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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:hearneg|hearneg]] and made on <tt>2014-01-21 01:07:05 UTC</tt>.<br>
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| : The original revision id was <tt>484173290</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>
| |
| <h4>Original Wikitext content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//130edo// divides the octave into 130 parts of size 9.231 cents each. It is the tenth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischismic. It also can be used to tune the rank-three temperament [[Breed family#Jove,%20aka%20Wonder|jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and 595/594 for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[Würschmidt family#Hemiw%FCrschmidt|hemiwürschmidt]] and [[Schismatic family#Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments#Harry|harry]] temperaments.
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| |
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| 7-limit commas: 2401/2400, 3136/3125, 19683/19600
| | == Theory == |
| | 130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s. |
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| |
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| 11-limit commas: 441/440, 540/539, 3136/3125, 4000/3993
| | As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]]. |
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| |
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| 13-limit commas: 3136/3125, 243/242, 441/440, 351/350, 364/363
| | === Prime harmonics === |
| | {{Harmonics in equal|130|columns=9}} |
| | {{Harmonics in equal|130|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 130edo (continued)}} |
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| |
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| 17-limit commas: 221/220, 364/363, 442/441, 595/594, 1275/1274, 4913/4875
| | === Subsets and supersets === |
| | Since 130 factors into 2 × 5 × 13, 130edo has subset edos {{EDOs| 2, 5, 10, 13, 26, and 65 }}. |
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| |
|
| ==Intervals==
| | [[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic. |
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| |
|
| || degree of 130edo || cents value || associated temperament || | | == Intervals == |
| || 0 || 0.00 || ||
| | {| class="wikitable center-all right-2 left-3" |
| || 1 || 9.23 || ||
| | |- |
| || 2 || 18.46 || ||
| | ! Degree |
| || 3 || 27.69 || ||
| | ! Cents |
| || 4 || 36.92 || ||
| | ! Approximate ratios |
| || 5 || 46.15 || ||
| | |- |
| || 6 || 55.38 || ||
| | | 0 |
| || 7 || 64.62 || ||
| | | 0.00 |
| || 8 || 73.85 || ||
| | | 1/1 |
| || 9 || 83.08 || [[Breedsmic temperaments#Harry|harry]] ||
| | |- |
| || 10 || 92.31 || ||
| | | 1 |
| || 11 || 101.54 || ||
| | | 9.23 |
| || 12 || 110.77 || ||
| | | ''126/125'', 144/143, 169/168, 176/175, 196/195, 225/224 |
| || 13 || 120 || ||
| | |- |
| || 14 || 129.23 || ||
| | | 2 |
| || 15 || 138.46 || ||
| | | 18.46 |
| || 16 || 147.69 || ||
| | | 78/77, 81/80, 91/90, 99/98, 100/99, 105/104, 121/120 |
| || 17 || 156.92 || ||
| | |- |
| || 18 || 166.15 || ||
| | | 3 |
| || 19 || 175.38 || [[Schismatic family#Sesquiquartififths|sesquart]] ||
| | | 27.69 |
| || 20 || 184.62 || ||
| | | 56/55, 64/63, 65/64, 66/65 |
| || 21 || 193.85 || [[Würschmidt family#Hemiw%FCrschmidt|hemiwürschmidt]] ||
| | |- |
| || 22 || 203.08 || ||
| | | 4 |
| || 23 || 212.31 || ||
| | | 36.92 |
| || 24 || 221.54 || ||
| | | 45/44, 49/48, 50/49, ''55/54'' |
| || 25 || 230.77 || ||
| | |- |
| || 26 || 240 || ||
| | | 5 |
| || 27 || 249.23 || hemischismic ||
| | | 46.15 |
| || 28 || 258.46 || ||
| | | 36/35, 40/39 |
| || 29 || 267.69 || ||
| | |- |
| || 30 || 276.92 || ||
| | | 6 |
| || 31 || 286.15 || ||
| | | 55.38 |
| || 32 || 295.38 || ||
| | | 33/32 |
| || 33 || 304.62 || ||
| | |- |
| || 34 || 313.85 || ||
| | | 7 |
| || 35 || 323.08 || ||
| | | 64.62 |
| || 36 || 332.31 || ||
| | | 27/26, 28/27 |
