Breedsmic temperaments: Difference between revisions

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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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]

Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4> = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.

It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.

=Hemififths=

Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo]] and [[140edo]] providing good tunings, and [[239edo]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&58 temperament and has wedgie <<2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.

Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo|99edo]] and [[140edo|140edo]] providing good tunings, and [[239edo|239edo]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&58 temperament and has wedgie <<2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.

By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.

By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo|99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.

==5-limit==

Line 24:

Line 15:

Map: [<1 1 -5|, <0 2 25|]

EDOs: 41, 58, 99, 239, 338, 915b, 1253bc

Badness: 0.3728

Line 31:

Line 24:

7 and 9-limit minimax

[|1 0 0 0>, |7/5, 0, 2/25, 0>, |0 0 1 0>, |8/5 0 13/25 0>]

Eigenvalues: 2, 5

Line 37:

Line 32:

Map: [<1 1 -5 -1|, <0 2 25 13|]

EDOs: [[41edo|41]], [[58edo|58]], [[99edo|99]], [[239edo|239]], [[338edo|338]]

Badness: 0.0222

==11-limit==

Commas: 243/242, 441/440, 896/891

Line 46:

Line 43:

Map: [<1 1 -5 -1 2|, <0 2 25 13 5|]

EDOs: 7, 17, 41, 58, 99

Badness: 0.0235

==13-limit==

Commas: 144/143, 196/195, 243/242, 364/363

Line 55:

Line 54:

Map: [<1 1 -5 -1 2 4|, <0 2 25 13 5 -1|]

EDOs: 7, 17, 41, 58, 99

Badness: 0.0191

Line 64:

Line 65:

Map: [<2 0 -35 -15 -47|, <0 2 25 13 34|]

EDOs: 58, 140, 198, 734bc, 932bcd, 1130bcd

Badness: 42.487

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Line 76:

Map: [<2 0 -35 -15 -47 -37|, <0 2 25 13 34 28|]

EDOs: 58, 140, 198, 536f, 734bcf, 932bcdf

Badness: 0.0212

=Tertiaseptal=

Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.

Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo|171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.

Commas: 2401/2400, 65625/65536

Line 84:

Line 89:

Map: [<1 3 2 3|, <0 -22 5 -3|]

EDOs: 15, 16, 31, 109, 140, 171

Badness: 0.0130

==11-limit==

Commas: 243/242, 441/440, 65625/65536

Line 93:

Line 100:

Map: [<1 3 2 3 7|, <0 -22 5 -3 -55|]

EDOs: 15, 16, 31, 171, 202

Badness: 0.0356

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Line 111:

Map: [<1 3 2 3 7 1|, <0 -22 5 -3 -55 42|]

EDOs: 31, 140e, 171, 373ef, 544ef

Badness: 0.0369

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Line 122:

Map: [<1 3 2 3 5|, <0 -22 5 -3 -24|]

EDOs: 31, 109, 140, 171e, 311e

Badness: 0.0302

Line 120:

Line 133:

Map: [<1 3 2 3 6|, <0 -44 10 -6 -79|]

EDOs: 31, 280, 311, 342, 2021cde, 3731cde

Badness: 0.0156

=Harry=

Commas: 2401/2400, 19683/19600

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Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is <<12 34 20 30 ...||.

Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with <<12 34 20 30 52 ...|| as the octave wedgie. [[130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.

Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with <<12 34 20 30 52 ...|| as the octave wedgie. [[130edo|130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.

[[~~POTE tuning~~|POTE generator]]: ~21/20 = 83.156

[[POTE_tuning|POTE generator]]: ~21/20 = 83.156

Map: [<2 4 7 7|, <0 -6 -17 -10|]

Wedgie: <<12 34 20 26 -2 -49||

EDOs: 14, 58, 72, 130, 202, 534, 938

Badness: 0.0341

==11-limit==

Commas: 243/242, 441/440, 4000/3993

[[~~POTE tuning~~|POTE generator]]: ~21/20 = 83.167

[[POTE_tuning|POTE generator]]: ~21/20 = 83.167

Map: [<2 4 7 7 9|, <0 -6 -17 -10 -15|]

EDOs: 14, 58, 72, 130, 202

Badness: 0.0159

==13-limit==

Commas: 243/242, 351/350, 441/440, 676/675

[[~~POTE tuning~~|POTE generator]]: ~21/20 = 83.116

[[POTE_tuning|POTE generator]]: ~21/20 = 83.116

Map: [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]

EDOs: 14, 58, 72, 130, 462

Badness: 0.0130

=Quasiorwell=

In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1>. It has a wedgie <<38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.

Line 167:

Line 189:

Map: [<1 31 0 9|, <0 -38 3 -8|]

EDOs: [[31edo|31]], [[177edo|177]], [[208edo|208]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]]

Badness: 0.0358

==11-limit==

Commas: 2401/2400, 3025/3024, 5632/5625

Line 176:

Line 200:

Map: [<1 31 0 9 53|, <0 -38 3 -8 -64|]

EDOs: [[31edo|31]], [[208edo|208]], [[239edo|239]], [[270edo|270]]

Badness: 0.0175

==13-limit==

Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095

Line 185:

Line 211:

Map: [<1 31 0 9 53 -59|, <0 -38 3 -8 -64 81|]

EDOs: [[31edo|31]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]]

Badness: 0.0179

=Decoid=

Commas: 2401/2400, 67108864/66976875

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Map: [<10 0 47 36|, <0 2 -3 -1|]

Wedgie: <<20 -30 -10 -94 -72 61||

EDOs: 10, 120, 130, 270

Badness: 0.0339

==11-limit==

Commas: 2401/2400, 5832/5825, 9801/9800

Line 204:

Line 235:

Map: [<10 0 47 36 98|, <0 2 -3 -1 -8|]

EDOs: 130, 270, 670, 940, 1210

Badness: 0.0187

==13-limit==

Commas: 676/675, 1001/1000, 1716/1715, 4225/4224

Line 213:

Line 246:

Map: [<10 0 47 36 98 37|, <0 2 -3 -1 -8 0|]

EDOs: 130, 270, 940, 1480

Badness: 0.0135

Line 222:

Line 257:

Map: [<1 3 12 8|, <0 -6 -41 -22|]

Weggie: <<6 41 22 51 18 -64||

EDOs: 72, 161, 233, 305

Badness: 0.0882

Line 232:

Line 270:

Map: [<1 3 12 8 7|, <0 -6 -41 -22 -15|]

EDOs: 72, 161, 233, 305

Badness: 0.0280

Line 241:

Line 281:

Map: [<1 3 12 8 7 7|, <0 -6 -41 -22 -15 -14|]

EDOs: 72, 161f, 233f

Badness: 0.0269

Line 252:

Line 294:

Map: [<1 11 42 25|, <0 -14 -59 -33|]

Wedgie: <<14 59 33 61 13 -89||

EDOs: 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d

Badness: 0.0167

Line 262:

Line 307:

Map: [<1 27 24 20|, <0 -34 -29 -23|]

Wedgie: <<34 29 23 -33 -59 -28||

EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c

Badness: 0.0373

Line 272:

Line 320:

Map: [<1 29 33 25|, <0 -42 -47 -34|]

Wedgie: <<42 47 34 -23 -64 -53||

EDOs: 72, 167, 239, 311, 694, 1005c

Badness: 0.0753

Line 282:

Line 333:

Map: [<1 29 33 25 25|, <0 -42 -47 -34 -33|]

EDOs: 72, 167, 239, 311, 1316c

Badness: 0.0229

Line 291:

Line 344:

Map: [<1 29 33 25 25 99|, <0 -42 -47 -34 -33 -146|]

EDOs: 72, 311, 694, 1005c, 1699cd

Badness: 0.0209

Line 300:

Line 355:

Map: [<1 1 19 11|, <0 2 -57 -28|]

Wedgie: <<2 -57 -28 -95 -50 95||

EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc

Badness: 0.0419

Line 310:

Line 368:

Map: [<1 1 19 11 -10|, <0 2 -57 -28 46|]

EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b

Badness: 0.0195

Line 319:

Line 379:

Map: [<1 1 19 11 -10 -20|, <0 2 -57 -28 46 81|]

EDOs: 41, 229, 270, 581, 851, 2283b, 3134b

Badness: 0.0138

Line 328:

Line 390:

Map: [<1 3 6 5|, <0 -20 -52 -31|]

Wedgie: <<20 52 31 36 -7 -74||

EDOs: 99, 212, 311, 410, 1131, 1541b

Badness: 0.0455

Line 338:

Line 403:

Map: [<1 25 -31 -8|, <0 -26 37 12|]

Wedgie: <<26 -37 -12 -119 -92 76||

EDOs: 10, 151, 161, 171, 3581bcd, 3752bcd, 3923bcd, 4094bcd, 4265bcd, 4436bcd, 4607bcd

Badness: 0.0441

Line 348:

Line 416:

Map: [<1 31 34 26|, <0 -52 -56 -41|]

Wedgie: <<52 56 41 -32 -81 -62||

EDOs: 76, 99, 274, 373, 472, 571, 1043, 1614

Badness: 0.0576

Line 358:

Line 429:

Map: [<1 19 0 6}, <0 -60 8 -11|]

Wedgie: <<60 -8 11 -152 -151 48||

EDOs: 31, 348, 379, 410, 441, 1354, 1795, 2236

Badness: 0.0458

Line 368:

