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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-02-03 05:19:21 UTC</tt>.<br>
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| : The original revision id was <tt>539465466</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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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">=<span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span>=
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| 77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Starling temperaments#Valentine%20temperament|valentine]], the 31&46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto.
| | == Theory == |
| | With [[3/1|harmonic 3]] less than a cent flat, [[5/1|harmonic 5]] a bit over three cents sharp and [[7/1|7]] less flat than that, 77edo represents an excellent tuning choice for both [[valentine]] (hence also [[Carlos Alpha]]), the {{nowrap|31 & 46}} temperament, and [[starling]], the [[rank-3 temperament]] [[tempering out]] [[126/125]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extension [[valentino]], as well as 11-limit starling and [[oxpecker]] temperaments. For desirers of purer/more convincing harmonies of 19, it's also a great choice for [[nestoria]] (the extension of schismic to prime 19) so that ~16:19:24 can be heard to concord in isolation. It also gives the optimal patent val for [[grackle]] and various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 (which gives valentine); it is a very good choice for full-subgroup [[unicorn]]. These are 7-limit [[unicorn family #Alicorn|alicorn]] and 11- and 13-limit [[unicorn family #Camahueto|camahueto]]. |
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| 77et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]]. | | 77et tempers out the [[schisma]] (32805/32768) in the [[5-limit]]; [[126/125]], [[1029/1024]], and [[6144/6125]] in the 7-limit; [[121/120]], [[176/175]], [[385/384]], and [[441/440]] in the 11-limit; and [[196/195]], [[351/350]], [[352/351]], [[676/675]] and [[729/728]] in the 13-limit. |
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| =Intervals=
| | The [[17/1|17]] and [[19/1|19]] are tuned fairly well, making it [[consistent]] to the no-11 [[21-odd-limit]]. The equal temperament tempers out [[256/255]] in the 17-limit; and [[171/170]], [[361/360]], [[513/512]], and [[1216/1215]] in the 19-limit. |
| ||~ Degree ||~ Cents
| |
| Value ||~ Approximate Ratios
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| in the 13-limit ||
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| ||> 0 ||> 0.000 ||= 1/1 ||
| |
| ||> 1 ||> 15.584 ||= 81/80, 99/98 ||
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| ||> 2 ||> 31.169 ||= 64/63, 49/48 ||
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| ||> 3 ||> 46.753 ||= 33/32, 36/35 ||
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| ||> 4 ||> 62.338 ||= 28/27, 26/25 ||
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| ||> 5 ||> 77.922 ||= 21/20, 25/24 ||
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| ||> 6 ||> 93.506 ||= ||
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| ||> 7 ||> 109.091 ||= 16/15 ||
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| ||> 8 ||> 124.675 ||= 15/14 ||
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| ||> 9 ||> 140.260 ||= 13/12 ||
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| ||> 10 ||> 155.844 ||= 12/11, 11/10 ||
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| ||> 11 ||> 171.429 ||= ||
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| ||> 12 ||> 187.013 ||= 10/9 ||
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| ||> 13 ||> 202.597 ||= 9/8 ||
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| ||> 14 ||> 218.182 ||= ||
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| ||> 15 ||> 233.766 ||= 8/7 ||
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| ||> 16 ||> 249.351 ||= 15/13 ||
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| ||> 17 ||> 264.935 ||= 7/6 ||
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| ||> 18 ||> 280.519 ||= 33/28 ||
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| ||> 19 ||> 296.104 ||= 32/27, 13/11 ||
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| ||> 20 ||> 311.688 ||= 6/5 ||
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| ||> 21 ||> 327.273 ||= ||
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| ||> 22 ||> 342.857 ||= 11/9, 39/32 ||
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| ||> 23 ||> 358.442 ||= 16/13 ||
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| ||> 24 ||> 374.026 ||= 56/45, 26/21 ||
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| ||> 25 ||> 389.610 ||= 5/4 ||
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| ||> 26 ||> 405.195 ||= 33/26, 81/64 ||
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| ||> 27 ||> 420.779 ||= 14/11, 32/25 ||
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| ||> 28 ||> 436.364 ||= 9/7 ||
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| ||> 29 ||> 451.948 ||= 13/10 ||
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| ||> 30 ||> 467.532 ||= 21/16 ||
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| ||> 31 ||> 483.117 ||= ||
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| ||> 32 ||> 498.701 ||= 4/3 ||