| || 37 || 341.54 || ||
| | |- |
| || 38 || 350.77 || ||
| | | 8 |
| || 39 || 360 || ||
| | | 73.85 |
| || 40 || 369.23 || ||
| | | 25/24, 26/25 |
| || 41 || 378.46 || ||
| | |- |
| || 42 || 387.69 || ||
| | | 9 |
| || 43 || 396.92 || ||
| | | 83.08 |
| || 44 || 406.15 || ||
| | | 21/20, 22/21 |
| || 45 || 415.38 || ||
| | |- |
| || 46 || 424.62 || ||
| | | 10 |
| || 47 || 433.85 || ||
| | | 92.31 |
| || 48 || 443.08 || ||
| | | 135/128 |
| || 49 || 452.31 || ||
| | |- |
| || 50 || 461.54 || || | | | 11 |
| || 51 || 470.77 || || | | | 101.54 |
| || 52 || 480 || || | | | 35/33 |
| || 53 || 489.23 || || | | |- |
| || 54 || 498.46 || ||
| | | 12 |
| || 55 || 507.69 || || | | | 110.77 |
| || 56 || 516.92 || || | | | 16/15 |
| || 57 || 526.15 || || | | |- |
| || 58 || 535.38 || || | | | 13 |
| || 59 || 544.62 || || | | | 120.00 |
| || 60 || 553.85 || || | | | 15/14 |
| || 61 || 563.08 || || | | |- |
| || 62 || 572.31 || || | | | 14 |
| || 63 || 581.54 || || | | | 129.23 |
| || 64 || 590.77 || || | | | 14/13 |
| || 65 || 600 || || | | |- |
| || 66 || 609.23 || || | | | 15 |
| || 67 || 618.46 || || | | | 138.46 |
| || 68 || 627.69 || || | | | 13/12 |
| || 69 || 636.92 || || | | |- |
| || 70 || 646.15 || || | | | 16 |
| || 71 || 655.38 || || | | | 147.69 |
| || 72 || 664.62 || || | | | 12/11 |
| || 73 || 673.85 || || | | |- |
| || 74 || 683.08 || || | | | 17 |
| || 75 || 692.31 || ||
| | | 156.92 |
| || 76 || 701.54 || ||
| | | 35/32 |
| || 77 || 710.77 || || | | |- |
| || 78 || 720 || || | | | 18 |
| || 79 || 729.23 || || | | | 166.15 |
| || 80 || 738.46 || || | | | 11/10 |
| || 81 || 747.69 || || | | |- |
| || 82 || 756.92 || || | | | 19 |
| || 83 || 766.15 || || | | | 175.38 |
| || 84 || 775.38 || || | | | 72/65 |
| || 85 || 784.62 || || | | |- |
| || 86 || 793.85 || || | | | 20 |
| || 87 || 803.08 || || | | | 184.62 |
| || 88 || 812.31 || || | | | 10/9 |
| || 89 || 821.54 || || | | |- |
| || 90 || 830.77 || || | | | 21 |
| || 91 || 840 || || | | | 193.85 |
| || 92 || 849.23 || ||
| | | 28/25 |
| || 93 || 858.46 || || | | |- |
| || 94 || 867.69 || || | | | 22 |
| || 95 || 876.92 || || | | | 203.08 |
| || 96 || 886.15 || || | | | 9/8 |
| || 97 || 895.38 || || | | |- |
| || 98 || 904.62 || || | | | 23 |
| || 99 || 913.85 || || | | | 212.31 |
| || 100 || 923.08 || || | | | 44/39 |
| || 101 || 932.31 || || | | |- |
| || 102 || 941.54 || || | | | 24 |
| || 103 || 950.77 || || | | | 221.54 |
| || 104 || 960 || || | | | 25/22 |
| || 105 || 969.23 || ||
| | |- |
| || 106 || 978.46 || || | | | 25 |
| || 107 || 987.69 || || | | | 230.77 |
| || 108 || 996.92 || || | | | 8/7 |
| || 109 || 1006.15 || || | | |- |
| || 110 || 1015.38 || || | | | 26 |
| || 111 || 1024.62 || || | | | 240.00 |
| || 112 || 1033.85 || || | | | 55/48 |
| || 113 || 1043.08 || || | | |- |
| || 114 || 1052.31 || ||
| | | 27 |
| || 115 || 1061.54 || ||
| | | 249.23 |
| || 116 || 1070.77 || ||
| | | 15/13 |
| || 117 || 1080 || || | | |- |
| || 118 || 1089.23 || || | | | 28 |
| || 119 || 1098.46 || || | | | 258.46 |
| || 120 || 1107.69 || || | | | 64/55 |
| || 121 || 1116.92 || || | | |- |
| || 122 || 1126.15 || ||
| | | 29 |
| || 123 || 1135.38 || ||
| | | 267.69 |
| || 124 || 1144.62 || || | | | 7/6 |
| || 125 || 1153.85 || ||
| | |- |
| || 126 || 1163.08 || || | | | 30 |
| || 127 || 1172.31 || || | | | 276.92 |
| || 128 || 1181.54 || || | | | 75/64 |
| || 129 || 1190.77 || || | | |- |
| | | 31 |
| | | 286.15 |
| | | 13/11 |
| | |- |
| | | 32 |
| | | 295.38 |
| | | 32/27 |
| | |- |
| | | 33 |
| | | 304.62 |
| | | 25/21 |
| | |- |
| | | 34 |
| | | 313.85 |
| | | 6/5 |
| | |- |
| | | 35 |
| | | 323.08 |
| | | 65/54 |
| | |- |
| | | 36 |
| | | 332.31 |
| | | 40/33 |
| | |- |
| | | 37 |
| | | 341.54 |
| | | 39/32 |
| | |- |
| | | 38 |
| | | 350.77 |
| | | 11/9, 27/22 |
| | |- |
| | | 39 |
| | | 360.00 |
| | | 16/13 |
| | |- |
| | | 40 |
| | | 369.23 |
| | | 26/21 |
| | |- |
| | | 41 |
| | | 378.46 |
| | | 56/45 |
| | |- |
| | | 42 |
| | | 387.69 |
| | | 5/4 |
| | |- |
| | | 43 |
| | | 396.92 |
| | | 44/35 |
| | |- |