Line 442:

Map: [<1 13 33 21|, <0 -32 -86 -51|]

Wedgie: <<32 86 51 62 -9 -123||

EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d

Badness: 0.0283

Line 378:

Line 455:

Map: [<1 5 1 3|, <0 -18 7 -1|]

Wedgie: <<18 -7 1 -53 -49 22||

EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd

Badness: 0.1584

Line 388:

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Map: [<1 5 1 3 1|, <0 -18 7 -1 13|]

EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde

Badness: 0.059

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Map: [<1 5 1 3 1 2|, <0 -18 7 -1 13 9|]

EDOs: 21, 37, 58, 153bcef, 211bcdef

Badness: 0.0322

Line 406:

Line 490:

Map: [<1 19 8 10|, <0 -46 -15 -19|]

Wedgie: <<46 15 19 -83 -99 2||

EDOs: 37, 103, 140, 243, 383, 1009cd, 1392cd

Badness: 0.1005

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Map: [<1 19 8 10 8|, <0 -46 -15 -19 -12|]

EDOs: 37, 103, 140, 243e

Badness: 0.0565

Line 425:

Line 514:

Map: [<1 19 8 10 8 9|, <0 -46 -15 -19 -12 -14|]

EDOs: 37, 103, 140, 243e

Badness: 0.0274

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Line 525:

Map: [<1 5 9 7|, <0 -22 -43 -27|]

EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc

Badness: 0.12567

Line 443:

Line 536:

Map: [<1 5 9 7 12|, <0 -22 -43 -27 -55|]

EDOs: 58, 103, 161, 425b, 586b, 747bc

Badness: 0.0400

Line 452:

Line 547:

Map: [<1 5 9 7 12 11|, <0 -22 -43 -27 -55 -47|]

EDOs: 58, 103, 161

Badness: 0.0218

Line 461:

Line 558:

Map: [<1 13 17 13|, <0 -28 -36 -25|]

Wedgie: <<[28 36 25 -8 -39 -43||

EDOs: 27, 76, 103, 130

Badness: 0.0796

Line 471:

Line 571:

Map: [<1 13 17 13 32|, <0 -28 -36 -25 -70|]

EDOs: 103, 130, 233, 363, 493e, 856be

Badness: 0.0368

Line 480:

Line 582:

Map: [<1 13 17 13 32 9|, <0 -28 -36 -25 -70 -13|]

EDOs: 103, 130, 233, 363

~~Badness: 0.0217</pre></div>~~

~~<h4>Original HTML content:</h4>~~

Badness: 0.0217

<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"><html><head><title>Breedsmic temperaments</title></head><body><a href="#Hemififths">Hemififths</a> | <a href="#Semihemi">Semihemi</a> | <a href="#Tertiaseptal">Tertiaseptal</a> | <a href="#Hemitert">Hemitert</a> | <a href="#Harry">Harry</a> | <a href="#Quasiorwell">Quasiorwell</a> | <a href="#Decoid">Decoid</a> | <a href="#Neominor">Neominor</a> | <a href="#Emmthird">Emmthird</a> | <a href="#Quinmite">Quinmite</a> | <a href="#Unthirds">Unthirds</a> | <a href="#Newt">Newt</a> | <a href="#Amicable">Amicable</a> | <a href="#Septidiasemi">Septidiasemi</a> | <a href="#Maviloid">Maviloid</a> | <a href="#Subneutral">Subneutral</a> | <a href="#Osiris">Osiris</a> | <a href="#Gorgik">Gorgik</a> | <a href="#Fibo">Fibo</a> | <a href="#Mintone">Mintone</a> | <a href="#Catafourth">Catafourth</a>

~~<br />~~

~~<br />~~

Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br />

~~<br />~~

It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.<br />

~~<br />~~

~~<h1 id="toc0"><a name="Hemififths"></a>Hemififths</h1>~~

Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with <a class="wiki_link" href="/99edo">99edo</a> and <a class="wiki_link" href="/140edo">140edo</a> providing good tunings, and <a class="wiki_link" href="/239edo">239edo</a> an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;58 temperament and has wedgie &lt;&lt;2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.<br />

~~<br />~~

By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. <a class="wiki_link" href="/99edo">99edo</a> is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.<br />

~~<br />~~

~~<h2 id="toc1"><a name="Hemififths-5-limit"></a>5-limit</h2>~~

~~Comma: 858993459200/847288609443<br />~~

~~<br />~~

~~POTE generator: ~655360/531441 = 351.476<br />~~

~~<br />~~

~~Map: [&lt;1 1 -5|, &lt;0 2 25|]<br />~~

~~EDOs: 41, 58, 99, 239, 338, 915b, 1253bc<br />~~

~~Badness: 0.3728<br />~~

~~<br />~~

~~<h2 id="toc2"><a name="Hemififths-7-limit"></a>7-limit</h2>~~

~~Commas: 2401/2400, 5120/5103<br />~~

~~<br />~~

~~7 and 9-limit minimax<br />~~

~~[|1 0 0 0&gt;, |7/5, 0, 2/25, 0&gt;, |0 0 1 0&gt;, |8/5 0 13/25 0&gt;]<br />~~

~~Eigenvalues: 2, 5<br />~~

~~<br />~~

~~Algebraic generator: (2 + sqrt(2))/2<br />~~

~~<br />~~

~~Map: [&lt;1 1 -5 -1|, &lt;0 2 25 13|]<br />~~

EDOs: <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/338edo">338</a><br />

~~Badness: 0.0222<br />~~

~~<br />~~

~~<h2 id="toc3"><a name="Hemififths-11-limit"></a>11-limit</h2>~~

~~Commas: 243/242, 441/440, 896/891<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 351.521<br />~~

~~<br />~~

~~Map: [&lt;1 1 -5 -1 2|, &lt;0 2 25 13 5|]<br />~~

~~EDOs: 7, 17, 41, 58, 99<br />~~

~~Badness: 0.0235<br />~~

~~<br />~~

~~<h2 id="toc4"><a name="Hemififths-13-limit"></a>13-limit</h2>~~

~~Commas: 144/143, 196/195, 243/242, 364/363<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 351.573<br />~~

~~<br />~~

~~Map: [&lt;1 1 -5 -1 2 4|, &lt;0 2 25 13 5 -1|]<br />~~

~~EDOs: 7, 17, 41, 58, 99<br />~~

~~Badness: 0.0191<br />~~

~~<br />~~

~~<h1 id="toc5"><a name="Semihemi"></a>Semihemi</h1>~~

~~Commas: 2401/2400, 3388/3375, 9801/9800<br />~~

~~<br />~~

~~POTE generator: ~49/40 = 351.505<br />~~

~~<br />~~

~~Map: [&lt;2 0 -35 -15 -47|, &lt;0 2 25 13 34|]<br />~~

~~EDOs: 58, 140, 198, 734bc, 932bcd, 1130bcd<br />~~

~~Badness: 42.487<br />~~

~~<br />~~

~~<h2 id="toc6"><a name="Semihemi-13-limit"></a>13-limit</h2>~~

~~Commas: 352/351, 676/675, 847/845, 1716/1715<br />~~

~~<br />~~

~~POTE generator: ~49/40 = 351.502<br />~~

~~<br />~~

~~Map: [&lt;2 0 -35 -15 -47 -37|, &lt;0 2 25 13 34 28|]<br />~~

~~EDOs: 58, 140, 198, 536f, 734bcf, 932bcdf<br />~~

~~Badness: 0.0212<br />~~

~~<br />~~

~~<h1 id="toc7"><a name="Tertiaseptal"></a>Tertiaseptal</h1>~~

Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. <a class="wiki_link" href="/171edo">171edo</a> makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.<br />

~~<br />~~

~~Commas: 2401/2400, 65625/65536<br />~~

~~<br />~~

~~POTE generator: ~256/245 = 77.191<br />~~

~~<br />~~

~~Map: [&lt;1 3 2 3|, &lt;0 -22 5 -3|]<br />~~

~~EDOs: 15, 16, 31, 109, 140, 171<br />~~

~~Badness: 0.0130<br />~~

~~<br />~~

~~<h2 id="toc8"><a name="Tertiaseptal-11-limit"></a>11-limit</h2>~~

~~Commas: 243/242, 441/440, 65625/65536<br />~~

~~<br />~~

~~POTE generator: ~256/245 = 77.227<br />~~

~~<br />~~

~~Map: [&lt;1 3 2 3 7|, &lt;0 -22 5 -3 -55|]<br />~~

~~EDOs: 15, 16, 31, 171, 202<br />~~

~~Badness: 0.0356<br />~~

~~<br />~~

~~<h2 id="toc9"><a name="Tertiaseptal-13-limit"></a>13-limit</h2>~~

~~Commas: 243/242, 441/440, 625/624, 3584/3575<br />~~

~~<br />~~

~~POTE generator: ~117/112 = 77.203<br />~~

~~<br />~~

~~Map: [&lt;1 3 2 3 7 1|, &lt;0 -22 5 -3 -55 42|]<br />~~

~~EDOs: 31, 140e, 171, 373ef, 544ef<br />~~

~~Badness: 0.0369<br />~~

~~<br />~~

~~<h2 id="toc10"><a name="Tertiaseptal-Tertia"></a>Tertia</h2>~~

~~Commas: 385/384, 1331/1323, 1375/1372<br />~~

~~<br />~~

~~POTE generator: ~22/21 = 77.173<br />~~

~~<br />~~

~~Map: [&lt;1 3 2 3 5|, &lt;0 -22 5 -3 -24|]<br />~~

~~EDOs: 31, 109, 140, 171e, 311e<br />~~

~~Badness: 0.0302<br />~~

~~<br />~~

~~<h1 id="toc11"><a name="Hemitert"></a>Hemitert</h1>~~

~~Commas: 2401/2400 3025/3024 65625/65536<br />~~

~~<br />~~

~~POTE generator: ~45/44 = 38.596<br />~~

~~<br />~~

~~Map: [&lt;1 3 2 3 6|, &lt;0 -44 10 -6 -79|]<br />~~

~~EDOs: 31, 280, 311, 342, 2021cde, 3731cde<br />~~

~~Badness: 0.0156<br />~~

~~<br />~~

~~<h1 id="toc12"><a name="Harry"></a>Harry</h1>~~

~~Commas: 2401/2400, 19683/19600<br />~~

~~<br />~~

Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&amp;72 temperament, with wedgie &lt;&lt;12 34 20 26 -2 -49||. The period is half an octave, and the generator 21/20, with generator tunings of 9\130 or 14\202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices.<br />