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| ||> 33 ||> 514.286 ||= 27/20 ||
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| ||> 34 ||> 529.870 ||= 49/36 ||
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| ||> 35 ||> 545.455 ||= 11/8, 15/11 ||
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| ||> 36 ||> 561.039 ||= 18/13 ||
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| ||> 37 ||> 576.623 ||= 7/5 ||
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| ||> 38 ||> 592.208 ||= 45/32 ||
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| ||> 39 ||> 607.792 ||= 64/45 ||
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| ||> 40 ||> 623.377 ||= 10/7 ||
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| ||> 41 ||> 638.961 ||= 13/9 ||
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| ||> 42 ||> 654.545 ||= 16/11, 22/15 ||
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| ||> 43 ||> 670.130 ||= 72/49 ||
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| ||> 44 ||> 685.714 ||= 40/27 ||
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| ||> 45 ||> 701.299 ||= 3/2 ||
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| ||> 46 ||> 716.883 ||= ||
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| ||> 47 ||> 732.468 ||= 32/21 ||
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| ||> 48 ||> 748.052 ||= 20/13 ||
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| ||> 49 ||> 763.636 ||= 14/9 ||
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| ||> 50 ||> 779.221 ||= 11/7, 25/16 ||
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| ||> 51 ||> 794.805 ||= 52/33, 128/81 ||
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| ||> 52 ||> 810.390 ||= 8/5 ||
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| ||> 53 ||> 825.974 ||= 45/28, 21/13 ||
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| ||> 54 ||> 841.558 ||= 13/8 ||
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| ||> 55 ||> 857.143 ||= 18/11, 64/39 ||
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| ||> 56 ||> 872.727 ||= ||
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| ||> 57 ||> 888.312 ||= 5/3 ||
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| ||> 58 ||> 903.896 ||= 27/16, 22/13 ||
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| ||> 59 ||> 919.481 ||= 56/33 ||
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| ||> 60 ||> 935.065 ||= 12/7 ||
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| ||> 61 ||> 950.649 ||= 26/15 ||
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| ||> 62 ||> 966.234 ||= 7/4 ||
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| ||> 63 ||> 981.818 ||= ||
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| ||> 64 ||> 997.403 ||= 16/9 ||
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| ||> 65 ||> 1012.987 ||= 9/5 ||
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| ||> 66 ||> 1028.571 ||= ||
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| ||> 67 ||> 1044.156 ||= 11/6, 20/11 ||
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| ||> 68 ||> 1059.740 ||= 24/13 ||
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| ||> 69 ||> 1075.325 ||= 28/15 ||
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| ||> 70 ||> 1090.909 ||= 15/8 ||
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| ||> 71 ||> 1106.494 ||= ||
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| ||> 72 ||> 1122.078 ||= 40/21, 48/25 ||
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| ||> 73 ||> 1137.662 ||= 27/14, 25/13 ||
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| ||> 74 ||> 1153.247 ||= 64/33, 35/18 ||
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| ||> 75 ||> 1168.831 ||= 63/32, 96/49 ||
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| ||> 76 ||> 1184.416 ||= 160/81, 196/99 ||
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| ||> 77 ||> 1200.000 ||= 2/1 ||
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| =Linear temperaments=
| | It also does surprisingly well (for its size) in a large range of very high odd-limits (41 to 125 range). |
| ||~ Periods
| |
| per Octave ||~ Generator ||~ Temperaments ||
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| ||> 1 ||> 1\77 || ||
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| ||> 1 ||> 2\77 || ||
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| ||> 1 ||> 3\77 || ||
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| ||> 1 ||> 4\77 || [[Unicorn]]/alicorn/camahueto/qilin ||
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| ||> 1 ||> 5\77 || [[Valentine]] ||
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| ||> 1 ||> 6\77 || ||
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| ||> 1 ||> 8\77 || ||
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| ||> 1 ||> 9\77 || [[Tsaharuk]] ||
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| ||> 1 ||> 10\77 || ||
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| ||> 1 ||> 12\77 || ||
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| ||> 1 ||> 13\77 || ||
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| ||> 1 ||> 15\77 || [[Guiron]] ||
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| ||> 1 ||> 16\77 || [[Hemischis]] ||
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| ||> 1 ||> 17\77 || ||
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| ||> 1 ||> 18\77 || ||
