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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:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:59:39 UTC</tt>.<br>
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| : The original revision id was <tt>602901646</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: #edd637; font-family: 'Times New Roman',Times,serif; font-size: 113%;">62 tone equal temperament</span>=
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| 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments.
| | == Theory == |
| | {{Nowrap| 62 {{=}} 2 × 31 }} and the [[patent val]] of 62edo is a [[contorsion|contorted]] [[31edo]] through the [[11-limit]], but it makes for a good tuning in the higher limits. In the 13-limit it [[tempering out|tempers out]] [[169/168]], [[1188/1183]], [[847/845]] and [[676/675]]; in the [[17-limit]] [[221/220]], [[273/272]], and [[289/288]]; in the [[19-limit]] [[153/152]], [[171/170]], [[209/208]], [[286/285]], and [[361/360]]. Unlike 31edo, which has a sharp profile for primes [[13/1|13]], [[17/1|17]], [[19/1|19]] and [[23/1|23]], 62edo has a flat profile for these, as it removes the distinction of otonal and utonal [[superparticular]] pairs of the primes (e.g. 13/12 vs 14/13 for prime 13) by tempering out the corresponding [[square-particular]]s. This flat tendency extends to higher primes too, as the first prime harmonic that is tuned sharper than its [[5/4]] is its [[59/32]]. Interestingly, the size differences between consecutive harmonics are monotonically decreasing for all first 24 harmonics, and 62edo is one of the few [[meantone]] edos that achieve this, great for those who seek higher-limit meantone harmony. |
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| Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel.
| | It provides the [[optimal patent val]] for [[gallium]], [[semivalentine]] and [[hemimeantone]] temperaments. |
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| ===**62-EDO Intervals**===
| | Using the 35\62 generator, which leads to the {{val| 62 97 143 173 }} val, 62edo is also an excellent tuning for septimal [[mavila]] temperament; alternatively {{val| 62 97 143 172 }} [[support]]s [[hornbostel]]. |
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| || **ARMODUE NOMENCLATURE 8;3 RELATION** ||
| | === Odd harmonics === |
| || * **Ɨ** = Thick (1/8-tone up)
| | {{Harmonics in equal|62}} |
| * **‡** = Semisharp (1/4-tone up)
| |
| * **b** = Flat (5/8-tone down)
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| * **◊** = Node (sharp/flat blindspot 1/2-tone)
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| * **#** = Sharp (5/8-tone up)
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| * **v** = Semiflat (1/4-tone down)
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| * **⌐** = Thin (1/8-tone down) ||
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| ||~ [[Degree]] ||~ Size ([[cent|Cents]]) ||~ Armodue notation ||~ Approximate intervals ||
| | === Subsets and supersets === |
| ||= 0 ||> 0.0000 ||= 1 || ||
| | Since 62 factors into 2 × 31, 62edo does not contain nontrivial subset edos other than [[2edo]] and 31edo. [[186edo]] and [[248edo]] are notable supersets. |
| ||= 1 ||> 19.3548 ||= 1Ɨ || ||
| |
| ||= 2 ||> 38.7097 ||= 1‡ (9#) || ||
| |
| ||= 3 ||> 58.0645 ||= 2b || ||
| |
| ||= 4 ||> 77.4194 ||= 1◊2 || ||
| |
| ||= 5 ||> 96.7742 ||= 1# || ||
| |
| ||= 6 ||> 116.1290 ||= 2v || ||
| |
| ||= 7 ||> 135.4839 ||= 2⌐ || ||
| |
| ||= 8 ||> 154.8387 ||= 2 || ||
| |
| ||= 9 ||> 174.1935 ||= 2Ɨ || ||
| |
| ||= 10 ||> 193.5484 ||= 2‡ || ||
| |
| ||= 11 ||> 212.9032 ||= 3b || · ||
| |
| ||= 12 ||> 232.2581 ||= 2◊3 || ||
| |
| ||= 13 ||> 251.6129 ||= 2# || ||
| |
| ||= 14 ||> 270.9677 ||= 3v || ||
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| ||= 15 ||> 290.3226 ||= 3⌐ || ||
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| ||= 16 ||> 309.6774 ||= 3 || ||
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| ||= 17 ||> 329.0323 ||= 3Ɨ || ||
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| ||= 18 ||> 348.3871 ||= 3‡ || ||
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| ||= 19 ||> 367.7419 ||= 4b || · ||
| |
| ||= 20 ||> 387.0968 ||= 3◊4 || ||
| |
| ||= 21 ||> 406.4516 ||= 3# || ||
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| ||= 22 ||> 425.8065 ||= 4v (5b) || ||
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| ||= 23 ||> 445.1613 ||= 4⌐ || ||
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| ||= 24 ||> 464.5161 ||= 4 || ||
| |