~~<br />~~

Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is &lt;&lt;12 34 20 30 ...||.<br />

~~<br />~~

Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with &lt;&lt;12 34 20 30 52 ...|| as the octave wedgie. <a class="wiki_link" href="/130edo">130edo</a> is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.<br />

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~21/20 = 83.156<br />~~

~~<br />~~

~~Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]<br />~~

~~Wedgie: &lt;&lt;12 34 20 26 -2 -49||<br />~~

~~EDOs: 14, 58, 72, 130, 202, 534, 938<br />~~

~~Badness: 0.0341<br />~~

~~<br />~~

~~<h2 id="toc13"><a name="Harry-11-limit"></a>11-limit</h2>~~

~~Commas: 243/242, 441/440, 4000/3993<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~21/20 = 83.167<br />~~

~~<br />~~

~~Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]<br />~~

~~EDOs: 14, 58, 72, 130, 202<br />~~

~~Badness: 0.0159<br />~~

~~<br />~~

~~<h2 id="toc14"><a name="Harry-13-limit"></a>13-limit</h2>~~

~~Commas: 243/242, 351/350, 441/440, 676/675<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~21/20 = 83.116<br />~~

~~<br />~~

~~Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]<br />~~

~~EDOs: 14, 58, 72, 130, 462<br />~~

~~Badness: 0.0130<br />~~

~~<br />~~

~~<h1 id="toc15"><a name="Quasiorwell"></a>Quasiorwell</h1>~~

In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br />

~~<br />~~

~~Adding 3025/3024 extends to the 11-limit and gives &lt;&lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.<br />~~

~~<br />~~

~~Commas: 2401/2400, 29360128/29296875<br />~~

~~<br />~~

~~POTE generator: ~1024/875 = 271.107<br />~~

~~<br />~~

~~Map: [&lt;1 31 0 9|, &lt;0 -38 3 -8|]<br />~~

EDOs: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/177edo">177</a>, <a class="wiki_link" href="/208edo">208</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/270edo">270</a>, <a class="wiki_link" href="/571edo">571</a>, <a class="wiki_link" href="/841edo">841</a>, <a class="wiki_link" href="/1111edo">1111</a><br />

~~Badness: 0.0358<br />~~

~~<br />~~

~~<h2 id="toc16"><a name="Quasiorwell-11-limit"></a>11-limit</h2>~~

~~Commas: 2401/2400, 3025/3024, 5632/5625<br />~~

~~<br />~~

~~POTE generator: ~90/77 = 271.111<br />~~

~~<br />~~

~~Map: [&lt;1 31 0 9 53|, &lt;0 -38 3 -8 -64|]<br />~~

EDOs: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/208edo">208</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/270edo">270</a><br />

~~Badness: 0.0175<br />~~

~~<br />~~

~~<h2 id="toc17"><a name="Quasiorwell-13-limit"></a>13-limit</h2>~~

~~Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095<br />~~

~~<br />~~

~~POTE generator: ~90/77 = 271.107<br />~~

~~<br />~~

~~Map: [&lt;1 31 0 9 53 -59|, &lt;0 -38 3 -8 -64 81|]<br />~~

EDOs: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/270edo">270</a>, <a class="wiki_link" href="/571edo">571</a>, <a class="wiki_link" href="/841edo">841</a>, <a class="wiki_link" href="/1111edo">1111</a><br />

~~Badness: 0.0179<br />~~

~~<br />~~

~~<h1 id="toc18"><a name="Decoid"></a>Decoid</h1>~~

~~Commas: 2401/2400, 67108864/66976875<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 231.099<br />~~

~~<br />~~

~~Map: [&lt;10 0 47 36|, &lt;0 2 -3 -1|]<br />~~

~~Wedgie: &lt;&lt;20 -30 -10 -94 -72 61||<br />~~

~~EDOs: 10, 120, 130, 270<br />~~

~~Badness: 0.0339<br />~~

~~<br />~~

~~<h2 id="toc19"><a name="Decoid-11-limit"></a>11-limit</h2>~~

~~Commas: 2401/2400, 5832/5825, 9801/9800<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 231.070<br />~~