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| ||> 1 ||> 19\77 || ||
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| ||> 1 ||> 20\77 || ||
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| ||> 1 ||> 23\77 || Restles ([[http://x31eq.com/cgi-bin/rt.cgi?ets=87+%26+77&limit=13|77&87]]) ||
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| ||> 1 ||> 24\77 || ||
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| ||> 1 ||> 25\77 || ||
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| ||> 1 ||> 26\77 || ||
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| ||> 1 ||> 27\77 || ||
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| ||> 1 ||> 29\77 || ||
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| ||> 1 ||> 30\77 || ||
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| ||> 1 ||> 31\77 || [[Hemiseven]] ||
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| ||> 1 ||> 32\77 || [[Hendecatonic]], [[Grackle|grackle]] ||
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| ||> 1 ||> 34\77 || Mabila ([[http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&limit=5|34&43]]) ||
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| ||> 1 ||> 36\77 || ||
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| ||> 1 ||> 37\77 || ||
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| ||> 1 ||> 38\77 || ||
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| ||> 7 ||> 1\77 || "[[TemperamentOrphanage|Absurdity]]" ([[http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5|7&84]]) ||
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| ||> 7 ||> 2\77 || ||
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| ||> 7 ||> 3\77 || ||
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| ||> 7 ||> 4\77 || ||
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| ||> 7 ||> 5\77 || ||
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| ||> 11 ||> 1\77 || ||
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| ||> 11 ||> 2\77 || ||
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| ||> 11 ||> 3\77 || ||
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| =Music= | | === Prime harmonics === |
| | {{Harmonics in equal|77|columns=9}} |
| | {{Harmonics in equal|77|columns=10|start=10|collapsed=true|title=Approximation of prime harmonics in 77edo (continued)}} |
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| //[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3|Star 1-GrimaldiA+Bmod]]// by [[Joel Grant Taylor]]
| | === Subsets and supersets === |
| //[[http://micro.soonlabel.com/star/20120830-77et-star.mp3|77et Star]]// by [[Chris Vaisvil]]
| | Since 77 factors into primes as {{nowrap|7 × 11}}, 77edo contains [[7edo]] and [[11edo]] as subset edos. |
| //[[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3|A Seed Planted]]// A Seed Planted by Jake Freivald, in an [[http://soonlabel.com/xenharmonic/archives/1391|organ version]] of Claudi Meneghin.</pre></div>
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| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>77edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x77 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span></h1>
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| <br />
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| 77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 <a class="wiki_link" href="/cent">cent</a>s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and <a class="wiki_link" href="/7_4">7/4s</a> less flat than that, it represents an excellent tuning choice for both <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament">valentine</a>, the 31&amp;46 temperament, and <a class="wiki_link" href="/Starling%20temperaments">starling</a>, the 126/125 <a class="wiki_link" href="/planar%20temperament">planar temperament</a>, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as <a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit">11-limit starling</a> and <a class="wiki_link" href="/Starling%20family#Oxpecker">oxpecker</a> temperaments. It also gives the optimal patent val for various members of the <a class="wiki_link" href="/unicorn%20family">unicorn family</a>, with a <a class="wiki_link" href="/generator">generator</a> of 4\77 instead of the 5\77 which gives valentine. These are 7-limit <a class="wiki_link" href="/Unicorn%20family#Alicorn">alicorn</a> and 11- and 13-limit camahueto.<br />
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| <br />
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| 77et tempers out 32805/32768 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 126/125, 1029/1024 and 6144/6125 in the <a class="wiki_link" href="/7-limit">7-limit</a>, 121/120, 176/175, 385/384 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the <a class="wiki_link" href="/13-limit">13-limit</a>.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1>
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| <table class="wiki_table">
| | == Intervals == |
| <tr>
| | {| class="wikitable center-all right-2 left-3" |
| <th>Degree<br />
| | |- |
| </th>
| | ! # |
| <th>Cents<br />
| | ! Cents |
| Value<br />
| | ! Approximate ratios* |
| </th>
| | ! [[Ups and downs notation]] |
| <th>Approximate Ratios<br />
| | |- |
| in the 13-limit<br />
| | | 0 |
| </th>
| | | 0.0 |
| </tr>
| | | 1/1 |
| <tr>
| | | {{UDnote|step=0}} |