| ||= 25 ||> 483.8710 ||= 4Ɨ (5v) || ||
| |
| ||= 26 ||> 503.2258 ||= 5⌐ (4‡) || ||
| |
| ||= 27 ||> 522.5806 ||= 5 || · ||
| |
| ||= 28 ||> 541.9355 ||= 5Ɨ || ||
| |
| ||= 29 ||> 561.2903 ||= 5‡ (4#) || ||
| |
| ||= 30 ||> 580.6452 ||= 6b || ||
| |
| ||= 31 ||> 600.0000 ||= 5◊6 || ||
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| ||= 32 ||> 619.3548 ||= 5# || ||
| |
| ||= 33 ||> 638.7097 ||= 6v || ||
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| ||= 34 ||> 658.0645 ||= 6⌐ || ||
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| ||= 35 ||> 677.4194 ||= 6 || · ||
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| ||= 36 ||> 696.7742 ||= 6Ɨ || ||
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| ||= 37 ||> 716.1290 ||= 6‡ || ||
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| ||= 38 ||> 735.4839 ||= 7b || ||
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| ||= 39 ||> 754.8387 ||= 6◊7 || ||
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| ||= 40 ||> 774.1935 ||= 6# || ||
| |
| ||= 41 ||> 793.5484 ||= 7v || ||
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| ||= 42 ||> 812.9032 ||= 7⌐ || ||
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| ||= 43 ||> 832.2581 ||= 7 || · ||
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| ||= 44 ||> 851.6129 ||= 7Ɨ || ||
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| ||= 45 ||> 870.9677 ||= 7‡ || ||
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| ||= 46 ||> 890.3226 ||= 8b || ||
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| ||= 47 ||> 909.6774 ||= 7◊8 || ||
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| ||= 48 ||> 929.0323 ||= 7# || ||
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| ||= 49 ||> 948.3871 ||= 8v || ||
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| ||= 50 ||> 967.7419 ||= 8⌐ || ||
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| ||= 51 ||> 987.0968 ||= 8 || · ||
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| ||= 52 ||> 1006.4516 ||= 8Ɨ || ||
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| ||= 53 ||> 1025.8065 ||= 8‡ || ||
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| ||= 54 ||> 1045.1613 ||= 9b || ||
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| ||= 55 ||> 1064.5161 ||= 8◊9 || ||
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| ||= 56 ||> 1083.8710 ||= 8# || ||
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| ||= 57 ||> 1103.2258 ||= 9v (1b) || ||
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| ||= 58 ||> 1122.5806 ||= 9⌐ || ||
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| ||= 59 ||> 1141.9355 ||= 9 || ||
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| ||= 60 ||> 1161.2903 ||= 9Ɨ (1v) || ||
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| ||= 61 ||> 1180.6452 ||= 1⌐ (9‡) || ||
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| ||= 62 ||> 1200.0000 ||= 1 || ||</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>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #edd637; font-family: 'Times New Roman',Times,serif; font-size: 113%;">62 tone equal temperament</span></h1>
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| <br />
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| 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | |
| <br />
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| Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3>
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| | === Miscellany === |
| | 62 years is the amount of years in a leap week calendar cycle which corresponds to a year of 365 days 5 hours 48 minutes 23 seconds, meaning it is both a simple cycle for a calendar, and 62 being a multiple of 31 makes it a harmonically useful and playable cycle. The corresponding maximal evenness scales are 15 & 62 and 11 & 62. |
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| <table class="wiki_table"> | | The 11 & 62 temperament is called mabon, named so because its associated year length corresponds to an autumnal equinoctial year. In the 2.9.7 subgroup tempers out 44957696/43046721, and the three generators of 17\62 correspond to [[16/9]]. It is possible to extend this to the 11-limit with comma basis {896/891, 1331/1296}, where 17\62 is mapped to [[11/9]] and two of them make [[16/11]]. In addition, three generators make the patent val 9/8, which is also created by combining the flat patent val fifth from 31edo with the sharp 37\62 fifth. |
| <tr>
| |