| | | 44 |
| | | 406.15 |
| | | 81/64 |
| | |- |
| | | 45 |
| | | 415.38 |
| | | 14/11 |
| | |- |
| | | 46 |
| | | 424.62 |
| | | 32/25 |
| | |- |
| | | 47 |
| | | 433.85 |
| | | 9/7 |
| | |- |
| | | 48 |
| | | 443.08 |
| | | 84/65, 128/99 |
| | |- |
| | | 49 |
| | | 452.31 |
| | | 13/10 |
| | |- |
| | | 50 |
| | | 461.54 |
| | | 64/49, ''72/55'' |
| | |- |
| | | 51 |
| | | 470.77 |
| | | 21/16 |
| | |- |
| | | 52 |
| | | 480.00 |
| | | 33/25 |
| | |- |
| | | 53 |
| | | 489.23 |
| | | 65/49 |
| | |- |
| | | 54 |
| | | 498.46 |
| | | 4/3 |
| | |- |
| | | 55 |
| | | 507.69 |
| | | 75/56 |
| | |- |
| | | 56 |
| | | 516.92 |
| | | 27/20 |
| | |- |
| | | 57 |
| | | 526.15 |
| | | 65/48 |
| | |- |
| | | 58 |
| | | 535.38 |
| | | 15/11 |
| | |- |
| | | 59 |
| | | 544.62 |
| | | 48/35 |
| | |- |
| | | 60 |
| | | 553.85 |
| | | 11/8 |
| | |- |
| | | 61 |
| | | 563.08 |
| | | 18/13 |
| | |- |
| | | 62 |
| | | 572.31 |
| | | 25/18 |
| | |- |
| | | 63 |
| | | 581.54 |
| | | 7/5 |
| | |- |
| | | 64 |
| | | 590.77 |
| | | 45/32 |
| | |- |
| | | 65 |
| | | 600.00 |
| | | 99/70, 140/99 |
| | |- |
| | |… |
| | |… |
| | |… |
| | |} |
|
| |
|
| | == Notation == |
| | === Ups and downs notation === |
| | 130edo can be notated using [[Kite's ups and downs notation|ups and downs]] and quarter-tone accidentals: |
| | {{Ups and downs sharpness|130|true}} |
| | === Sagittal notation === |
| | 130edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan single-shaft|Spartan extension]], with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the [[243/242|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table: |
| | {| class="wikitable" data-darkreader-inline-color="" style="text-align: center;" |
| | ! colspan="2" |Steps |
| | !0 |
| | ! 1 |
| | ! 2 |
| | ! 3 |
| | ! 4 |
| | ! 5 |
| | ! 6 |
| | ! 7 |
| | ! 8 |
| | ! 9 |
| | ! 10 |
| | ! 11 |
| | ! 12 |
| | |- |
| | ! rowspan="3" |Symbol |
| | !Evo+SZ |
| | | rowspan="3" |<big>{{sagittal||//|}}</big> |
| | | rowspan="3" |<big>{{sagittal||(}}</big> |
| | | rowspan="3" |<big>{{sagittal|/|}}</big> |
| | | rowspan="3" |<big>{{sagittal||)}}</big> |
| | | rowspan="3" |<big>{{sagittal|//|}}</big> |
| | | rowspan="3" |<big>{{sagittal|/|)}}</big> |
| | |<big>{{Sagittal|t}}</big> |
| | |<small>{{Sagittal|t}}<big>{{sagittal||(}}</big></small> |
| | |<small>{{Sagittal|t}}<big>{{sagittal|/|}}</big></small> |
| | |<small>{{Sagittal|t}}<big>{{sagittal||)}}</big></small> |
| | |<small>{{Sagittal|t}}<big>{{sagittal|//|}}</big></small> |
| | |<small>{{Sagittal|t}}<big>{{sagittal|/|)}}</big></small> |
| | | rowspan="2" |<big>{{sagittal|#}}</big> |
| | |- |
| | !Evo |
| | | rowspan="2" |<big>{{sagittal|/|\}}</big> |
| | |<small>{{sagittal|#}}<big>{{sagittal|\!)}}</big></small> |
| | |<small>{{sagittal|#}}</small><small><big>{{sagittal|\\!}}</big></small> |
| | |<small>{{sagittal|#}}<big>{{sagittal|!)}}</big></small> |
| | |<small>{{sagittal|#}}<big>{{sagittal|\!}}</big></small> |
| | |<small>{{sagittal|#}}<big>{{sagittal|!(}}</big></small> |
| | |- |
| | !Revo |
| | |<big>{{sagittal|(|3=\}}</big> |
| | |<big>{{sagittal|)||(}}</big> |
| | |<big>{{sagittal|||)}}</big> |
| | |<big>{{sagittal|||\}}</big> |
| | |<big>{{sagittal|/||)}}</big> |
| | |<big>{{sagittal|/||\}}</big> |
| | |} |
|
| |
|
| ==Music==
| | Because it uses the entire Spartan extension, it allows no accidental enharmonic respellings. |
| [[http://www.archive.org/details/TheParadiseOfCantor|The Paradise of Cantor]] [[http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3|play]] by [[Gene Ward Smith]]</pre></div>
| |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>130edo</title></head><body><em>130edo</em> divides the octave into 130 parts of size 9.231 cents each. It is the tenth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> but not a gap edo. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischismic. It also can be used to tune the rank-three temperament <a class="wiki_link" href="/Breed%20family#Jove,%20aka%20Wonder">jove</a>, tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and 595/594 for the 17-limit. It gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit <a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%FCrschmidt">hemiwürschmidt</a> and <a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths">sesquart</a> and 13-limit <a class="wiki_link" href="/Breedsmic%20temperaments#Harry">harry</a> temperaments.<br />