| <td style="text-align: right;">0<br />
| | |- |
| </td>
| | | 1 |
| <td style="text-align: right;">0.000<br />
| | | 15.6 |
| </td>
| | | 81/80, 91/90, 99/98, 105/104 |
| <td style="text-align: center;">1/1<br />
| | | {{UDnote|step=1}} |
| </td>
| | |- |
| </tr>
| | | 2 |
| <tr>
| | | 31.2 |
| <td style="text-align: right;">1<br />
| | | 49/48, 55/54, 64/63, 65/64, ''100/99'' |
| </td>
| | | {{UDnote|step=2}} |
| <td style="text-align: right;">15.584<br />
| | |- |
| </td>
| | | 3 |
| <td style="text-align: center;">81/80, 99/98<br />
| | | 46.8 |
| </td>
| | | 33/32, 36/35, 40/39, ''45/44'', ''50/49'' |
| </tr>
| | | {{UDnote|step=3}} |
| <tr>
| | |- |
| <td style="text-align: right;">2<br />
| | | 4 |
| </td>
| | | 62.3 |
| <td style="text-align: right;">31.169<br />
| | | 26/25, 27/26, 28/27 |
| </td>
| | | {{UDnote|step=4}} |
| <td style="text-align: center;">64/63, 49/48<br />
| | |- |
| </td>
| | | 5 |
| </tr>
| | | 77.9 |
| <tr>
| | | 21/20, 22/21, 25/24 |
| <td style="text-align: right;">3<br />
| | | {{UDnote|step=5}} |
| </td>
| | |- |
| <td style="text-align: right;">46.753<br />
| | | 6 |
| </td>
| | | 93.5 |
| <td style="text-align: center;">33/32, 36/35<br />
| | | 18/17, 19/18, 20/19 |
| </td>
| | | {{UDnote|step=6}} |
| </tr>
| | |- |
| <tr>
| | | 7 |
| <td style="text-align: right;">4<br />
| | | 109.1 |
| </td>
| | | 16/15, 17/16 |
| <td style="text-align: right;">62.338<br />
| | | {{UDnote|step=7}} |
| </td>
| | |- |
| <td style="text-align: center;">28/27, 26/25<br />
| | | 8 |
| </td>
| | | 124.7 |
| </tr>
| | | 14/13, 15/14 |
| <tr>
| | | {{UDnote|step=8}} |
| <td style="text-align: right;">5<br />
| | |- |
| </td>
| | | 9 |
| <td style="text-align: right;">77.922<br />
| | | 140.3 |
| </td>
| | | 13/12 |
| <td style="text-align: center;">21/20, 25/24<br />
| | | {{UDnote|step=9}} |
| </td>
| | |- |
| </tr>
| | | 10 |
| <tr>
| | | 155.8 |
| <td style="text-align: right;">6<br />
| | | ''11/10'', 12/11 |
| </td>
| | | {{UDnote|step=10}} |
| <td style="text-align: right;">93.506<br />
| | |- |
| </td>
| | | 11 |
| <td style="text-align: center;"><br />
| | | 171.4 |
| </td>
| | | 21/19 |
| </tr>
| | | {{UDnote|step=11}} |
| <tr>
| | |- |
| <td style="text-align: right;">7<br />
| | | 12 |
| </td>
| | | 187.0 |
| <td style="text-align: right;">109.091<br />
| | | 10/9 |
| </td>
| | | {{UDnote|step=12}} |
| <td style="text-align: center;">16/15<br />
| | |- |
| </td>
| | | 13 |
| </tr>
| | | 202.6 |
| <tr>
| | | 9/8 |
| <td style="text-align: right;">8<br />
| | | {{UDnote|step=13}} |
| </td>
| | |- |
| <td style="text-align: right;">124.675<br />
| | | 14 |
| </td>
| | | 218.2 |
| <td style="text-align: center;">15/14<br />
| | | 17/15 |
| </td>
| | | {{UDnote|step=14}} |
| </tr>
| | |- |
| <tr>
| | | 15 |
| <td style="text-align: right;">9<br />
| | | 233.8 |
| </td>
| | | 8/7 |
| <td style="text-align: right;">140.260<br />
| | | {{UDnote|step=15}} |
| </td>
| | |- |
| <td style="text-align: center;">13/12<br />
| | | 16 |
| </td>
| | | 249.4 |
| </tr>
| | | 15/13, 22/19 |
| <tr>
| | | {{UDnote|step=16}} |
| <td style="text-align: right;">10<br />
| | |- |
| </td>
| | | 17 |
| <td style="text-align: right;">155.844<br />
| | | 264.9 |
| </td>
| | | 7/6 |
| <td style="text-align: center;">12/11, 11/10<br />
| | | {{UDnote|step=17}} |
| </td>
| | |- |
| </tr>
| | | 18 |
| <tr>
| | | 280.5 |
| <td style="text-align: right;">11<br />
| | | 20/17 |
| </td>
| | | {{UDnote|step=18}} |
| <td style="text-align: right;">171.429<br />
| | |- |
| </td>
| | | 19 |
| <td style="text-align: center;"><br />
| | | 296.1 |
| </td>
| | | 13/11, 19/16, 32/27 |
| </tr>
| | | {{UDnote|step=19}} |
| <tr>
| | |- |
| <td style="text-align: right;">12<br />
| | | 20 |
| </td>
| | | 311.7 |
| <td style="text-align: right;">187.013<br />
| | | 6/5 |
| </td>
| | | {{UDnote|step=20}} |
| <td style="text-align: center;">10/9<br />
| | |- |
| </td>
| | | 21 |
| </tr>
| | | 327.3 |
| <tr>
| | | 98/81 |
| <td style="text-align: right;">13<br />
| | | {{UDnote|step=21}} |
| </td>
| | |- |
| <td style="text-align: right;">202.597<br />
| | | 22 |
| </td>
| | | 342.9 |
| <td style="text-align: center;">9/8<br />
| | | 11/9, 17/14 |
| </td>
| | | {{UDnote|step=22}} |
| </tr>
| | |- |
| <tr>
| | | 23 |
| <td style="text-align: right;">14<br />
| | | 358.4 |
| </td>
| | | 16/13, 21/17 |
| <td style="text-align: right;">218.182<br />
| | | {{UDnote|step=23}} |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | 24 |
| </td>
| | | 374.0 |
| </tr>
| | | 26/21, 56/45 |
| <tr>
| | | {{UDnote|step=24}} |
| <td style="text-align: right;">15<br />
| | |- |
| </td>
| | | 25 |
| <td style="text-align: right;">233.766<br />
| | | 389.6 |
| </td>
| | | 5/4 |
| <td style="text-align: center;">8/7<br />
| | | {{UDnote|step=25}} |
| </td>
| | |- |
| </tr>
| | | 26 |
| <tr>
| | | 405.2 |
| <td style="text-align: right;">16<br />
| | | 19/15, 24/19, 33/26 |
| </td>
| | | {{UDnote|step=26}} |
| <td style="text-align: right;">249.351<br />
| | |- |
| </td>
| | | 27 |
| <td style="text-align: center;">15/13<br />
| | | 420.8 |
| </td>
| | | 14/11, 32/25 |
| </tr>
| | | {{UDnote|step=27}} |
| <tr>
| | |- |
| <td style="text-align: right;">17<br />
| | | 28 |
| </td>
| | | 436.4 |
| <td style="text-align: right;">264.935<br />
| | | 9/7 |
| </td>
| | | {{UDnote|step=28}} |
| <td style="text-align: center;">7/6<br />
| | |- |
| </td>
| | | 29 |
| </tr>
| | | 451.9 |