| <td><strong>ARMODUE NOMENCLATURE 8;3 RELATION</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node (sharp/flat blindspot 1/2-tone)</li><li><strong>#</strong> = Sharp (5/8-tone up)</li><li><strong>v</strong> = Semiflat (1/4-tone down)</li><li><strong>⌐</strong> = Thin (1/8-tone down)</li></ul></td>
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| </tr>
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| </table>
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| <br /> | | The 15 & 62 temperament, corresponding to the leap day cycle, is [[demivalentine]] in the 13-limit. |
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| | == Intervals == |
| | {| class="wikitable center-all right-2 left-3" |
| | |- |
| | ! Steps |
| | ! Cents |
| | ! Approximate ratios* |
| | ! [[Ups and downs notation]] |
| | |- |
| | | 0 |
| | | 0.00 |
| | | 1/1 |
| | | {{UDnote|step=0}} |
| | |- |
| | | 1 |
| | | 19.35 |
| | | 65/64, 66/65, 78/77, 91/90, 105/104 |
| | | {{UDnote|step=1}} |
| | |- |
| | | 2 |
| | | 38.71 |
| | | ''33/32'', 36/35, 45/44, 49/48, 50/49, 55/54, 56/55, ''64/63'' |
| | | {{UDnote|step=2}} |
| | |- |
| | | 3 |
| | | 58.06 |
| | | ''26/25'', 27/26 |
| | | {{UDnote|step=3}} |
| | |- |
| | | 4 |
| | | 77.42 |
| | | 21/20, 22/21, 23/22, 24/23, 25/24, ''28/27'' |
| | | {{UDnote|step=4}} |
| | |- |
| | | 5 |
| | | 96.77 |
| | | 17/16, 18/17, 19/18, 20/19 |
| | | {{UDnote|step=5}} |
| | |- |
| | | 6 |
| | | 116.13 |
| | | 15/14, 16/15 |
| | | {{UDnote|step=6}} |
| | |- |
| | | 7 |
| | | 135.48 |
| | | 13/12, 14/13 |
| | | {{UDnote|step=7}} |
| | |- |
| | | 8 |
| | | 154.84 |
| | | ''11/10'', 12/11, 23/21 |
| | | {{UDnote|step=8}} |
| | |- |
| | | 9 |
| | | 174.19 |
| | | 21/19 |
| | | {{UDnote|step=9}} |
| | |- |
| | | 10 |
| | | 193.55 |
| | | ''9/8'', ''10/9'', 19/17, 28/25 |
| | | {{UDnote|step=10}} |
| | |- |
| | | 11 |
| | | 212.90 |
| | | 17/15 |
| | | {{UDnote|step=11}} |
| | |- |
| | | 12 |
| | | 232.26 |
| | | 8/7 |
| | | {{UDnote|step=12}} |
| | |- |
| | | 13 |
| | | 251.61 |
| | | 15/13, 22/19 |
| | | {{UDnote|step=13}} |
| | |- |
| | | 14 |
| | | 270.97 |
| | | 7/6 |
| | | {{UDnote|step=14}} |
| | |- |
| | | 15 |
| | | 290.32 |
| | | 13/11, 19/16, 20/17 |
| | | {{UDnote|step=15}} |
| | |- |
| | | 16 |
| | | 309.68 |
| | | 6/5 |
| | | {{UDnote|step=16}} |
| | |- |
| | | 17 |
| | | 329.03 |
| | | 17/14, 23/19 |
| | | {{UDnote|step=18}} |
| | |- |
| | | 18 |
| | | 348.39 |
| | | 11/9, 27/22, 28/23 |
| | | {{UDnote|step=18}} |
| | |- |
| | | 19 |
| | | 367.74 |
| | | 16/13, 21/17, 26/21 |
| | | {{UDnote|step=19}} |
| | |- |
| | | 20 |
| | | 387.10 |
| | | 5/4 |
| | | {{UDnote|step=20}} |
| | |- |
| | | 21 |
| | | 406.45 |
| | | 19/15, 24/19 |
| | | {{UDnote|step=21}} |
| | |- |
| | | 22 |
| | | 425.81 |
| | | 9/7, 14/11, 23/18, 32/25 |
| | | {{UDnote|step=22}} |
| | |- |
| | | 23 |
| | | 445.16 |
| | | 13/10, 22/17 |
| | | {{UDnote|step=23}} |
| | |- |
| | | 24 |
| | | 464.52 |
| | | 17/13, 21/16, 30/23 |
| | | {{UDnote|step=24}} |
| | |- |
| | | 25 |
| | | 483.87 |
| | | 25/19 |
| | | {{UDnote|step=25}} |
| | |- |
| | | 26 |
| | | 503.23 |
| | | 4/3 |
| | | {{UDnote|step=26}} |
| | |- |
| | | 27 |
| | | 522.58 |
| | | 19/14, 23/17 |
| | | {{UDnote|step=27}} |
| | |- |
| | | 28 |
| | | 541.94 |
| | | 11/8, 15/11, 26/19 |
| | | {{UDnote|step=28}} |
| | |- |
| | | 29 |
| | | 561.29 |
| | | 18/13 |
| | | {{UDnote|step=29}} |
| | |- |
| | | 30 |
| | | 580.65 |
| | | 7/5, ''25/18'', 32/23 |
| | | {{UDnote|step=30}} |
| | |- |
| | | 31 |
| | | 600.00 |
| | | 17/12, 24/17 |
| | | {{UDnote|step=10}} |
| | |- |
| | | 32 |
| | | 619.35 |
| | | 10/7, 23/16, ''36/25'' |
| | | {{UDnote|step=32}} |
| | |- |
| | | 33 |
| | | 638.71 |
| | | 13/9 |
| | | {{UDnote|step=33}} |
| | |- |
| | | 34 |
| | | 658.06 |
| | | 16/11, 19/13, 22/15 |
| | | {{UDnote|step=34}} |
| | |- |
| | | 35 |
| | | 677.42 |
| | | 28/19, 34/23 |
| | | {{UDnote|step=35}} |
| | |- |
| | | 36 |
| | | 696.77 |
| | | 3/2 |
| | | {{UDnote|step=36}} |
| | |- |
| | | 37 |
| | | 716.13 |
| | | 38/25 |
| | | {{UDnote|step=37}} |
| | |- |
| | | 38 |
| | | 735.48 |
| | | 23/15, 26/17, 32/21 |
| | | {{UDnote|step=38}} |
| | |- |
| | | 39 |
| | | 754.84 |
| | | 17/11, 20/13 |
| | | {{UDnote|step=39}} |
| | |- |
| | | 40 |
| | | 774.19 |
| | | 11/7, 14/9, 25/16, 36/23 |
| | | {{UDnote|step=40}} |
| | |- |
| | | 41 |
| | | 793.55 |
| | | 19/12, 30/19 |
| | | {{UDnote|step=41}} |
| | |- |
| | | 42 |
| | | 812.90 |
| | | 8/5 |
| | | {{UDnote|step=42}} |
| | |- |
| | | 43 |
| | | 832.26 |
| | | 13/8, 21/13, 34/21 |
| | | {{UDnote|step=43}} |
| | |- |
| | | 44 |
| | | 851.61 |
| | | 18/11, 23/14, 44/27 |
| | | {{UDnote|step=44}} |
| | |- |
| | | 45 |