| |
| <br />
| |
| 7-limit commas: 2401/2400, 3136/3125, 19683/19600<br />
| |
| <br />
| |
| 11-limit commas: 441/440, 540/539, 3136/3125, 4000/3993<br />
| |
| <br />
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| 13-limit commas: 3136/3125, 243/242, 441/440, 351/350, 364/363<br />
| |
| <br />
| |
| 17-limit commas: 221/220, 364/363, 442/441, 595/594, 1275/1274, 4913/4875<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h2>
| |
| <br />
| |
|
| |
|
| | == Approximation to JI == |
| | === Zeta peak index === |
| | {{ZPI |
| | | zpi = 796 |
| | | steps = 130.003910460506 |
| | | step size = 9.23049157328654 |
| | | tempered height = 10.355108 |
| | | pure height = 10.339572 |
| | | integral = 1.634018 |
| | | gap = 19.594551 |
| | | octave = 1199.96390452725 |
| | | consistent = 16 |
| | | distinct = 16 |
| | }} |
|
| |
|
| <table class="wiki_table">
| | == Regular temperament properties == |
| <tr>
| | {| class="wikitable center-4 center-5 center-6" |
| <td>degree of 130edo<br />
| | |- |
| </td>
| | ! rowspan="2" | [[Subgroup]] |
| <td>cents value<br />
| | ! rowspan="2" | [[Comma list]] |
| </td>
| | ! rowspan="2" | [[Mapping]] |
| <td>associated temperament<br />
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) |
| </td>
| | ! colspan="2" | Tuning error |
| </tr>
| | |- |
| <tr>
| | ! [[TE error|Absolute]] (¢) |
| <td>0<br />
| | ! [[TE simple badness|Relative]] (%) |
| </td>
| | |- |
| <td>0.00<br />
| | | 2.3.5.7 |
| </td>
| | | 2401/2400, 3136/3125, 19683/19600 |
| <td><br />
| | | {{Mapping| 130 206 302 365 }} |
| </td>
| | | −0.119 |
| </tr>
| | | 0.311 |
| <tr>
| | | 3.37 |
| <td>1<br />
| | |- |
| </td>
| | | 2.3.5.7.11 |
| <td>9.23<br />
| | | 243/242, 441/440, 3136/3125, 4000/3993 |
| </td>
| | | {{Mapping| 130 206 302 365 450 }} |
| <td><br />
| | | −0.241 |
| </td>
| | | 0.370 |
| </tr>
| | | 4.02 |
| <tr>
| | |- |
| <td>2<br />
| | | 2.3.5.7.11.13 |
| </td>
| | | 243/242, 351/350, 364/363, 441/440, 3136/3125 |
| <td>18.46<br />
| | | {{Mapping| 130 206 302 365 450 481 }} |
| </td>
| | | −0.177 |
| <td><br />
| | | 0.367 |
| </td>
| | | 3.98 |
| </tr>
| | |} |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>27.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>36.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>46.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>55.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>64.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>73.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>83.08<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Breedsmic%20temperaments#Harry">harry</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>92.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>101.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>110.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>120<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>129.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>138.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>147.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>156.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>166.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
| |
| <td>175.38<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths">sesquart</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>184.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>193.85<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%FCrschmidt">hemiwürschmidt</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>203.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>212.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>221.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>230.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>240<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>249.23<br />