| <tr>
| | | 13/10 |
| <td style="text-align: right;">18<br />
| | | {{UDnote|step=29}} |
| </td>
| | |- |
| <td style="text-align: right;">280.519<br />
| | | 30 |
| </td>
| | | 467.5 |
| <td style="text-align: center;">33/28<br />
| | | 17/13, 21/16 |
| </td>
| | | {{UDnote|step=30}} |
| </tr>
| | |- |
| <tr>
| | | 31 |
| <td style="text-align: right;">19<br />
| | | 483.1 |
| </td>
| | | 120/91 |
| <td style="text-align: right;">296.104<br />
| | | {{UDnote|step=31}} |
| </td>
| | |- |
| <td style="text-align: center;">32/27, 13/11<br />
| | | 32 |
| </td>
| | | 498.7 |
| </tr>
| | | 4/3 |
| <tr>
| | | {{UDnote|step=32}} |
| <td style="text-align: right;">20<br />
| | |- |
| </td>
| | | 33 |
| <td style="text-align: right;">311.688<br />
| | | 514.3 |
| </td>
| | | 27/20 |
| <td style="text-align: center;">6/5<br />
| | | {{UDnote|step=33}} |
| </td>
| | |- |
| </tr>
| | | 34 |
| <tr>
| | | 529.9 |
| <td style="text-align: right;">21<br />
| | | 19/14 |
| </td>
| | | {{UDnote|step=34}} |
| <td style="text-align: right;">327.273<br />
| | |- |
| </td>
| | | 35 |
| <td style="text-align: center;"><br />
| | | 545.5 |
| </td>
| | | 11/8, ''15/11'', 26/19 |
| </tr>
| | | {{UDnote|step=35}} |
| <tr>
| | |- |
| <td style="text-align: right;">22<br />
| | | 36 |
| </td>
| | | 561.0 |
| <td style="text-align: right;">342.857<br />
| | | 18/13 |
| </td>
| | | {{UDnote|step=36}} |
| <td style="text-align: center;">11/9, 39/32<br />
| | |- |
| </td>
| | | 37 |
| </tr>
| | | 576.6 |
| <tr>
| | | 7/5 |
| <td style="text-align: right;">23<br />
| | | {{UDnote|step=37}} |
| </td>
| | |- |
| <td style="text-align: right;">358.442<br />
| | | 38 |
| </td>
| | | 592.2 |
| <td style="text-align: center;">16/13<br />
| | | 24/17, 38/27, 45/32 |
| </td>
| | | {{UDnote|step=38}} |
| </tr>
| | |- |
| <tr>
| | | … |
| <td style="text-align: right;">24<br />
| | | … |
| </td>
| | | … |
| <td style="text-align: right;">374.026<br />
| | |} |
| </td>
| | <nowiki/>* As a 19-limit temperament |
| <td style="text-align: center;">56/45, 26/21<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">25<br />
| |
| </td>
| |
| <td style="text-align: right;">389.610<br />
| |
| </td>
| |
| <td style="text-align: center;">5/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">26<br />
| |
| </td>
| |
| <td style="text-align: right;">405.195<br />
| |
| </td>
| |
| <td style="text-align: center;">33/26, 81/64<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">27<br />
| |
| </td>
| |
| <td style="text-align: right;">420.779<br />
| |
| </td>
| |
| <td style="text-align: center;">14/11, 32/25<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">28<br />
| |
| </td>
| |
| <td style="text-align: right;">436.364<br />
| |
| </td>
| |
| <td style="text-align: center;">9/7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">29<br />
| |
| </td>
| |
| <td style="text-align: right;">451.948<br />
| |
| </td>
| |
| <td style="text-align: center;">13/10<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">30<br />
| |
| </td>
| |
| <td style="text-align: right;">467.532<br />
| |
| </td>
| |
| <td style="text-align: center;">21/16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">31<br />
| |
| </td>
| |
| <td style="text-align: right;">483.117<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">32<br />
| |
| </td>
| |
| <td style="text-align: right;">498.701<br />
| |
| </td>
| |
| <td style="text-align: center;">4/3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">33<br />
| |
| </td>
| |
| <td style="text-align: right;">514.286<br />
| |
| </td>
| |
| <td style="text-align: center;">27/20<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">34<br />
| |
| </td>
| |
| <td style="text-align: right;">529.870<br />
| |
| </td>
| |
| <td style="text-align: center;">49/36<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">35<br />
| |
| </td>
| |
| <td style="text-align: right;">545.455<br />
| |
| </td>
| |
| <td style="text-align: center;">11/8, 15/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">36<br />
| |
| </td>
| |
| <td style="text-align: right;">561.039<br />
| |
| </td>
| |
| <td style="text-align: center;">18/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">37<br />
| |
| </td>
| |
| <td style="text-align: right;">576.623<br />
| |
| </td>
| |
| <td style="text-align: center;">7/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">38<br />
| |
| </td>
| |
| <td style="text-align: right;">592.208<br />
| |
| </td>
| |
| <td style="text-align: center;">45/32<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">39<br />
| |
| </td>
| |
| <td style="text-align: right;">607.792<br />
| |
| </td>
| |
| <td style="text-align: center;">64/45<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">40<br />
| |
| </td>
| |
| <td style="text-align: right;">623.377<br />
| |
| </td>
| |
| <td style="text-align: center;">10/7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">41<br />
| |
| </td>
| |
| <td style="text-align: right;">638.961<br />
| |
| </td>
| |
| <td style="text-align: center;">13/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">42<br />
| |
| </td>
| |
| <td style="text-align: right;">654.545<br />
| |
| </td>
| |
| <td style="text-align: center;">16/11, 22/15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">43<br />
| |
| </td>
| |
| <td style="text-align: right;">670.130<br />
| |
| </td>
| |