| | | 870.97 |
| | | 28/17, 38/23 |
| | | {{UDnote|step=45}} |
| | |- |
| | | 46 |
| | | 890.32 |
| | | 5/3 |
| | | {{UDnote|step=46}} |
| | |- |
| | | 47 |
| | | 909.68 |
| | | 17/10, 22/13, 32/19 |
| | | {{UDnote|step=47}} |
| | |- |
| | | 48 |
| | | 929.03 |
| | | 12/7 |
| | | {{UDnote|step=48}} |
| | |- |
| | | 49 |
| | | 948.39 |
| | | 19/11, 26/15 |
| | | {{UDnote|step=49}} |
| | |- |
| | | 50 |
| | | 967.74 |
| | | 7/4 |
| | | {{UDnote|step=50}} |
| | |- |
| | | 51 |
| | | 987.10 |
| | | 30/17 |
| | | {{UDnote|step=51}} |
| | |- |
| | | 52 |
| | | 1006.45 |
| | | ''9/5'', ''16/9'', 25/14, 34/19 |
| | | {{UDnote|step=52}} |
| | |- |
| | | 53 |
| | | 1025.81 |
| | | 38/21 |
| | | {{UDnote|step=53}} |
| | |- |
| | | 54 |
| | | 1045.16 |
| | | 11/6, ''20/11'', 42/23 |
| | | {{UDnote|step=54}} |
| | |- |
| | | 55 |
| | | 1064.52 |
| | | 13/7, 24/13 |
| | | {{UDnote|step=55}} |
| | |- |
| | | 56 |
| | | 1083.87 |
| | | 15/8, 28/15 |
| | | {{UDnote|step=56}} |
| | |- |
| | | 57 |
| | | 1103.23 |
| | | 17/9, 19/10, 32/17, 36/19 |
| | | {{UDnote|step=57}} |
| | |- |
| | | 58 |
| | | 1122.58 |
| | | 21/11, 23/12, ''27/14'', 40/21, 44/23, 48/25 |
| | | {{UDnote|step=58}} |
| | |- |
| | | 59 |
| | | 1141.94 |
| | | ''25/13'', 52/27 |
| | | {{UDnote|step=59}} |
| | |- |
| | | 60 |
| | | 1161.29 |
| | | 35/18, 49/25, 55/28, ''63/32'', ''64/33'', 88/45, 96/49, 108/55 |
| | | {{UDnote|step=60}} |
| | |- |
| | | 61 |
| | | 1180.65 |
| | | 65/33, 77/39, 128/65, 180/91, 208/105 |
| | | {{UDnote|step=61}} |
| | |- |
| | | 62 |
| | | 1200.00 |
| | | 2/1 |
| | | {{UDnote|step=62}} |
| | |} |
| | <nowiki />* 23-limit patent val, inconsistent intervals in ''italic'' |
|
| |
|
| <table class="wiki_table">
| | == Notation == |
| <tr>
| | === Ups and downs notation === |
| <th><a class="wiki_link" href="/Degree">Degree</a><br />
| | 62edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat. |
| </th>
| | {{Sharpness-sharp4a}} |
| <th>Size (<a class="wiki_link" href="/cent">Cents</a>)<br />
| | [[Alternative symbols for ups and downs notation]] uses sharps and flats and quarter-tone accidentals combined with arrows, borrowed from extended [[Helmholtz–Ellis notation]]: |
| </th>
| | {{Sharpness-sharp4}} |
| <th>Armodue notation<br />
| | === Sagittal notation === |
| </th>
| | This notation uses the same sagittal sequence as EDOs [[69edo#Sagittal notation|69]] and [[76edo#Sagittal notation|76]], and is a superset of the notation for [[31edo#Sagittal notation|31-EDO]]. |
| <th>Approximate intervals<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: right;">0.0000<br />
| |
| </td>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td style="text-align: right;">19.3548<br />
| |
| </td>
| |
| <td style="text-align: center;">1Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td style="text-align: right;">38.7097<br />
| |
| </td>
| |
| <td style="text-align: center;">1‡ (9#)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3<br />
| |
| </td>
| |
| <td style="text-align: right;">58.0645<br />
| |
| </td>
| |
| <td style="text-align: center;">2b<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">4<br />
| |
| </td>
| |
| <td style="text-align: right;">77.4194<br />
| |
| </td>
| |
| <td style="text-align: center;">1◊2<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5<br />
| |
| </td>
| |
| <td style="text-align: right;">96.7742<br />
| |
| </td>
| |
| <td style="text-align: center;">1#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">6<br />
| |
| </td>
| |
| <td style="text-align: right;">116.1290<br />
| |
| </td>
| |
| <td style="text-align: center;">2v<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">7<br />
| |
| </td>
| |
| <td style="text-align: right;">135.4839<br />
| |
| </td>
| |
| <td style="text-align: center;">2⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">8<br />
| |
| </td>
| |
| <td style="text-align: right;">154.8387<br />
| |
| </td>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">9<br />
| |
| </td>
| |
| <td style="text-align: right;">174.1935<br />
| |
| </td>
| |
| <td style="text-align: center;">2Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">10<br />
| |
| </td>
| |
| <td style="text-align: right;">193.5484<br />
| |
| </td>
| |
| <td style="text-align: center;">2‡<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">11<br />
| |
| </td>
| |
| <td style="text-align: right;">212.9032<br />
| |
| </td>
| |
| <td style="text-align: center;">3b<br />
| |
| </td>
| |
| <td>·<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">12<br />
| |
| </td>
| |
