;18 15 13 43 42 -18 -30 6 0 -12 48 42 76 70 -14]]<br />
</td>
        <td>Kleiboh<br />
</td>
        <td>6.913<br />
</td>
        <td>176/175 275/273 325/324 540/539<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]]<br />
</td>
        <td>Semaja<br />
</td>
        <td>6.343<br />
</td>
        <td>121/120 169/168 176/175 275/273<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;20 -1 38 36 29 -48 4 -12 -28 91 87 71 -30 -59 -33]]<br />
</td>
        <td><br />
</td>
        <td>8.717<br />
</td>
        <td>99/98 169/168 176/175 4235/4212<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;21 -9 24 6 -4 -63 -21 -63 -84 81 45 24 -66 -100 -36]]<br />
</td>
        <td><br />
</td>
        <td>9.168<br />
</td>
        <td>99/98 121/120 176/175 2200/2197<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;22 36 10 29 16 6 -46 -30 -56 -78 -57 -96 47 8 -52]]<br />
</td>
        <td><br />
</td>
        <td>8.657<br />
</td>
        <td>121/120 169/168 325/324 640/637<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;23 28 49 52 36 -9 13 3 -28 35 24 -20 -23 -80 -68]]<br />
</td>
        <td><br />
</td>
        <td>8.776<br />
</td>
        <td>99/98 169/168 275/273 2662/2625<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;24 20 35 22 3 -24 -12 -48 -84 25 -18 -67 -59 -121 -71]]<br />
</td>
        <td><br />
</td>
        <td>8.623<br />
</td>
        <td>99/98 121/120 275/273 4225/4224<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;25 12 21 45 23 -39 -37 -15 -56 15 63 9 54 -13 -87]]<br />
</td>
        <td><br />
</td>
        <td>8.025<br />
</td>
        <td>169/168 176/175 275/273 540/539<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;26 4 7 15 43 -54 -62 -66 -28 5 21 85 18 95 93]]<br />
</td>
        <td><br />
</td>
        <td>9.145<br />
</td>
        <td>121/120 176/175 676/675 1040/1029<br />
</td>
    </tr>
</table>

</body></html>
Retrieved from "https://en.xen.wiki/index.php?title=List_of_edo-distinct_53et_rank_two_temperaments&oldid=18757"