| <td style="text-align: center;">72/49<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">44<br />
| |
| </td>
| |
| <td style="text-align: right;">685.714<br />
| |
| </td>
| |
| <td style="text-align: center;">40/27<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">45<br />
| |
| </td>
| |
| <td style="text-align: right;">701.299<br />
| |
| </td>
| |
| <td style="text-align: center;">3/2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">46<br />
| |
| </td>
| |
| <td style="text-align: right;">716.883<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">47<br />
| |
| </td>
| |
| <td style="text-align: right;">732.468<br />
| |
| </td>
| |
| <td style="text-align: center;">32/21<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">48<br />
| |
| </td>
| |
| <td style="text-align: right;">748.052<br />
| |
| </td>
| |
| <td style="text-align: center;">20/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">49<br />
| |
| </td>
| |
| <td style="text-align: right;">763.636<br />
| |
| </td>
| |
| <td style="text-align: center;">14/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">50<br />
| |
| </td>
| |
| <td style="text-align: right;">779.221<br />
| |
| </td>
| |
| <td style="text-align: center;">11/7, 25/16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">51<br />
| |
| </td>
| |
| <td style="text-align: right;">794.805<br />
| |
| </td>
| |
| <td style="text-align: center;">52/33, 128/81<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">52<br />
| |
| </td>
| |
| <td style="text-align: right;">810.390<br />
| |
| </td>
| |
| <td style="text-align: center;">8/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">53<br />
| |
| </td>
| |
| <td style="text-align: right;">825.974<br />
| |
| </td>
| |
| <td style="text-align: center;">45/28, 21/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">54<br />
| |
| </td>
| |
| <td style="text-align: right;">841.558<br />
| |
| </td>
| |
| <td style="text-align: center;">13/8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">55<br />
| |
| </td>
| |
| <td style="text-align: right;">857.143<br />
| |
| </td>
| |
| <td style="text-align: center;">18/11, 64/39<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">56<br />
| |
| </td>
| |
| <td style="text-align: right;">872.727<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">57<br />
| |
| </td>
| |
| <td style="text-align: right;">888.312<br />
| |
| </td>
| |
| <td style="text-align: center;">5/3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">58<br />
| |
| </td>
| |
| <td style="text-align: right;">903.896<br />
| |
| </td>
| |
| <td style="text-align: center;">27/16, 22/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">59<br />
| |
| </td>
| |
| <td style="text-align: right;">919.481<br />
| |
| </td>
| |
| <td style="text-align: center;">56/33<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">60<br />
| |
| </td>
| |
| <td style="text-align: right;">935.065<br />
| |
| </td>
| |
| <td style="text-align: center;">12/7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">61<br />
| |
| </td>
| |
| <td style="text-align: right;">950.649<br />
| |
| </td>
| |
| <td style="text-align: center;">26/15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">62<br />
| |
| </td>
| |
| <td style="text-align: right;">966.234<br />
| |
| </td>
| |
| <td style="text-align: center;">7/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">63<br />
| |
| </td>
| |
| <td style="text-align: right;">981.818<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">64<br />
| |
| </td>
| |
| <td style="text-align: right;">997.403<br />
| |
| </td>
| |
| <td style="text-align: center;">16/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">65<br />
| |
| </td>
| |
| <td style="text-align: right;">1012.987<br />
| |
| </td>
| |
| <td style="text-align: center;">9/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">66<br />
| |
| </td>
| |
| <td style="text-align: right;">1028.571<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">67<br />
| |
| </td>
| |
| <td style="text-align: right;">1044.156<br />
| |
| </td>
| |
| <td style="text-align: center;">11/6, 20/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">68<br />
| |
| </td>
| |
| <td style="text-align: right;">1059.740<br />
| |
| </td>
| |
| <td style="text-align: center;">24/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">69<br />
| |
| </td>
| |
| <td style="text-align: right;">1075.325<br />
| |
| </td>
| |
| <td style="text-align: center;">28/15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">70<br />
| |
| </td>
| |
| <td style="text-align: right;">1090.909<br />
| |
| </td>
| |
| <td style="text-align: center;">15/8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">71<br />
| |
| </td>
| |
| <td style="text-align: right;">1106.494<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">72<br />
| |
| </td>
| |
| <td style="text-align: right;">1122.078<br />
| |
| </td>
| |
| <td style="text-align: center;">40/21, 48/25<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">73<br />
| |
| </td>
| |
| <td style="text-align: right;">1137.662<br />
| |
| </td>
| |
| <td style="text-align: center;">27/14, 25/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">74<br />
| |
| </td>
| |
| <td style="text-align: right;">1153.247<br />
| |
| </td>
| |