| <td style="text-align: right;">232.2581<br />
| |
| </td>
| |
| <td style="text-align: center;">2◊3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">13<br />
| |
| </td>
| |
| <td style="text-align: right;">251.6129<br />
| |
| </td>
| |
| <td style="text-align: center;">2#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">14<br />
| |
| </td>
| |
| <td style="text-align: right;">270.9677<br />
| |
| </td>
| |
| <td style="text-align: center;">3v<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">15<br />
| |
| </td>
| |
| <td style="text-align: right;">290.3226<br />
| |
| </td>
| |
| <td style="text-align: center;">3⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">16<br />
| |
| </td>
| |
| <td style="text-align: right;">309.6774<br />
| |
| </td>
| |
| <td style="text-align: center;">3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">17<br />
| |
| </td>
| |
| <td style="text-align: right;">329.0323<br />
| |
| </td>
| |
| <td style="text-align: center;">3Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">18<br />
| |
| </td>
| |
| <td style="text-align: right;">348.3871<br />
| |
| </td>
| |
| <td style="text-align: center;">3‡<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">19<br />
| |
| </td>
| |
| <td style="text-align: right;">367.7419<br />
| |
| </td>
| |
| <td style="text-align: center;">4b<br />
| |
| </td>
| |
| <td>·<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">20<br />
| |
| </td>
| |
| <td style="text-align: right;">387.0968<br />
| |
| </td>
| |
| <td style="text-align: center;">3◊4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">21<br />
| |
| </td>
| |
| <td style="text-align: right;">406.4516<br />
| |
| </td>
| |
| <td style="text-align: center;">3#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">22<br />
| |
| </td>
| |
| <td style="text-align: right;">425.8065<br />
| |
| </td>
| |
| <td style="text-align: center;">4v (5b)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">23<br />
| |
| </td>
| |
| <td style="text-align: right;">445.1613<br />
| |
| </td>
| |
| <td style="text-align: center;">4⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">24<br />
| |
| </td>
| |
| <td style="text-align: right;">464.5161<br />
| |
| </td>
| |
| <td style="text-align: center;">4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">25<br />
| |
| </td>
| |
| <td style="text-align: right;">483.8710<br />
| |
| </td>
| |
| <td style="text-align: center;">4Ɨ (5v)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">26<br />
| |
| </td>
| |
| <td style="text-align: right;">503.2258<br />
| |
| </td>
| |
| <td style="text-align: center;">5⌐ (4‡)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">27<br />
| |
| </td>
| |
| <td style="text-align: right;">522.5806<br />
| |
| </td>
| |
| <td style="text-align: center;">5<br />
| |
| </td>
| |
| <td>·<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">28<br />
| |
| </td>
| |
| <td style="text-align: right;">541.9355<br />
| |
| </td>
| |
| <td style="text-align: center;">5Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">29<br />
| |
| </td>
| |
| <td style="text-align: right;">561.2903<br />
| |
| </td>
| |
| <td style="text-align: center;">5‡ (4#)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">30<br />
| |
| </td>
| |
| <td style="text-align: right;">580.6452<br />
| |
| </td>
| |
| <td style="text-align: center;">6b<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">31<br />
| |
| </td>
| |
| <td style="text-align: right;">600.0000<br />
| |
| </td>
| |
| <td style="text-align: center;">5◊6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">32<br />
| |
| </td>
| |
| <td style="text-align: right;">619.3548<br />
| |
| </td>
| |
| <td style="text-align: center;">5#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">33<br />
| |
| </td>
| |
| <td style="text-align: right;">638.7097<br />
| |
| </td>
| |
| <td style="text-align: center;">6v<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">34<br />
| |
| </td>
| |
| <td style="text-align: right;">658.0645<br />
| |
| </td>
| |
| <td style="text-align: center;">6⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">35<br />
| |
| </td>
| |
| <td style="text-align: right;">677.4194<br />
| |
| </td>
| |
| <td style="text-align: center;">6<br />
| |
| </td>
| |
| <td>·<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">36<br />
| |
| </td>
| |
| <td style="text-align: right;">696.7742<br />
| |
| </td>
| |
| <td style="text-align: center;">6Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">37<br />
| |