| |
| </td>
| |
| <td>hemischismic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>258.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>267.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>276.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td>286.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>295.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>304.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>313.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
| |
| </td>
| |
| <td>323.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td>332.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td>341.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38<br />
| |
| </td>
| |
| <td>350.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>360<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td>369.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41<br />
| |
| </td>
| |
| <td>378.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td>387.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>396.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>406.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>415.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>424.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td>433.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td>443.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>452.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>461.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>51<br />
| |
| </td>
| |
| <td>470.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>480<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>489.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>498.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>507.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56<br />
| |
| </td>
| |
| <td>516.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>57<br />
| |
| </td>
| |
| <td>526.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>58<br />
| |
| </td>
| |
| <td>535.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>59<br />
| |
| </td>
| |
| <td>544.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>60<br />
| |
| </td>
| |
| <td>553.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>61<br />
| |
| </td>
| |
| <td>563.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>62<br />
| |
| </td>
| |
| <td>572.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>63<br />
| |
| </td>
| |
| <td>581.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>64<br />
| |
| </td>
| |
| <td>590.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>65<br />
| |
| </td>
| |
| <td>600<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>66<br />
| |
| </td>
| |
| <td>609.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>67<br />
| |
| </td>
| |
| <td>618.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>68<br />
| |
| </td>
| |
| <td>627.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>69<br />
| |
| </td>
| |
| <td>636.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>70<br />
| |
| </td>
| |
| <td>646.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>71<br />
| |
| </td>
| |
| <td>655.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>72<br />
| |
| </td>
| |
| <td>664.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>73<br />
| |
| </td>
| |
| <td>673.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>74<br />
| |
| </td>
| |
| <td>683.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>75<br />
| |
| </td>
| |
| <td>692.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>76<br />
| |
| </td>
| |
| <td>701.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>77<br />
| |
| </td>
| |
| <td>710.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>78<br />
| |
| </td>
| |
| <td>720<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>79<br />
| |