~~<br />~~

~~Map: [&lt;10 0 47 36 98|, &lt;0 2 -3 -1 -8|]<br />~~

~~EDOs: 130, 270, 670, 940, 1210<br />~~

~~Badness: 0.0187<br />~~

~~<br />~~

~~<h2 id="toc20"><a name="Decoid-13-limit"></a>13-limit</h2>~~

~~Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 231.083<br />~~

~~<br />~~

~~Map: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]<br />~~

~~EDOs: 130, 270, 940, 1480<br />~~

~~Badness: 0.0135<br />~~

~~<br />~~

~~<h1 id="toc21"><a name="Neominor"></a>Neominor</h1>~~

~~Commas: 2401/2400, 177147/175616<br />~~

~~<br />~~

~~POTE generator: ~189/160 = 283.280<br />~~

~~<br />~~

~~Map: [&lt;1 3 12 8|, &lt;0 -6 -41 -22|]<br />~~

~~Weggie: &lt;&lt;6 41 22 51 18 -64||<br />~~

~~EDOs: 72, 161, 233, 305<br />~~

~~Badness: 0.0882<br />~~

~~<br />~~

~~<h2 id="toc22"><a name="Neominor-11-limit"></a>11-limit</h2>~~

~~Commas: 243/242, 441/440, 35937/35840<br />~~

~~<br />~~

~~POTE: ~33/28 = 283.276<br />~~

~~<br />~~

~~Map: [&lt;1 3 12 8 7|, &lt;0 -6 -41 -22 -15|]<br />~~

~~EDOs: 72, 161, 233, 305<br />~~

~~Badness: 0.0280<br />~~

~~<br />~~

~~<h2 id="toc23"><a name="Neominor-13-limit"></a>13-limit</h2>~~

~~Commas: 169/168, 243/242, 364/363, 441/440<br />~~

~~<br />~~

~~POTE generator: ~13/11 = 283.294<br />~~

~~<br />~~

~~Map: [&lt;1 3 12 8 7 7|, &lt;0 -6 -41 -22 -15 -14|]<br />~~

~~EDOs: 72, 161f, 233f<br />~~

~~Badness: 0.0269<br />~~

~~<br />~~

~~<h1 id="toc24"><a name="Emmthird"></a>Emmthird</h1>~~

~~The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.<br />~~

~~<br />~~

~~Commas: 2401/2400, 14348907/14336000<br />~~

~~<br />~~

~~POTE generator: ~2744/2187 = 392.988<br />~~

~~<br />~~

~~Map: [&lt;1 11 42 25|, &lt;0 -14 -59 -33|]<br />~~

~~Wedgie: &lt;&lt;14 59 33 61 13 -89||<br />~~

~~EDOs: 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d<br />~~

~~Badness: 0.0167<br />~~

~~<br />~~

~~<h1 id="toc25"><a name="Quinmite"></a>Quinmite</h1>~~

~~Commas: 2401/2400, 1959552/1953125<br />~~

~~<br />~~

~~POTE generator: ~25/21 = 302.997<br />~~

~~<br />~~

~~Map: [&lt;1 27 24 20|, &lt;0 -34 -29 -23|]<br />~~

~~Wedgie: &lt;&lt;34 29 23 -33 -59 -28||<br />~~

~~EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c<br />~~

~~Badness: 0.0373<br />~~

~~<br />~~

~~<h1 id="toc26"><a name="Unthirds"></a>Unthirds</h1>~~

~~Commas: 2401/2400, 68359375/68024448<br />~~

~~<br />~~

~~POTE generator: ~3969/3125 = 416.717<br />~~

~~<br />~~

~~Map: [&lt;1 29 33 25|, &lt;0 -42 -47 -34|]<br />~~

~~Wedgie: &lt;&lt;42 47 34 -23 -64 -53||<br />~~

~~EDOs: 72, 167, 239, 311, 694, 1005c<br />~~

~~Badness: 0.0753<br />~~

~~<br />~~

~~<h2 id="toc27"><a name="Unthirds-11-limit"></a>11-limit</h2>~~

~~Commas: 2401/2400, 3025/3024, 4000/3993<br />~~

~~<br />~~

~~POTE generator: ~14/11 = 416.718<br />~~

~~<br />~~

~~Map: [&lt;1 29 33 25 25|, &lt;0 -42 -47 -34 -33|]<br />~~

~~EDOs: 72, 167, 239, 311, 1316c<br />~~

~~Badness: 0.0229<br />~~

~~<br />~~

~~<h2 id="toc28"><a name="Unthirds-13-limit"></a>13-limit</h2>~~

~~Commas: 625/624, 1575/1573, 2080/2079, 2401/2400<br />~~

~~<br />~~

~~POTE generator: ~14/11 = 416.716<br />~~

~~<br />~~

~~Map: [&lt;1 29 33 25 25 99|, &lt;0 -42 -47 -34 -33 -146|]<br />~~

~~EDOs: 72, 311, 694, 1005c, 1699cd<br />~~

~~Badness: 0.0209<br />~~

~~<br />~~

~~<h1 id="toc29"><a name="Newt"></a>Newt</h1>~~

~~Commas: 2401/2400, 33554432/33480783<br />~~

~~<br />~~

~~POTE generator: ~49/40 = 351.113<br />~~

~~<br />~~

~~Map: [&lt;1 1 19 11|, &lt;0 2 -57 -28|]<br />~~

~~Wedgie: &lt;&lt;2 -57 -28 -95 -50 95||<br />~~

~~EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc<br />~~

~~Badness: 0.0419<br />~~

~~<br />~~

~~<h2 id="toc30"><a name="Newt-11-limit"></a>11-limit</h2>~~

~~Commas: 2401/2400, 3025/3024, 19712/19683<br />~~

~~<br />~~

~~POTE generator: ~49/40 = 351.115<br />~~

~~<br />~~

~~Map: [&lt;1 1 19 11 -10|, &lt;0 2 -57 -28 46|]<br />~~

~~EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b<br />~~

~~Badness: 0.0195<br />~~

~~<br />~~

~~<h2 id="toc31"><a name="Newt-13-limit"></a>13-limit</h2>~~

~~Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095<br />~~

~~<br />~~

~~POTE genertaor: ~49/40 = 351.117<br />~~

~~<br />~~

~~Map: [&lt;1 1 19 11 -10 -20|, &lt;0 2 -57 -28 46 81|]<br />~~

~~EDOs: 41, 229, 270, 581, 851, 2283b, 3134b<br />~~

~~Badness: 0.0138<br />~~

~~<br />~~

~~<h1 id="toc32"><a name="Amicable"></a>Amicable</h1>~~

~~Commas: 2401/2400, 1600000/1594323<br />~~

~~<br />~~

~~POTE generator: ~21/20 = 84.880<br />~~

~~<br />~~

~~Map: [&lt;1 3 6 5|, &lt;0 -20 -52 -31|]<br />~~

~~Wedgie: &lt;&lt;20 52 31 36 -7 -74||<br />~~

~~EDOs: 99, 212, 311, 410, 1131, 1541b<br />~~

~~Badness: 0.0455<br />~~

~~<br />~~

~~<h1 id="toc33"><a name="Septidiasemi"></a>Septidiasemi</h1>~~

~~Commas: 2401/2400, 2152828125/2147483648<br />~~

~~<br />~~

~~POTE generator: ~15/14 = 119.297<br />~~

~~<br />~~

~~Map: [&lt;1 25 -31 -8|, &lt;0 -26 37 12|]<br />~~

~~Wedgie: &lt;&lt;26 -37 -12 -119 -92 76||<br />~~

~~EDOs: 10, 151, 161, 171, 3581bcd, 3752bcd, 3923bcd, 4094bcd, 4265bcd, 4436bcd, 4607bcd<br />~~

~~Badness: 0.0441<br />~~

~~<br />~~

~~<h1 id="toc34"><a name="Maviloid"></a>Maviloid</h1>~~

~~Commas: 2401/2400, 1224440064/1220703125<br />~~

~~<br />~~

~~POTE generator: ~1296/875 = 678.810<br />~~

~~<br />~~

~~Map: [&lt;1 31 34 26|, &lt;0 -52 -56 -41|]<br />~~

~~Wedgie: &lt;&lt;52 56 41 -32 -81 -62||<br />~~

~~EDOs: 76, 99, 274, 373, 472, 571, 1043, 1614<br />~~

~~Badness: 0.0576<br />~~

~~<br />~~

~~<h1 id="toc35"><a name="Subneutral"></a>Subneutral</h1>~~

~~Commas: 2401/2400, 274877906944/274658203125<br />~~

~~<br />~~

~~POTE generator: ~57344/46875 = 348.301<br />~~

~~<br />~~

~~Map: [&lt;1 19 0 6}, &lt;0 -60 8 -11|]<br />~~

~~Wedgie: &lt;&lt;60 -8 11 -152 -151 48||<br />~~

~~EDOs: 31, 348, 379, 410, 441, 1354, 1795, 2236<br />~~

~~Badness: 0.0458<br />~~

~~<br />~~

~~<h1 id="toc36"><a name="Osiris"></a>Osiris</h1>~~

~~Commas: 2401/2400, 31381059609/31360000000<br />~~

~~<br />~~

~~POTE generator: ~2800/2187 = 428.066<br />~~

~~<br />~~

~~Map: [&lt;1 13 33 21|, &lt;0 -32 -86 -51|]<br />~~

~~Wedgie: &lt;&lt;32 86 51 62 -9 -123||<br />~~

~~EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d<br />~~

~~Badness: 0.0283<br />~~

~~<br />~~

~~<h1 id="toc37"><a name="Gorgik"></a>Gorgik</h1>~~

~~Commas: 2401/2400, 28672/28125<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 227.512<br />~~

~~<br />~~

~~Map: [&lt;1 5 1 3|, &lt;0 -18 7 -1|]<br />~~

~~Wedgie: &lt;&lt;18 -7 1 -53 -49 22||<br />~~

~~EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd<br />~~

~~Badness: 0.1584<br />~~

~~<br />~~

~~<h2 id="toc38"><a name="Gorgik-11-limit"></a>11-limit</h2>~~

~~Commas: 176/175, 2401/2400, 2560/2541<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 227.500<br />~~

~~<br />~~

~~Map: [&lt;1 5 1 3 1|, &lt;0 -18 7 -1 13|]<br />~~

~~EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde<br />~~

~~Badness: 0.059<br />~~

~~<br />~~

~~<h2 id="toc39"><a name="Gorgik-13-limit"></a>13-limit</h2>~~

~~Commas: 176/175, 196/195, 364/363, 512/507<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 227.493<br />~~