| </td>
| |
| <td style="text-align: right;">716.1290<br />
| |
| </td>
| |
| <td style="text-align: center;">6‡<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">38<br />
| |
| </td>
| |
| <td style="text-align: right;">735.4839<br />
| |
| </td>
| |
| <td style="text-align: center;">7b<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">39<br />
| |
| </td>
| |
| <td style="text-align: right;">754.8387<br />
| |
| </td>
| |
| <td style="text-align: center;">6◊7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">40<br />
| |
| </td>
| |
| <td style="text-align: right;">774.1935<br />
| |
| </td>
| |
| <td style="text-align: center;">6#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">41<br />
| |
| </td>
| |
| <td style="text-align: right;">793.5484<br />
| |
| </td>
| |
| <td style="text-align: center;">7v<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">42<br />
| |
| </td>
| |
| <td style="text-align: right;">812.9032<br />
| |
| </td>
| |
| <td style="text-align: center;">7⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">43<br />
| |
| </td>
| |
| <td style="text-align: right;">832.2581<br />
| |
| </td>
| |
| <td style="text-align: center;">7<br />
| |
| </td>
| |
| <td>·<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">44<br />
| |
| </td>
| |
| <td style="text-align: right;">851.6129<br />
| |
| </td>
| |
| <td style="text-align: center;">7Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">45<br />
| |
| </td>
| |
| <td style="text-align: right;">870.9677<br />
| |
| </td>
| |
| <td style="text-align: center;">7‡<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">46<br />
| |
| </td>
| |
| <td style="text-align: right;">890.3226<br />
| |
| </td>
| |
| <td style="text-align: center;">8b<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">47<br />
| |
| </td>
| |
| <td style="text-align: right;">909.6774<br />
| |
| </td>
| |
| <td style="text-align: center;">7◊8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">48<br />
| |
| </td>
| |
| <td style="text-align: right;">929.0323<br />
| |
| </td>
| |
| <td style="text-align: center;">7#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">49<br />
| |
| </td>
| |
| <td style="text-align: right;">948.3871<br />
| |
| </td>
| |
| <td style="text-align: center;">8v<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">50<br />
| |
| </td>
| |
| <td style="text-align: right;">967.7419<br />
| |
| </td>
| |
| <td style="text-align: center;">8⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">51<br />
| |
| </td>
| |
| <td style="text-align: right;">987.0968<br />
| |
| </td>
| |
| <td style="text-align: center;">8<br />
| |
| </td>
| |
| <td>·<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">52<br />
| |
| </td>
| |
| <td style="text-align: right;">1006.4516<br />
| |
| </td>
| |
| <td style="text-align: center;">8Ɨ<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">53<br />
| |
| </td>
| |
| <td style="text-align: right;">1025.8065<br />
| |
| </td>
| |
| <td style="text-align: center;">8‡<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">54<br />
| |
| </td>
| |
| <td style="text-align: right;">1045.1613<br />
| |
| </td>
| |
| <td style="text-align: center;">9b<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">55<br />
| |
| </td>
| |
| <td style="text-align: right;">1064.5161<br />
| |
| </td>
| |
| <td style="text-align: center;">8◊9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">56<br />
| |
| </td>
| |
| <td style="text-align: right;">1083.8710<br />
| |
| </td>
| |
| <td style="text-align: center;">8#<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">57<br />
| |
| </td>
| |
| <td style="text-align: right;">1103.2258<br />
| |
| </td>
| |
| <td style="text-align: center;">9v (1b)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">58<br />
| |
| </td>
| |
| <td style="text-align: right;">1122.5806<br />
| |
| </td>
| |
| <td style="text-align: center;">9⌐<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">59<br />
| |
| </td>
| |
| <td style="text-align: right;">1141.9355<br />
| |
| </td>
| |
| <td style="text-align: center;">9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">60<br />
| |
| </td>
| |
| <td style="text-align: right;">1161.2903<br />
| |
| </td>
| |
| <td style="text-align: center;">9Ɨ (1v)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">61<br />
| |
| </td>
| |
| <td style="text-align: right;">1180.6452<br />
| |
| </td>
| |
| <td style="text-align: center;">1⌐ (9‡)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">62<br />
| |
| </td>