| </td>
| |
| <td>729.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>80<br />
| |
| </td>
| |
| <td>738.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>81<br />
| |
| </td>
| |
| <td>747.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>82<br />
| |
| </td>
| |
| <td>756.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>83<br />
| |
| </td>
| |
| <td>766.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>84<br />
| |
| </td>
| |
| <td>775.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>85<br />
| |
| </td>
| |
| <td>784.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>86<br />
| |
| </td>
| |
| <td>793.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>87<br />
| |
| </td>
| |
| <td>803.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>88<br />
| |
| </td>
| |
| <td>812.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>89<br />
| |
| </td>
| |
| <td>821.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>90<br />
| |
| </td>
| |
| <td>830.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>91<br />
| |
| </td>
| |
| <td>840<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>92<br />
| |
| </td>
| |
| <td>849.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>93<br />
| |
| </td>
| |
| <td>858.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>94<br />
| |
| </td>
| |
| <td>867.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>95<br />
| |
| </td>
| |
| <td>876.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>96<br />
| |
| </td>
| |
| <td>886.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>97<br />
| |
| </td>
| |
| <td>895.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>98<br />
| |
| </td>
| |
| <td>904.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>99<br />
| |
| </td>
| |
| <td>913.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>100<br />
| |
| </td>
| |
| <td>923.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>101<br />
| |
| </td>
| |
| <td>932.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>102<br />
| |
| </td>
| |
| <td>941.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>103<br />
| |
| </td>
| |
| <td>950.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>104<br />
| |
| </td>
| |
| <td>960<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>105<br />
| |
| </td>
| |
| <td>969.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>106<br />
| |
| </td>
| |
| <td>978.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>107<br />
| |
| </td>
| |
| <td>987.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>108<br />
| |
| </td>
| |
| <td>996.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>109<br />
| |
| </td>
| |
| <td>1006.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>110<br />
| |
| </td>
| |
| <td>1015.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>111<br />
| |
| </td>
| |
| <td>1024.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>112<br />
| |
| </td>
| |
| <td>1033.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>113<br />
| |
| </td>
| |
| <td>1043.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>114<br />
| |
| </td>
| |
| <td>1052.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>115<br />
| |
| </td>
| |
| <td>1061.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>116<br />
| |
| </td>
| |
| <td>1070.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>117<br />
| |
| </td>
| |
| <td>1080<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>118<br />
| |
| </td>
| |
| <td>1089.23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>119<br />
| |
| </td>
| |
| <td>1098.46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>120<br />
| |
| </td>
| |
| <td>1107.69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>121<br />
| |
| </td>
| |
| <td>1116.92<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>122<br />
| |
| </td>
| |
| <td>1126.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>123<br />
| |
| </td>
| |
| <td>1135.38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>124<br />