~~<br />~~

~~Map: [&lt;1 5 1 3 1 2|, &lt;0 -18 7 -1 13 9|]<br />~~

~~EDOs: 21, 37, 58, 153bcef, 211bcdef<br />~~

~~Badness: 0.0322<br />~~

~~<br />~~

~~<h1 id="toc40"><a name="Fibo"></a>Fibo</h1>~~

~~Commas: 2401/2400, 341796875/339738624<br />~~

~~<br />~~

~~POTE generator: ~125/96 = 454.310<br />~~

~~<br />~~

~~Map: [&lt;1 19 8 10|, &lt;0 -46 -15 -19|]<br />~~

~~Wedgie: &lt;&lt;46 15 19 -83 -99 2||<br />~~

~~EDOs: 37, 103, 140, 243, 383, 1009cd, 1392cd<br />~~

~~Badness: 0.1005<br />~~

~~<br />~~

~~<h2 id="toc41"><a name="Fibo-11-limit"></a>11-limit</h2>~~

~~Commas: 385/384, 1375/1372, 43923/43750<br />~~

~~<br />~~

~~POTE generator: ~100/77 = 454.318<br />~~

~~<br />~~

~~Map: [&lt;1 19 8 10 8|, &lt;0 -46 -15 -19 -12|]<br />~~

~~EDOs: 37, 103, 140, 243e<br />~~

~~Badness: 0.0565<br />~~

~~<br />~~

~~<h2 id="toc42"><a name="Fibo-13-limit"></a>13-limit</h2>~~

~~Commas: 385/384, 625/624, 847/845, 1375/1372<br />~~

~~<br />~~

~~POTE generator: ~13/10 = 454.316<br />~~

~~<br />~~

~~Map: [&lt;1 19 8 10 8 9|, &lt;0 -46 -15 -19 -12 -14|]<br />~~

~~EDOs: 37, 103, 140, 243e<br />~~

~~Badness: 0.0274<br />~~

~~<br />~~

~~<h1 id="toc43"><a name="Mintone"></a>Mintone</h1>~~

~~Commas: 2401/2400, 177147/175000<br />~~

~~<br />~~

~~POTE generator: ~10/9 = 186.343<br />~~

~~<br />~~

~~Map: [&lt;1 5 9 7|, &lt;0 -22 -43 -27|]<br />~~

~~EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc<br />~~

~~Badness: 0.12567<br />~~

~~<br />~~

~~<h2 id="toc44"><a name="Mintone-11-limit"></a>11-limit</h2>~~

~~Commas: 243/242, 441/440, 43923/43750<br />~~

~~<br />~~

~~POTE generator: ~10/9 = 186.345<br />~~

~~<br />~~

~~Map: [&lt;1 5 9 7 12|, &lt;0 -22 -43 -27 -55|]<br />~~

~~EDOs: 58, 103, 161, 425b, 586b, 747bc<br />~~

~~Badness: 0.0400<br />~~

~~<br />~~

~~<h2 id="toc45"><a name="Mintone-13-limit"></a>13-limit</h2>~~

~~Commas: 243/242, 351/350, 441/440, 847/845<br />~~

~~<br />~~

~~POTE generator: ~10/9 = 186.347<br />~~

~~<br />~~

~~Map: [&lt;1 5 9 7 12 11|, &lt;0 -22 -43 -27 -55 -47|]<br />~~

~~EDOs: 58, 103, 161<br />~~

~~Badness: 0.0218<br />~~

~~<br />~~

~~<h1 id="toc46"><a name="Catafourth"></a>Catafourth</h1>~~

~~Commas: 2400/2401, 78732/78125<br />~~

~~<br />~~

~~POTE generator: ~250/189 = 489.235<br />~~

~~<br />~~

~~Map: [&lt;1 13 17 13|, &lt;0 -28 -36 -25|]<br />~~

~~Wedgie: &lt;&lt;[28 36 25 -8 -39 -43||<br />~~

~~EDOs: 27, 76, 103, 130<br />~~

~~Badness: 0.0796<br />~~

~~<br />~~

~~<h2 id="toc47"><a name="Catafourth-11-limit"></a>11-limit</h2>~~

~~Commas: 243/242, 441/440, 78408/78125<br />~~

~~<br />~~

~~POTE generator: ~250/189 = 489.252<br />~~

~~<br />~~

~~Map: [&lt;1 13 17 13 32|, &lt;0 -28 -36 -25 -70|]<br />~~

~~EDOs: 103, 130, 233, 363, 493e, 856be<br />~~

~~Badness: 0.0368<br />~~

~~<br />~~

~~<h2 id="toc48"><a name="Catafourth-13-limit"></a>13-limit</h2>~~

~~Commas: 243/242, 351/350, 441/440, 10985/10976<br />~~

~~<br />~~

~~POTE generator: ~65/49 = 489.256<br />~~

~~<br />~~

~~Map: [&lt;1 13 17 13 32 9|, &lt;0 -28 -36 -25 -70 -13|]<br />~~

~~EDOs: 103, 130, 233, 363<br />~~

Badness: 0.0217~~</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+__FORCETOC__
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-01-27 13:47:30 UTC</tt>.<br>
-: The original revision id was <tt>538718916</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|flat]]
 Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.
 It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.
 =Hemififths=
-Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo]] and [[140edo]] providing good tunings, and [[239edo]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;58 temperament and has wedgie &lt;&lt;2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.
+Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo|99edo]] and [[140edo|140edo]] providing good tunings, and [[239edo|239edo]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;58 temperament and has wedgie &lt;&lt;2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.
-By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.
+By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo|99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.
 ==5-limit==
@@ Line 24: / Line 15: @@
 Map: [&lt;1 1 -5|, &lt;0 2 25|]
 EDOs: 41, 58, 99, 239, 338, 915b, 1253bc
 Badness: 0.3728
@@ Line 31: / Line 24: @@
 and 9-limit minimax
 [|1 0 0 0&gt;, |7/5, 0, 2/25, 0&gt;, |0 0 1 0&gt;, |8/5 0 13/25 0&gt;]
 Eigenvalues: 2, 5
@@ Line 37: / Line 32: @@
 Map: [&lt;1 1 -5 -1|, &lt;0 2 25 13|]
 EDOs: [[41edo|41]], [[58edo|58]], [[99edo|99]], [[239edo|239]], [[338edo|338]]
 Badness: 0.0222
 ==11-limit==
 Commas: 243/242, 441/440, 896/891
@@ Line 46: / Line 43: @@
 Map: [&lt;1 1 -5 -1 2|, &lt;0 2 25 13 5|]
 EDOs: 7, 17, 41, 58, 99
 Badness: 0.0235
 ==13-limit==
 Commas: 144/143, 196/195, 243/242, 364/363
@@ Line 55: / Line 54: @@
 Map: [&lt;1 1 -5 -1 2 4|, &lt;0 2 25 13 5 -1|]
 EDOs: 7, 17, 41, 58, 99
 Badness: 0.0191
@@ Line 64: / Line 65: @@
 Map: [&lt;2 0 -35 -15 -47|, &lt;0 2 25 13 34|]
 EDOs: 58, 140, 198, 734bc, 932bcd, 1130bcd
 Badness: 42.487
@@ Line 73: / Line 76: @@
 Map: [&lt;2 0 -35 -15 -47 -37|, &lt;0 2 25 13 34 28|]
 EDOs: 58, 140, 198, 536f, 734bcf, 932bcdf
 Badness: 0.0212
 =Tertiaseptal=
-Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
+Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo|171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
 Commas: 2401/2400, 65625/65536
@@ Line 84: / Line 89: @@
 Map: [&lt;1 3 2 3|, &lt;0 -22 5 -3|]
 EDOs: 15, 16, 31, 109, 140, 171
 Badness: 0.0130
 ==11-limit==
 Commas: 243/242, 441/440, 65625/65536
@@ Line 93: / Line 100: @@
 Map: [&lt;1 3 2 3 7|, &lt;0 -22 5 -3 -55|]
 EDOs: 15, 16, 31, 171, 202
 Badness: 0.0356
@@ Line 102: / Line 111: @@
 Map: [&lt;1 3 2 3 7 1|, &lt;0 -22 5 -3 -55 42|]
 EDOs: 31, 140e, 171, 373ef, 544ef
 Badness: 0.0369
@@ Line 111: / Line 122: @@
 Map: [&lt;1 3 2 3 5|, &lt;0 -22 5 -3 -24|]
 EDOs: 31, 109, 140, 171e, 311e
 Badness: 0.0302
@@ Line 120: / Line 133: @@
 Map: [&lt;1 3 2 3 6|, &lt;0 -44 10 -6 -79|]
 EDOs: 31, 280, 311, 342, 2021cde, 3731cde
 Badness: 0.0156
 =Harry=
 Commas: 2401/2400, 19683/19600
@@ Line 130: / Line 145: @@
 Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is &lt;&lt;12 34 20 30 ...||.
-Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with &lt;&lt;12 34 20 30 52 ...|| as the octave wedgie. [[130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
+Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with &lt;&lt;12 34 20 30 52 ...|| as the octave wedgie. [[130edo|130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
-[[POTE tuning|POTE generator]]: ~21/20 = 83.156
+[[POTE_tuning|POTE generator]]: ~21/20 = 83.156
 Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]
 Wedgie: &lt;&lt;12 34 20 26 -2 -49||
 EDOs: 14, 58, 72, 130, 202, 534, 938
 Badness: 0.0341
 ==11-limit==
 Commas: 243/242, 441/440, 4000/3993
-[[POTE tuning|POTE generator]]: ~21/20 = 83.167
+[[POTE_tuning|POTE generator]]: ~21/20 = 83.167
 Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]
 EDOs: 14, 58, 72, 130, 202
 Badness: 0.0159
 ==13-limit==
 Commas: 243/242, 351/350, 441/440, 676/675
-[[POTE tuning|POTE generator]]: ~21/20 = 83.116
+[[POTE_tuning|POTE generator]]: ~21/20 = 83.116
 Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]
 EDOs: 14, 58, 72, 130, 462
 Badness: 0.0130
 =Quasiorwell=
 In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.
@@ Line 167: / Line 189: @@
 Map: [&lt;1 31 0 9|, &lt;0 -38 3 -8|]
 EDOs: [[31edo|31]], [[177edo|177]], [[208edo|208]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]]
 Badness: 0.0358
 ==11-limit==
 Commas: 2401/2400, 3025/3024, 5632/5625
@@ Line 176: / Line 200: @@
 Map: [&lt;1 31 0 9 53|, &lt;0 -38 3 -8 -64|]
 EDOs: [[31edo|31]], [[208edo|208]], [[239edo|239]], [[270edo|270]]
 Badness: 0.0175
 ==13-limit==
 Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095
@@ Line 185: / Line 211: @@
 Map: [&lt;1 31 0 9 53 -59|, &lt;0 -38 3 -8 -64 81|]
 EDOs: [[31edo|31]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]]
 Badness: 0.0179
 =Decoid=
 Commas: 2401/2400, 67108864/66976875
@@ Line 194: / Line 222: @@
 Map: [&lt;10 0 47 36|, &lt;0 2 -3 -1|]
 Wedgie: &lt;&lt;20 -30 -10 -94 -72 61||
 EDOs: 10, 120, 130, 270
 Badness: 0.0339
 ==11-limit==
 Commas: 2401/2400, 5832/5825, 9801/9800
@@ Line 204: / Line 235: @@
 Map: [&lt;10 0 47 36 98|, &lt;0 2 -3 -1 -8|]
 EDOs: 130, 270, 670, 940, 1210
 Badness: 0.0187
 ==13-limit==
 Commas: 676/675, 1001/1000, 1716/1715, 4225/4224
@@ Line 213: / Line 246: @@
 Map: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]
 EDOs: 130, 270, 940, 1480
 Badness: 0.0135
@@ Line 222: / Line 257: @@
 Map: [&lt;1 3 12 8|, &lt;0 -6 -41 -22|]
 Weggie: &lt;&lt;6 41 22 51 18 -64||
 EDOs: 72, 161, 233, 305
 Badness: 0.0882
@@ Line 232: / Line 270: @@
 Map: [&lt;1 3 12 8 7|, &lt;0 -6 -41 -22 -15|]
 EDOs: 72, 161, 233, 305
 Badness: 0.0280
@@ Line 241: / Line 281: @@
 Map: [&lt;1 3 12 8 7 7|, &lt;0 -6 -41 -22 -15 -14|]
 EDOs: 72, 161f, 233f
 Badness: 0.0269
@@ Line 252: / Line 294: @@
 Map: [&lt;1 11 42 25|,  &lt;0 -14 -59 -33|]
 Wedgie: &lt;&lt;14 59 33 61 13 -89||
 EDOs: 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d
 Badness: 0.0167
@@ Line 262: / Line 307: @@
 Map: [&lt;1 27 24 20|, &lt;0 -34 -29 -23|]
 Wedgie: &lt;&lt;34 29 23 -33 -59 -28||
 EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c
 Badness: 0.0373
@@ Line 272: / Line 320: @@
 Map: [&lt;1 29 33 25|, &lt;0 -42 -47 -34|]
 Wedgie: &lt;&lt;42 47 34 -23 -64 -53||
 EDOs: 72, 167, 239, 311, 694, 1005c
 Badness: 0.0753
@@ Line 282: / Line 333: @@
 Map: [&lt;1 29 33 25 25|, &lt;0 -42 -47 -34 -33|]
 EDOs: 72, 167, 239, 311, 1316c
 Badness: 0.0229
@@ Line 291: / Line 344: @@
 Map: [&lt;1 29 33 25 25 99|, &lt;0 -42 -47 -34 -33 -146|]