| |
| <td style="text-align: right;">1200.0000<br />
| |
| </td>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | ==== Evo flavor ==== |
| | <imagemap> |
| | File:62-EDO_Evo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 703 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 170 106 [[1053/1024]] |
| | rect 170 80 290 106 [[33/32]] |
| | default [[File:62-EDO_Evo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ==== Revo flavor ==== |
| | <imagemap> |
| | File:62-EDO_Revo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 687 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 170 106 [[1053/1024]] |
| | rect 170 80 290 106 [[33/32]] |
| | default [[File:62-EDO_Revo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ==== Evo-SZ flavor ==== |
| | <imagemap> |
| | File:62-EDO_Evo-SZ_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 170 106 [[1053/1024]] |
| | rect 170 80 290 106 [[33/32]] |
| | default [[File:62-EDO_Evo-SZ_Sagittal.svg]] |
| | </imagemap> |
| | |
| | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. |
| | |
| | === Armodue notation === |
| | ; Armodue nomenclature 8;3 relation |
| | * '''Ɨ''' = Thick (1/8-tone up) |
| | * '''‡''' = Semisharp (1/4-tone up) |
| | * '''b''' = Flat (5/8-tone down) |
| | * '''◊''' = Node (sharp/flat blindspot 1/2-tone) |
| | * '''#''' = Sharp (5/8-tone up) |
| | * '''v''' = Semiflat (1/4-tone down) |
| | * '''⌐''' = Thin (1/8-tone down) |
| | |
| | {| class="wikitable center-all right-3 left-5 mw-collapsible mw-collapsed" |
| | |- |
| | ! colspan="2" | # |
| | ! Cents |
| | ! Armodue notation |
| | ! Associated ratio |
| | |- |
| | | 0 |
| | | |
| | | 0.0 |
| | | 1 |
| | | |
| | |- |
| | | 1 |
| | | |
| | | 19.4 |
| | | 1Ɨ |
| | | |
| | |- |
| | | 2 |
| | | |
| | | 38.7 |
| | | 1‡ (9#) |
| | | |
| | |- |
| | | 3 |
| | | |
| | | 58.1 |
| | | 2b |
| | | |
| | |- |
| | | 4 |
| | | |
| | | 77.4 |
| | | 1◊2 |
| | | |
| | |- |
| | | 5 |
| | | |
| | | 96.8 |
| | | 1# |
| | | |
| | |- |
| | | 6 |
| | | |
| | | 116.1 |
| | | 2v |
| | | |
| | |- |
| | | 7 |
| | | |
| | | 135.5 |
| | | 2⌐ |
| | | |
| | |- |
| | | 8 |
| | | |
| | | 154.8 |
| | | 2 |
| | | 11/10~12/11 |
| | |- |
| | | 9 |
| | | |
| | | 174.2 |
| | | 2Ɨ |
| | | |
| | |- |
| | | 10 |
| | | |
| | | 193.5 |
| | | 2‡ |
| | | |
| | |- |
| | | 11 |
| | | |
| | | 212.9 |
| | | 3b |
| | | 8/7 |
| | |- |
| | | 12 |
| | | |
| | | 232.3 |
| | | 2◊3 |
| | | |
| | |- |
| | | 13 |
| | | |
| | | 251.6 |
| | | 2# |
| | | |
| | |- |
| | | 14 |
| | | |
| | | 271.0 |
| | | 3v |
| | | |
| | |- |
| | | 15 |
| | | |
| | | 290.3 |
| | | 3⌐ |
| | | |
| | |- |
| | | 16 |
| | | |
| | | 309.7 |
| | | 3 |
| | | 6/5~7/6 |
| | |- |
| | | 17 |
| | | |
| | | 329.0 |
| | | 3Ɨ |
| | | |
| | |- |
| | | 18 |
| | | |
| | | 348.4 |
| | | 3‡ |
| | | |
| | |- |
| | | 19 |
| | | · |
| | | 367.7 |
| | | 4b |
| | | 5/4 |
| | |- |
| | | 20 |
| | | |
| | | 387.1 |
| | | 3◊4 |
| | | |
| | |- |
| | | 21 |
| | | |
| | | 406.5 |
| | | 3# |
| | | |
| | |- |
| | | 22 |
| | | |
| | | 425.8 |
| | | 4v (5b) |
| | | |
| | |- |
| | | 23 |
| | | |
| | | 445.2 |
| | | 4⌐ |
| | | |
| | |- |
| | | 24 |
| | | |
| | | 464.5 |
| | | 4 |
| | | |
| | |- |
| | | 25 |
| | | |
| | | 483.9 |
| | | 4Ɨ (5v) |
| | | |
| | |- |
| | | 26 |
| | | |
| | | 503.2 |
| | | 5⌐ (4‡) |
| | | |
| | |- |
| | | 27 |
| | | · |
| | | 522.6 |
| | | 5 |
| | | 4/3~11/8 |
| | |- |
| | | 28 |
| | | |
| | | 541.9 |
| | | 5Ɨ |
| | | |
| | |- |
| | | 29 |
| | | |
| | | 561.3 |
| | | 5‡ (4#) |
| | | |
| | |- |
| | | 30 |
| | | |
| | | 580.6 |
| | | 6b |
| | | 10/7 |
| | |- |
| | | 31 |
| | | |
| | | 600.0 |
| | | 5◊6 |
| | | |
| | |- |
| | | 32 |
| | | |
| | | 619.4 |
| | | 5# |
| | | 7/5 |
| | |- |
| | | 33 |
| | | |
| | | 638.7 |
| | | 6v |
| | | |
| | |- |
| | | 34 |
| | | |
| | | 658.1 |
| | | 6⌐ |
| | | |
| | |- |
| | | 35 |
| | | · |
| | | 677.4 |
| | | 6 |
| | | 3/2~16/11 |
| | |- |
| | | 36 |
| | | |
| | | 696.8 |
| | | 6Ɨ |
| | | |
| | |- |
| | | 37 |
| | | |
| | | 716.1 |
| | | 6‡ |
| | | |
| | |- |
| | | 38 |
| | | |
| | | 735.5 |
| | | 7b |
| | | |
| | |- |
| | | 39 |
| | | |
| | | 754.8 |
| | | 6◊7 |
| | | |
| | |- |
| | | 40 |
| | | |
| | | 774.2 |
| | | 6# |
| | | |
| | |- |
| | | 41 |
| | | |
| | | 793.5 |
| | | 7v |
| | | |
| | |- |
| | | 42 |
| | | |
| | | 812.9 |
| | | 7⌐ |
| | | |
| | |- |
| | | 43 |
| | | · |
| | | 832.3 |
| | | 7 |
| | | 8/5 |
| | |- |
| | | 44 |
| | | |
| | | 851.6 |
| | | 7Ɨ |
| | | |
| | |- |
| | | 45 |
| | | |
| | | 871.0 |
| | | 7‡ |
| | | |
| | |- |
| | | 46 |
| | | |
| | | 890.3 |
| | | 8b |
| | | 5/3~12/7 |
| | |- |
| | | 47 |
| | | |