| <td style="text-align: center;">64/33, 35/18<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">75<br />
| |
| </td>
| |
| <td style="text-align: right;">1168.831<br />
| |
| </td>
| |
| <td style="text-align: center;">63/32, 96/49<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">76<br />
| |
| </td>
| |
| <td style="text-align: right;">1184.416<br />
| |
| </td>
| |
| <td style="text-align: center;">160/81, 196/99<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">77<br />
| |
| </td>
| |
| <td style="text-align: right;">1200.000<br />
| |
| </td>
| |
| <td style="text-align: center;">2/1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | == Notation == |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Linear temperaments</h1>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | === Ups and downs notation === |
| <tr>
| |
| <th>Periods<br />
| |
| per Octave<br />
| |
| </th>
| |
| <th>Generator<br />
| |
| </th>
| |
| <th>Temperaments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">1\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">2\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">3\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">4\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Unicorn">Unicorn</a>/alicorn/camahueto/qilin<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">5\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Valentine">Valentine</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">6\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">8\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">9\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Tsaharuk">Tsaharuk</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">10\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">12\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">13\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">15\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Guiron">Guiron</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">16\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Hemischis">Hemischis</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">17\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">18\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">19\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">20\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">23\77<br />
| |
| </td>
| |
| <td>Restles (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=87+%26+77&amp;limit=13" rel="nofollow">77&amp;87</a>)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">24\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">25\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">26\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">27\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">29\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">30\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">31\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Hemiseven">Hemiseven</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">32\77<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Hendecatonic">Hendecatonic</a>, <a class="wiki_link" href="/Grackle">grackle</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">34\77<br />
| |
| </td>
| |
| <td>Mabila (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&amp;limit=5" rel="nofollow">34&amp;43</a>)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">36\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">37\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">38\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">7<br />
| |
| </td>
| |
| <td style="text-align: right;">1\77<br />
| |
| </td>
| |
| <td>&quot;<a class="wiki_link" href="/TemperamentOrphanage">Absurdity</a>&quot; (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&amp;limit=5" rel="nofollow">7&amp;84</a>)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">7<br />
| |
| </td>
| |
| <td style="text-align: right;">2\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">7<br />
| |
| </td>
| |
| <td style="text-align: right;">3\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">7<br />
| |
| </td>
| |
| <td style="text-align: right;">4\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">7<br />
| |
| </td>
| |
| <td style="text-align: right;">5\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">11<br />
| |
| </td>
| |
| <td style="text-align: right;">1\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">11<br />
| |
| </td>
| |
| <td style="text-align: right;">2\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: right;">11<br />
| |
| </td>
| |
| <td style="text-align: right;">3\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | 77edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc. |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h1>
| | {{Sharpness-sharp7a}} |
| <br />
| | |
| <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3" rel="nofollow">Star 1-GrimaldiA+Bmod</a></em> by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a><br />
| | Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used: |
| <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/star/20120830-77et-star.mp3" rel="nofollow">77et Star</a></em> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
| | {{Sharpness-sharp7}} |