 EDOs: 72, 311, 694, 1005c, 1699cd
 Badness: 0.0209
@@ Line 300: / Line 355: @@
 Map: [&lt;1 1 19 11|, &lt;0 2 -57 -28|]
 Wedgie: &lt;&lt;2 -57 -28 -95 -50 95||
 EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc
 Badness: 0.0419
@@ Line 310: / Line 368: @@
 Map: [&lt;1 1 19 11 -10|, &lt;0 2 -57 -28 46|]
 EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b
 Badness: 0.0195
@@ Line 319: / Line 379: @@
 Map: [&lt;1 1 19 11 -10 -20|, &lt;0 2 -57 -28 46 81|]
 EDOs: 41, 229, 270, 581, 851, 2283b, 3134b
 Badness: 0.0138
@@ Line 328: / Line 390: @@
 Map: [&lt;1 3 6 5|, &lt;0 -20 -52 -31|]
 Wedgie: &lt;&lt;20 52 31 36 -7 -74||
 EDOs: 99, 212, 311, 410, 1131, 1541b
 Badness: 0.0455
@@ Line 338: / Line 403: @@
 Map: [&lt;1 25 -31 -8|, &lt;0 -26 37 12|]
 Wedgie: &lt;&lt;26 -37 -12 -119 -92 76||
 EDOs: 10, 151, 161, 171, 3581bcd, 3752bcd, 3923bcd, 4094bcd, 4265bcd, 4436bcd, 4607bcd
 Badness: 0.0441
@@ Line 348: / Line 416: @@
 Map: [&lt;1 31 34 26|, &lt;0 -52 -56 -41|]
 Wedgie: &lt;&lt;52 56 41 -32 -81 -62||
 EDOs: 76, 99, 274, 373, 472, 571, 1043, 1614
 Badness: 0.0576
@@ Line 358: / Line 429: @@
 Map: [&lt;1 19 0 6}, &lt;0 -60 8 -11|]
 Wedgie: &lt;&lt;60 -8 11 -152 -151 48||
 EDOs: 31, 348, 379, 410, 441, 1354, 1795, 2236
 Badness: 0.0458
@@ Line 368: / Line 442: @@
 Map: [&lt;1 13 33 21|, &lt;0 -32 -86 -51|]
 Wedgie: &lt;&lt;32 86 51 62 -9 -123||
 EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d
 Badness: 0.0283
@@ Line 378: / Line 455: @@
 Map: [&lt;1 5 1 3|, &lt;0 -18 7 -1|]
 Wedgie: &lt;&lt;18 -7 1 -53 -49 22||
 EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd
 Badness: 0.1584
@@ Line 388: / Line 468: @@
 Map: [&lt;1 5 1 3 1|, &lt;0 -18 7 -1 13|]
 EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde
 Badness: 0.059
@@ Line 397: / Line 479: @@
 Map: [&lt;1 5 1 3 1 2|, &lt;0 -18 7 -1 13 9|]
 EDOs: 21, 37, 58, 153bcef, 211bcdef
 Badness: 0.0322
@@ Line 406: / Line 490: @@
 Map: [&lt;1 19 8 10|, &lt;0 -46 -15 -19|]
 Wedgie: &lt;&lt;46 15 19 -83 -99 2||
 EDOs: 37, 103, 140, 243, 383, 1009cd, 1392cd
 Badness: 0.1005
@@ Line 416: / Line 503: @@
 Map: [&lt;1 19 8 10 8|, &lt;0 -46 -15 -19 -12|]
 EDOs: 37, 103, 140, 243e
 Badness: 0.0565
@@ Line 425: / Line 514: @@
 Map: [&lt;1 19 8 10 8 9|, &lt;0 -46 -15 -19 -12 -14|]
 EDOs: 37, 103, 140, 243e
 Badness: 0.0274
@@ Line 434: / Line 525: @@
 Map: [&lt;1 5 9 7|, &lt;0 -22 -43 -27|]
 EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc
 Badness: 0.12567
@@ Line 443: / Line 536: @@
 Map: [&lt;1 5 9 7 12|, &lt;0 -22 -43 -27 -55|]
 EDOs: 58, 103, 161, 425b, 586b, 747bc
 Badness: 0.0400
@@ Line 452: / Line 547: @@
 Map: [&lt;1 5 9 7 12 11|, &lt;0 -22 -43 -27 -55 -47|]
 EDOs: 58, 103, 161
 Badness: 0.0218
@@ Line 461: / Line 558: @@
 Map: [&lt;1 13 17 13|, &lt;0 -28 -36 -25|]
 Wedgie: &lt;&lt;[28 36 25 -8 -39 -43||
 EDOs: 27, 76, 103, 130
 Badness: 0.0796
@@ Line 471: / Line 571: @@
 Map: [&lt;1 13 17 13 32|, &lt;0 -28 -36 -25 -70|]
 EDOs: 103, 130, 233, 363, 493e, 856be
 Badness: 0.0368
@@ Line 480: / Line 582: @@
 Map:  [&lt;1 13 17 13 32 9|, &lt;0 -28 -36 -25 -70 -13|]
 EDOs: 103, 130, 233, 363
-Badness: 0.0217</pre></div>
-<h4>Original HTML content:</h4>
+Badness: 0.0217
-<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;Breedsmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:98:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;a href="#Hemififths"&gt;Hemififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt; | &lt;a href="#Semihemi"&gt;Semihemi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt; | &lt;a href="#Tertiaseptal"&gt;Tertiaseptal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt; | &lt;a href="#Hemitert"&gt;Hemitert&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt; | &lt;a href="#Harry"&gt;Harry&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt; | &lt;a href="#Quasiorwell"&gt;Quasiorwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt; | &lt;a href="#Decoid"&gt;Decoid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt; | &lt;a href="#Neominor"&gt;Neominor&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt;&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt; | &lt;a href="#Emmthird"&gt;Emmthird&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt; | &lt;a href="#Quinmite"&gt;Quinmite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt; | &lt;a href="#Unthirds"&gt;Unthirds&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt;&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt;&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt; | &lt;a href="#Newt"&gt;Newt&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt;&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt;&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;!-- ws:start:WikiTextTocRule:131: --&gt; | &lt;a href="#Amicable"&gt;Amicable&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt; | &lt;a href="#Septidiasemi"&gt;Septidiasemi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt; | &lt;a href="#Maviloid"&gt;Maviloid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&gt; | &lt;a href="#Subneutral"&gt;Subneutral&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&gt; | &lt;a href="#Osiris"&gt;Osiris&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&gt; | &lt;a href="#Gorgik"&gt;Gorgik&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt;&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt;&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt; | &lt;a href="#Fibo"&gt;Fibo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt;&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt; | &lt;a href="#Mintone"&gt;Mintone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt; | &lt;a href="#Catafourth"&gt;Catafourth&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt;&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt;&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:148 --&gt;&lt;br /&gt;
-&lt;br /&gt;
-Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&amp;gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.&lt;br /&gt;
-&lt;br /&gt;
-It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Hemififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Hemififths&lt;/h1&gt;
- Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt; providing good tunings, and &lt;a class="wiki_link" href="/239edo"&gt;239edo&lt;/a&gt; an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;amp;58 temperament and has wedgie &amp;lt;&amp;lt;2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.&lt;br /&gt;
-&lt;br /&gt;
-By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Hemififths-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;5-limit&lt;/h2&gt;
-Comma: 858993459200/847288609443&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~655360/531441 = 351.476&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 -5|, &amp;lt;0 2 25|]&lt;br /&gt;
-EDOs: 41, 58, 99, 239, 338, 915b, 1253bc&lt;br /&gt;
-Badness: 0.3728&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="Hemififths-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit&lt;/h2&gt;
-Commas: 2401/2400, 5120/5103&lt;br /&gt;
-&lt;br /&gt;
-and 9-limit minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |7/5, 0, 2/25, 0&amp;gt;, |0 0 1 0&amp;gt;, |8/5 0 13/25 0&amp;gt;]&lt;br /&gt;
-Eigenvalues: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: (2 + sqrt(2))/2&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 -5 -1|, &amp;lt;0 2 25 13|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;, &lt;a class="wiki_link" href="/239edo"&gt;239&lt;/a&gt;, &lt;a class="wiki_link" href="/338edo"&gt;338&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0222&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="Hemififths-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit&lt;/h2&gt;
- Commas: 243/242, 441/440, 896/891&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 351.521&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 -5 -1 2|, &amp;lt;0 2 25 13 5|]&lt;br /&gt;
-EDOs: 7, 17, 41, 58, 99&lt;br /&gt;
-Badness: 0.0235&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="Hemififths-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
- Commas: 144/143, 196/195, 243/242, 364/363&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 351.573&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 -5 -1 2 4|, &amp;lt;0 2 25 13 5 -1|]&lt;br /&gt;
-EDOs: 7, 17, 41, 58, 99&lt;br /&gt;
-Badness: 0.0191&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Semihemi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Semihemi&lt;/h1&gt;
-Commas: 2401/2400, 3388/3375, 9801/9800&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~49/40 = 351.505&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -35 -15 -47|, &amp;lt;0 2 25 13 34|]&lt;br /&gt;
-EDOs: 58, 140, 198, 734bc, 932bcd, 1130bcd&lt;br /&gt;
-Badness: 42.487&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="Semihemi-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
-Commas: 352/351, 676/675, 847/845, 1716/1715&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~49/40 = 351.502&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -35 -15 -47 -37|, &amp;lt;0 2 25 13 34 28|]&lt;br /&gt;
-EDOs: 58, 140, 198, 536f, 734bcf, 932bcdf&lt;br /&gt;
-Badness: 0.0212&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Tertiaseptal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Tertiaseptal&lt;/h1&gt;
- Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 2401/2400, 65625/65536&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~256/245 = 77.191&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 2 3|, &amp;lt;0 -22 5 -3|]&lt;br /&gt;
-EDOs: 15, 16, 31, 109, 140, 171&lt;br /&gt;
-Badness: 0.0130&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="Tertiaseptal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h2&gt;