| | | 909.7 |
| | | 7◊8 |
| | | |
| | |- |
| | | 48 |
| | | |
| | | 929.0 |
| | | 7# |
| | | |
| | |- |
| | | 49 |
| | | |
| | | 948.4 |
| | | 8v |
| | | |
| | |- |
| | | 50 |
| | | |
| | | 967.7 |
| | | 8⌐ |
| | | |
| | |- |
| | | 51 |
| | | |
| | | 987.1 |
| | | 8 |
| | | 7/4 |
| | |- |
| | | 52 |
| | | |
| | | 1006.5 |
| | | 8Ɨ |
| | | |
| | |- |
| | | 53 |
| | | |
| | | 1025.8 |
| | | 8‡ |
| | | |
| | |- |
| | | 54 |
| | | |
| | | 1045.2 |
| | | 9b |
| | | 11/6~20/11 |
| | |- |
| | | 55 |
| | | |
| | | 1064.5 |
| | | 8◊9 |
| | | |
| | |- |
| | | 56 |
| | | |
| | | 1083.9 |
| | | 8# |
| | | |
| | |- |
| | | 57 |
| | | |
| | | 1103.2 |
| | | 9v (1b) |
| | | |
| | |- |
| | | 58 |
| | | |
| | | 1122.6 |
| | | 9⌐ |
| | | |
| | |- |
| | | 59 |
| | | |
| | | 1141.9 |
| | | 9 |
| | | |
| | |- |
| | | 60 |
| | | |
| | | 1161.3 |
| | | 9Ɨ (1v) |
| | | |
| | |- |
| | | 61 |
| | | |
| | | 1180.6 |
| | | 1⌐ (9‡) |
| | | |
| | |- |
| | | 62 |
| | | |
| | | 1200.0 |
| | | 1 |
| | | |
| | |} |
| | |
| | == Approximation to JI == |
| | === Zeta peak index === |
| | {{ZPI |
| | | zpi = 314 |
| | | steps = 61.9380472360525 |
| | | step size = 19.3741981471691 |
| | | tempered height = 6.262952 |
| | | pure height = 4.11259 |
| | | integral = 0.952068 |
| | | gap = 15.026453 |
| | | octave = 1201.20028512448 |
| | | consistent = 8 |
| | | distinct = 8 |
| | }} |
| | |
| | == Regular temperament properties == |
| | 62edo is contorted 31edo through the 11-limit. |
| | {| 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]] (%) |
| | |- |
| | | 2.3.5.7.11.13 |
| | | 81/80, 99/98, 121/120, 126/125, 169/168 |
| | | {{mapping| 62 98 144 174 214 229 }} |
| | | +1.38 |
| | | 1.41 |
| | | 7.28 |
| | |- |
| | | 2.3.5.7.11.13.17 |
| | | 81/80, 99/98, 121/120, 126/125, 169/168, 221/220 |
| | | {{mapping| 62 98 144 174 214 229 253 }} |
| | | +1.47 |
| | | 1.32 |
| | | 6.83 |
| | |- |
| | | 2.3.5.7.11.13.17.19 |
| | | 81/80, 99/98, 121/120, 126/125, 153/152, 169/168, 209/208 |
| | | {{mapping| 62 98 144 174 214 229 253 263 }} |
| | | +1.50 |
| | | 1.24 |
| | | 6.40 |
| | |- |
| | | 2.3.5.7.11.13.17.19.23 |
| | | 81/80, 99/98, 121/120, 126/125, 153/152, 161/160, 169/168, 209/208 |
| | | {{mapping| 62 98 144 174 214 229 253 263 280 }} |
| | | +1.55 |
| | | 1.18 |
| | | 6.09 |
| | |} |
| | |
| | === 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 |
| | | 3\62 |
| | | 58.1 |
| | | 27/26 |
| | | [[Hemisecordite]] |
| | |- |
| | | 1 |
| | | 7\62 |
| | | 135.5 |
| | | 13/12 |
| | | [[Doublethink]] |
| | |- |
| | | 1 |
| | | 13\62 |
| | | 251.6 |
| | | 15/13 |
| | | [[Hemimeantone]] |
| | |- |
| | | 1 |
| | | 17\62 |
| | | 329.0 |
| | | 16/11 |
| | | [[Mabon]] |
| | |- |
| | | 1 |
| | | 29\62 |
| | | 561.3 |
| | | 18/13 |
| | | [[Demivalentine]] |
| | |- |
| | | 2 |
| | | 3\62 |
| | | 58.1 |
| | | 27/26 |
| | | [[Semihemisecordite]] |
| | |- |
| | | 2 |
| | | 4\62 |
| | | 77.4 |
| | | 21/20 |
| | | [[Semivalentine]] |
| | |- |
| | | 2 |
| | | 6\62 |
| | | 116.1 |
| | | 15/14 |
| | | [[Semimiracle]] |
| | |- |
| | | 2 |
| | | 26\62 |
| | | 503.2 |
| | | 4/3 |
| | | [[Semimeantone]] |
| | |- |
| | | 31 |
| | | 29\62<br>(1\62) |
| | | 561.3<br>(19.4) |
| | | 11/8<br>(196/195) |
| | | [[Kumhar]] (62e) |
| | |- |
| | | 31 |
| | | 19\62<br>(1\62) |
| | | 367.7<br>(19.4) |
| | | 16/13<br>(77/76) |
| | | [[Gallium]] |
| | |} |
| | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct |
| | |
| | == Instruments == |
| | |
| | === Lumatone === |
| | * [[Lumatone mapping for 62edo]] |
| | |
| | === Skip fretting === |
| | '''[[Skip fretting]] system 62 6 11''' has strings tuned 11\62 apart, while frets are 6\62. |
| | |
| | On a 4-string bass, here are your open strings: |
| | |
| | 0 11 22 33 |
| | |
| | A good supraminor 3rd is found on the 2nd string, 1st fret. A supermajor third is found on the open 3rd string. The major 6th can be found on the 4th string, 2nd fret. |
| | |
| | 5-string bass |
| | |
| | 51 0 11 22 33 |
| | |
| | This adds an interval of a major 7th (minus an 8ve) at the first string, 1st fret. |
| | |
| | 6-string guitar |
| | |
| | 0 11 22 33 44 55 |
| | |
| | ”Major” 020131 |
| | |
| | 7-string guitar |
| | |
| | 0 11 22 33 44 55 4 |
| | |
| | |
| | '''Skip fretting system 62 9 11''' is another 62edo skip fretting system. The 5th is on the 5th string. The major 3rd is on the 2nd string, 1st fret. |
| | {{todo|add illustration|text=Base it off of the diagram from [[User:MisterShafXen/Skip fretting system 62 9 11]]}} |
| | |
| | == Music == |
| | ; [[Bryan Deister]] |
| | * [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025) |