| <em><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3" rel="nofollow">A Seed Planted</a></em> A Seed Planted by Jake Freivald, in an <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1391" rel="nofollow">organ version</a> of Claudi Meneghin.</body></html></pre></div>
| | |
| | === Sagittal notation === |
| | ==== Evo flavor ==== |
| | <imagemap> |
| | File:77-EDO_Evo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 591 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 120 106 [[81/80]] |
| | rect 120 80 220 106 [[64/63]] |
| | rect 220 80 340 106 [[33/32]] |
| | default [[File:77-EDO_Evo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ==== Revo flavor ==== |
| | <imagemap> |
| | File:77-EDO_Revo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 543 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 120 106 [[81/80]] |
| | rect 120 80 220 106 [[64/63]] |
| | rect 220 80 340 106 [[33/32]] |
| | default [[File:77-EDO_Revo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | == Approximation to JI == |
| | === Zeta peak index === |
| | {{ZPI |
| | | zpi = 414 |
| | | steps = 76.9918536925042 |
| | | step size = 15.5860645308353 |
| | | tempered height = 8.194847 |
| | | pure height = 8.145298 |
| | | integral = 1.311364 |
| | | gap = 17.029289 |
| | | octave = 1200.12696887432 |
| | | consistent = 10 |
| | | distinct = 10 |
| | }} |
| | |
| | == Regular temperament properties == |
| | {| class="wikitable center-4 center-5 center-6" |
| | |- |
| | ! rowspan="2" | [[Subgroup]] |
| | ! rowspan="2" | [[Comma list]] |
| | ! rowspan="2" | [[Mapping]] |
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) |
| | ! colspan="2" | Tuning error |
| | |- |
| | ! [[TE error|Absolute]] (¢) |
| | ! [[TE simple badness|Relative]] (%) |
| | |- |
| | | 2.3 |
| | | {{monzo| -122 77 }} |
| | | {{mapping| 77 122 }} |
| | | +0.207 |
| | | 0.207 |
| | | 1.33 |
| | |- |
| | | 2.3.5 |
| | | 32805/32768, 1594323/1562500 |
| | | {{mapping| 77 122 179 }} |
| | | −0.336 |
| | | 0.785 |
| | | 5.04 |
| | |- |
| | | 2.3.5.7 |
| | | 126/125, 1029/1024, 10976/10935 |
| | | {{mapping| 77 122 179 216 }} |
| | | −0.021 |
| | | 0.872 |
| | | 5.59 |
| | |- |
| | | 2.3.5.7.11 |
| | | 121/120, 126/125, 176/175, 10976/10935 |
| | | {{mapping| 77 122 179 216 266 }} |
| | | +0.322 |
| | | 1.039 |
| | | 6.66 |
| | |- |
| | | 2.3.5.7.11.13 |
| | | 121/120, 126/125, 176/175, 196/195, 676/675 |
| | | {{mapping| 77 122 179 216 266 285 }} |
| | | +0.222 |
| | | 0.974 |
| | | 6.25 |
| | |} |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br>ratio* |
| | ! Temperament |
| | |- |
| | | 1 |
| | | 4\77 |
| | | 62.3 |
| | | 28/27 |
| | | [[Unicorn]] / alicorn (77e) / camahueto (77) / qilin (77) |
| | |- |
| | | 1 |
| | | 5\77 |
| | | 77.9 |
| | | 21/20 |
| | | [[Valentine]] |
| | |- |
| | | 1 |
| | | 9\77 |
| | | 140.3 |
| | | 13/12 |
| | | [[Tsaharuk]] |
| | |- |
| | | 1 |
| | | 15\77 |
| | | 233.8 |
| | | 8/7 |
| | | [[Guiron]] |
| | |- |
| | | 1 |
| | | 16\77 |
| | | 249.4 |
| | | 15/13 |
| | | [[Hemischis]] (77e) |
| | |- |
| | | 1 |
| | | 20\77 |
| | | 311.7 |
| | | 6/5 |
| | | [[Oolong]] |
| | |- |
| | | 1 |
| | | 23\77 |
| | | 358.4 |
| | | 16/13 |
| | | [[Restles]] |
| | |- |
| | | 1 |
| | | 31\77 |
| | | 483.1 |
| | | 45/34 |
| | | [[Hemiseven]] |
| | |- |
| | | 1 |
| | | 32\77 |
| | | 498.7 |
| | | 4/3 |
| | | [[Grackle]] |
| | |- |
| | | 1 |
| | | 34\77 |
| | | 529.9 |
| | | 512/375 |
| | | [[Tuskaloosa]] / [[muscogee]] |
| | |- |
| | | 1 |
| | | 36\77 |
| | | 561.0 |
| | | 18/13 |
| | | [[Demivalentine]] |
| | |- |
| | | 7 |
| | | 32\77<br>(1\77) |
| | | 498.7<br>(15.6) |
| | | 4/3<br>(81/80) |
| | | [[Absurdity]] |
| | |- |
| | | 11 |
| | | 32\77<br>(3\77) |
| | | 498.7<br>(46.8) |
| | | 4/3<br>(36/35) |
| | | [[Hendecatonic]] |
| | |} |
| | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct |
| | |
| | == Instruments == |
| | |
| | === Skip fretting === |
| | '''Skip fretting system 77 9 11''' is a [[skip fretting]] system that tunes strings 11\77 apart, with frets placed at intervals of 9\77, or 8.555...-edo. All examples on this page are for 7-string [[guitar]]. |
| | |
| | ; Intervals |
| | 0\77=1/1: string 2 open |
| | |
| | 77\77=2/1: string 7 fret 11 |
| | |
| | 45\77=3/2: string 2 fret 5 |
| | |
| | 25\77=5/4: string 1 fret 4 |
| | |
| | 62\77=7/4: string 6 fret 2 |
| | |
| | 35\77=11/8: string 4 fret 10 |
| | |
| | 54\77=13/8: string 2 fret 6 |
| | |
| | 7\77=17/16: string 1 fret 2 |
| | |
| | 19\77=19/16: string 5 fret 7 |
| | |
| | 40\77=23/16: string 4 fret 2 |
| | |
| | ; Chords |
| | x00030x: Neutral 9th (saj6, v5) |
| | |
| | === Keyboards === |
| | |
| | [[Lumatone mapping for 77edo|Lumatone mappings for 77edo]] are available. |
| | |
| | == Music == |
| | ; [[Bryan Deister] |
| | * [https://www.youtube.com/shorts/wSZez2KgP2U ''microtonal improvisation in 77edo''] (2025) |
| | |
| | ; [[Jake Freivald]] |
| | * [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 ''A Seed Planted'']{{dead link}}, in an [https://web.archive.org/web/20190412162407/http://soonlabel.com/xenharmonic/archives/1391 organ version] of [[Claudi Meneghin]]. |
| | |
| | ; [[Joel Grant Taylor]] |
| | * [https://web.archive.org/web/20201127015546/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 ''Star 1-GrimaldiA+Bmod''] |
| | |
| | ; [[Chris Vaisvil]] |
| | * [http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star''] |
| | |
| | [[Category:Listen]] |
| | [[Category:Star]] |
| | [[Category:Starling]] |
| | [[Category:Valentine]] |