- Commas: 243/242, 441/440, 65625/65536&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~256/245 = 77.227&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 2 3 7|, &amp;lt;0 -22 5 -3 -55|]&lt;br /&gt;
-EDOs: 15, 16, 31, 171, 202&lt;br /&gt;
-Badness: 0.0356&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Tertiaseptal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;
-Commas: 243/242, 441/440, 625/624, 3584/3575&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~117/112 = 77.203&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 2 3 7 1|, &amp;lt;0 -22 5 -3 -55 42|]&lt;br /&gt;
-EDOs: 31, 140e, 171, 373ef, 544ef&lt;br /&gt;
-Badness: 0.0369&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Tertiaseptal-Tertia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Tertia&lt;/h2&gt;
-Commas: 385/384, 1331/1323, 1375/1372&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~22/21 = 77.173&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 2 3 5|, &amp;lt;0 -22 5 -3 -24|]&lt;br /&gt;
-EDOs: 31, 109, 140, 171e, 311e&lt;br /&gt;
-Badness: 0.0302&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="Hemitert"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Hemitert&lt;/h1&gt;
-Commas: 2401/2400 3025/3024 65625/65536&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~45/44 = 38.596&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 2 3 6|, &amp;lt;0 -44 10 -6 -79|]&lt;br /&gt;
-EDOs: 31, 280, 311, 342, 2021cde, 3731cde&lt;br /&gt;
-Badness: 0.0156&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="Harry"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Harry&lt;/h1&gt;
- Commas: 2401/2400, 19683/19600&lt;br /&gt;
-&lt;br /&gt;
-Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&amp;amp;72 temperament, with wedgie &amp;lt;&amp;lt;12 34 20 26 -2 -49||. The period is half an octave, and the generator 21/20, with generator tunings of 9\130 or 14\202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices.&lt;br /&gt;
-&lt;br /&gt;
-Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is &amp;lt;&amp;lt;12 34 20 30 ...||.&lt;br /&gt;
-&lt;br /&gt;
-Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with &amp;lt;&amp;lt;12 34 20 30 52 ...|| as the octave wedgie. &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt; is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~21/20 = 83.156&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 4 7 7|, &amp;lt;0 -6 -17 -10|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;12 34 20 26 -2 -49||&lt;br /&gt;
-EDOs: 14, 58, 72, 130, 202, 534, 938&lt;br /&gt;
-Badness: 0.0341&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Harry-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
- Commas: 243/242, 441/440, 4000/3993&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~21/20 = 83.167&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 4 7 7 9|, &amp;lt;0 -6 -17 -10 -15|]&lt;br /&gt;
-EDOs: 14, 58, 72, 130, 202&lt;br /&gt;
-Badness: 0.0159&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="Harry-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
- Commas: 243/242, 351/350, 441/440, 676/675&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~21/20 = 83.116&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 4 7 7 9 11|, &amp;lt;0 -6 -17 -10 -15 -26|]&lt;br /&gt;
-EDOs: 14, 58, 72, 130, 462&lt;br /&gt;
-Badness: 0.0130&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Quasiorwell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Quasiorwell&lt;/h1&gt;
- In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&amp;gt;. It has a wedgie &amp;lt;&amp;lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.&lt;br /&gt;
-&lt;br /&gt;
-Adding 3025/3024 extends to the 11-limit and gives &amp;lt;&amp;lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 2401/2400, 29360128/29296875&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~1024/875 = 271.107&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 31 0 9|, &amp;lt;0 -38 3 -8|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/177edo"&gt;177&lt;/a&gt;, &lt;a class="wiki_link" href="/208edo"&gt;208&lt;/a&gt;, &lt;a class="wiki_link" href="/239edo"&gt;239&lt;/a&gt;, &lt;a class="wiki_link" href="/270edo"&gt;270&lt;/a&gt;, &lt;a class="wiki_link" href="/571edo"&gt;571&lt;/a&gt;, &lt;a class="wiki_link" href="/841edo"&gt;841&lt;/a&gt;, &lt;a class="wiki_link" href="/1111edo"&gt;1111&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0358&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Quasiorwell-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
- Commas: 2401/2400, 3025/3024, 5632/5625&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~90/77 = 271.111&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 31 0 9 53|, &amp;lt;0 -38 3 -8 -64|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/208edo"&gt;208&lt;/a&gt;, &lt;a class="wiki_link" href="/239edo"&gt;239&lt;/a&gt;, &lt;a class="wiki_link" href="/270edo"&gt;270&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0175&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Quasiorwell-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
- Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~90/77 = 271.107&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 31 0 9 53 -59|, &amp;lt;0 -38 3 -8 -64 81|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/239edo"&gt;239&lt;/a&gt;, &lt;a class="wiki_link" href="/270edo"&gt;270&lt;/a&gt;, &lt;a class="wiki_link" href="/571edo"&gt;571&lt;/a&gt;, &lt;a class="wiki_link" href="/841edo"&gt;841&lt;/a&gt;, &lt;a class="wiki_link" href="/1111edo"&gt;1111&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0179&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Decoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Decoid&lt;/h1&gt;
- Commas: 2401/2400, 67108864/66976875&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 231.099&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;10 0 47 36|, &amp;lt;0 2 -3 -1|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;20 -30 -10 -94 -72 61||&lt;br /&gt;
-EDOs: 10, 120, 130, 270&lt;br /&gt;
-Badness: 0.0339&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="Decoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
- Commas: 2401/2400, 5832/5825, 9801/9800&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 231.070&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;10 0 47 36 98|, &amp;lt;0 2 -3 -1 -8|]&lt;br /&gt;
-EDOs: 130, 270, 670, 940, 1210&lt;br /&gt;
-Badness: 0.0187&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Decoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
- Commas: 676/675, 1001/1000, 1716/1715, 4225/4224&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 231.083&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;10 0 47 36 98 37|, &amp;lt;0 2 -3 -1 -8 0|]&lt;br /&gt;
-EDOs: 130, 270, 940, 1480&lt;br /&gt;
-Badness: 0.0135&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Neominor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Neominor&lt;/h1&gt;
-Commas: 2401/2400, 177147/175616&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~189/160 = 283.280&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 12 8|, &amp;lt;0 -6 -41 -22|]&lt;br /&gt;
-Weggie: &amp;lt;&amp;lt;6 41 22 51 18 -64||&lt;br /&gt;
-EDOs: 72, 161, 233, 305&lt;br /&gt;
-Badness: 0.0882&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="Neominor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;11-limit&lt;/h2&gt;
-Commas: 243/242, 441/440, 35937/35840&lt;br /&gt;
-&lt;br /&gt;
-POTE: ~33/28 = 283.276&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 12 8 7|, &amp;lt;0 -6 -41 -22 -15|]&lt;br /&gt;
-EDOs: 72, 161, 233, 305&lt;br /&gt;
-Badness: 0.0280&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="Neominor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
-Commas: 169/168, 243/242, 364/363, 441/440&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~13/11 = 283.294&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 12 8 7 7|, &amp;lt;0 -6 -41 -22 -15 -14|]&lt;br /&gt;
-EDOs: 72, 161f, 233f&lt;br /&gt;
-Badness: 0.0269&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="Emmthird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Emmthird&lt;/h1&gt;
-The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 2401/2400, 14348907/14336000&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~2744/2187 = 392.988&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 11 42 25|,  &amp;lt;0 -14 -59 -33|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;14 59 33 61 13 -89||&lt;br /&gt;
-EDOs: 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d&lt;br /&gt;
-Badness: 0.0167&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Quinmite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Quinmite&lt;/h1&gt;
-Commas: 2401/2400, 1959552/1953125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~25/21 = 302.997&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 27 24 20|, &amp;lt;0 -34 -29 -23|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;34 29 23 -33 -59 -28||&lt;br /&gt;
-EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c&lt;br /&gt;
-Badness: 0.0373&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Unthirds"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Unthirds&lt;/h1&gt;
-Commas: 2401/2400, 68359375/68024448&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3969/3125 = 416.717&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 29 33 25|, &amp;lt;0 -42 -47 -34|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;42 47 34 -23 -64 -53||&lt;br /&gt;
-EDOs: 72, 167, 239, 311, 694, 1005c&lt;br /&gt;
-Badness: 0.0753&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="Unthirds-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
-Commas: 2401/2400, 3025/3024, 4000/3993&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~14/11 = 416.718&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 29 33 25 25|, &amp;lt;0 -42 -47 -34 -33|]&lt;br /&gt;
-EDOs: 72, 167, 239, 311, 1316c&lt;br /&gt;
-Badness: 0.0229&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="Unthirds-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
-Commas: 625/624, 1575/1573, 2080/2079, 2401/2400&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~14/11 = 416.716&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 29 33 25 25 99|, &amp;lt;0 -42 -47 -34 -33 -146|]&lt;br /&gt;
-EDOs: 72, 311, 694, 1005c, 1699cd&lt;br /&gt;
-Badness: 0.0209&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="Newt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Newt&lt;/h1&gt;
-Commas: 2401/2400, 33554432/33480783&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~49/40 = 351.113&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 19 11|, &amp;lt;0 2 -57 -28|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;2 -57 -28 -95 -50 95||&lt;br /&gt;
-EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc&lt;br /&gt;
-Badness: 0.0419&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="Newt-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;11-limit&lt;/h2&gt;
-Commas: 2401/2400, 3025/3024, 19712/19683&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~49/40 = 351.115&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 19 11 -10|, &amp;lt;0 2 -57 -28 46|]&lt;br /&gt;
-EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b&lt;br /&gt;
-Badness: 0.0195&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="Newt-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;13-limit&lt;/h2&gt;
-Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095&lt;br /&gt;
-&lt;br /&gt;
-POTE genertaor: ~49/40 = 351.117&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 19 11 -10 -20|, &amp;lt;0 2 -57 -28 46 81|]&lt;br /&gt;
-EDOs: 41, 229, 270, 581, 851, 2283b, 3134b&lt;br /&gt;
-Badness: 0.0138&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="Amicable"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Amicable&lt;/h1&gt;
-Commas: 2401/2400, 1600000/1594323&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~21/20 = 84.880&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 6 5|, &amp;lt;0 -20 -52 -31|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;20 52 31 36 -7 -74||&lt;br /&gt;
-EDOs: 99, 212, 311, 410, 1131, 1541b&lt;br /&gt;
-Badness: 0.0455&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc33"&gt;&lt;a name="Septidiasemi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Septidiasemi&lt;/h1&gt;
-Commas: 2401/2400, 2152828125/2147483648&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~15/14 = 119.297&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 25 -31 -8|, &amp;lt;0 -26 37 12|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;26 -37 -12 -119 -92 76||&lt;br /&gt;
-EDOs: 10, 151, 161, 171, 3581bcd, 3752bcd, 3923bcd, 4094bcd, 4265bcd, 4436bcd, 4607bcd&lt;br /&gt;
-Badness: 0.0441&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="Maviloid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Maviloid&lt;/h1&gt;
-Commas: 2401/2400, 1224440064/1220703125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~1296/875 = 678.810&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 31 34 26|, &amp;lt;0 -52 -56 -41|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;52 56 41 -32 -81 -62||&lt;br /&gt;
-EDOs: 76, 99, 274, 373, 472, 571, 1043, 1614&lt;br /&gt;
-Badness: 0.0576&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Subneutral"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Subneutral&lt;/h1&gt;
-Commas: 2401/2400, 274877906944/274658203125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~57344/46875 = 348.301&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 19 0 6}, &amp;lt;0 -60 8 -11|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;60 -8 11 -152 -151 48||&lt;br /&gt;
-EDOs: 31, 348, 379, 410, 441, 1354, 1795, 2236&lt;br /&gt;
-Badness: 0.0458&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc36"&gt;&lt;a name="Osiris"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Osiris&lt;/h1&gt;
-Commas: 2401/2400, 31381059609/31360000000&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~2800/2187 = 428.066&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 13 33 21|, &amp;lt;0 -32 -86 -51|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;32 86 51 62 -9 -123||&lt;br /&gt;
-EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d&lt;br /&gt;
-Badness: 0.0283&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="Gorgik"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;Gorgik&lt;/h1&gt;
-Commas: 2401/2400, 28672/28125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 227.512&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 1 3|, &amp;lt;0 -18 7 -1|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;18 -7 1 -53 -49 22||&lt;br /&gt;
-EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd&lt;br /&gt;
-Badness: 0.1584&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Gorgik-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;11-limit&lt;/h2&gt;
-Commas: 176/175, 2401/2400, 2560/2541&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 227.500&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 1 3 1|, &amp;lt;0 -18 7 -1 13|]&lt;br /&gt;
-EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde&lt;br /&gt;
-Badness: 0.059&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Gorgik-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13-limit&lt;/h2&gt;
-Commas: 176/175, 196/195, 364/363, 512/507&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 227.493&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 1 3 1 2|, &amp;lt;0 -18 7 -1 13 9|]&lt;br /&gt;
-EDOs: 21, 37, 58, 153bcef, 211bcdef&lt;br /&gt;
-Badness: 0.0322&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc40"&gt;&lt;a name="Fibo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Fibo&lt;/h1&gt;
-Commas: 2401/2400, 341796875/339738624&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~125/96 = 454.310&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 19 8 10|, &amp;lt;0 -46 -15 -19|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;46 15 19 -83 -99 2||&lt;br /&gt;
-EDOs: 37, 103, 140, 243, 383, 1009cd, 1392cd&lt;br /&gt;
-Badness: 0.1005&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Fibo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;11-limit&lt;/h2&gt;
-Commas: 385/384, 1375/1372, 43923/43750&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~100/77 = 454.318&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 19 8 10 8|, &amp;lt;0 -46 -15 -19 -12|]&lt;br /&gt;
-EDOs: 37, 103, 140, 243e&lt;br /&gt;
-Badness: 0.0565&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="Fibo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;13-limit&lt;/h2&gt;
-Commas: 385/384, 625/624, 847/845, 1375/1372&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~13/10 = 454.316&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 19 8 10 8 9|, &amp;lt;0 -46 -15 -19 -12 -14|]&lt;br /&gt;
-EDOs: 37, 103, 140, 243e&lt;br /&gt;
-Badness: 0.0274&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Mintone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Mintone&lt;/h1&gt;
-Commas: 2401/2400, 177147/175000&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 186.343&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 9 7|, &amp;lt;0 -22 -43 -27|]&lt;br /&gt;
-EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc&lt;br /&gt;
-Badness: 0.12567&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Mintone-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;11-limit&lt;/h2&gt;
-Commas: 243/242, 441/440, 43923/43750&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 186.345&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 9 7 12|, &amp;lt;0 -22 -43 -27 -55|]&lt;br /&gt;
-EDOs: 58, 103, 161, 425b, 586b, 747bc&lt;br /&gt;
-Badness: 0.0400&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Mintone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;13-limit&lt;/h2&gt;
-Commas: 243/242, 351/350, 441/440, 847/845&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 186.347&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 9 7 12 11|, &amp;lt;0 -22 -43 -27 -55 -47|]&lt;br /&gt;
-EDOs: 58, 103, 161&lt;br /&gt;
-Badness: 0.0218&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc46"&gt;&lt;a name="Catafourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;Catafourth&lt;/h1&gt;
-Commas: 2400/2401, 78732/78125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~250/189 = 489.235&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 13 17 13|, &amp;lt;0 -28 -36 -25|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;[28 36 25 -8 -39 -43||&lt;br /&gt;
-EDOs: 27, 76, 103, 130&lt;br /&gt;
-Badness: 0.0796&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Catafourth-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;11-limit&lt;/h2&gt;
-Commas: 243/242, 441/440, 78408/78125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~250/189 = 489.252&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 13 17 13 32|, &amp;lt;0 -28 -36 -25 -70|]&lt;br /&gt;
-EDOs: 103, 130, 233, 363, 493e, 856be&lt;br /&gt;
-Badness: 0.0368&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Catafourth-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;13-limit&lt;/h2&gt;
-Commas: 243/242, 351/350, 441/440, 10985/10976&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~65/49 = 489.256&lt;br /&gt;
-&lt;br /&gt;
-Map:  [&amp;lt;1 13 17 13 32 9|, &amp;lt;0 -28 -36 -25 -70 -13|]&lt;br /&gt;
-EDOs: 103, 130, 233, 363&lt;br /&gt;
-Badness: 0.0217&lt;/body&gt;&lt;/html&gt;</pre></div>