| |
| </td>
| |
| <td>1144.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>125<br />
| |
| </td>
| |
| <td>1153.85<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>126<br />
| |
| </td>
| |
| <td>1163.08<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>127<br />
| |
| </td>
| |
| <td>1172.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>128<br />
| |
| </td>
| |
| <td>1181.54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>129<br />
| |
| </td>
| |
| <td>1190.77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | === Rank-2 temperaments === |
| <br />
| | Note: temperaments supported by [[65edo|65et]] are not included. |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h2>
| | |
| <a class="wiki_link_ext" href="http://www.archive.org/details/TheParadiseOfCantor" rel="nofollow">The Paradise of Cantor</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a></body></html></pre></div>
| | {| 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\130 |
| | | 27.69 |
| | | 64/63 |
| | | [[Arch]] |
| | |- |
| | | 1 |
| | | 7\130 |
| | | 64.62 |
| | | 26/25 |
| | | [[Rectified hebrew]] |
| | |- |
| | | 1 |
| | | 9\130 |
| | | 83.08 |
| | | 21/20 |
| | | [[Sextilifourths]] |
| | |- |
| | | 1 |
| | | 19\130 |
| | | 175.38 |
| | | 72/65 |
| | | [[Sesquiquartififths]] / [[sesquart]] |
| | |- |
| | | 1 |
| | | 21\130 |
| | | 193.85 |
| | | 28/25 |
| | | [[Hemiwürschmidt]] |
| | |- |
| | | 1 |
| | | 27\130 |
| | | 249.23 |
| | | 15/13 |
| | | [[Hemischis]] |
| | |- |
| | | 1 |
| | | 41\130 |
| | | 378.46 |
| | | 56/45 |
| | | [[Subpental]] |
| | |- |
| | | 2 |
| | | 6\130 |
| | | 55.38 |
| | | 33/32 |
| | | [[Septisuperfourth]] |
| | |- |
| | | 2 |
| | | 9\130 |
| | | 83.08 |
| | | 21/20 |
| | | [[Harry]] |
| | |- |
| | | 2 |
| | | 17\130 |
| | | 156.92 |
| | | 35/32 |
| | | [[Bison]] |
| | |- |
| | | 2 |
| | | 19\130 |
| | | 175.38 |
| | | 448/405 |
| | | [[Bisesqui]] |
| | |- |
| | | 2 |
| | | 54\130<br>(11\130) |
| | | 498.46<br>(101.54) |
| | | 4/3<br>(35/33) |
| | | [[Bischismic]] |
| | |- |
| | | 5 |
| | | 27\130<br>(1\130) |
| | | 249.23<br>(9.23) |
| | | 81/70<br>(176/175) |
| | | [[Hemiquintile]] |
| | |- |
| | | 10 |
| | | 27\130<br>(1\130) |
| | | 249.23<br>(9.23) |
| | | 15/13<br>(176/175) |
| | | [[Decoid]] |
| | |- |
| | | 10 |
| | | 54\130<br>(2\130) |
| | | 498.46<br>(18.46) |
| | | 4/3<br>(81/80) |
| | | [[Decile]] |
| | |- |
| | | 26 |
| | | 54\130<br>(1\130) |
| | | 498.46<br>(9.23) |
| | | 4/3<br>(225/224) |
| | | [[Bosonic]] |
| | |} |
| | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |
| | |
| | == Scales == |
| | {| class="wikitable" |
| | |+ style="font-size: 105%;" | 14-tone temperament of "Narrative Wars"<br />as an example of using 130edo: |
| | |- |
| | ! Step |
| | ! Cents |
| | ! Distance to the nearest JI interval<br />(selected ratios) |
| | |- |
| | | 13 (13/130) |
| | | 120.000 |
| | | [[15/14]] (+0.557{{c}}) |
| | |- |
| | | 7 (20/130) |
| | | 184.615 |
| | | [[10/9]] (+2.211{{c}}) |
| | |- |
| | | 9 (29/130) |
| | | 267.692 |
| | | [[7/6]] (+0,821{{c}}) |
| | |- |
| | | 9 (38/130) |
| | | 350.769 |
| | | [[11/9]] (+3.361{{c}}) |
| | |- |
| | | 9 (47/130) |
| | | 433.846 |
| | | [[9/7]] (−1.238{{c}}) |
| | |- |
| | | 7 (54/130) |
| | | 498.462 |
| | | [[4/3]] (+0.417{{c}}) |
| | |- |
| | | 13 (67/130) |
| | | 618.462 |
| | | [[10/7]] (+0.974{{c}}) |
| | |- |
| | | 9 (76/130) |
| | | 701.538 |
| | | [[3/2]] (−0.417{{c}}) |
| | |- |
| | | 7 (83/130) |
| | | 766.154 |
| | | [[14/9]] (+1.238{{c}}) |
| | |- |
| | | 13 (96/130) |
| | | 886.154 |
| | | [[5/3]] (+1.795{{c}}) |
| | |- |
| | | 5 (101/130) |
| | | 932.308 |
| | | [[12/7]] (−0.821{{c}}) |
| | |- |
| | | 13 (114/130) |
| | | 1052.308 |
| | | [[11/6]] (+2.945{{c}}) |
| | |- |
| | | 7 (121/130) |
| | | 1116.923 |
| | | [[21/11]] (−2.540{{c}}) |
| | |- |
| | | 9 (130/130) |
| | | 1200.000 |
| | | [[Octave]] (2/1, 0{{c}}) |
| | |} |
| | |
| | == Instruments == |
| | [[Lumatone mapping for 130edo]] |
| | |
| | == Music == |
| | {{Catrel|130edo tracks}} |
| | |
| | ; [[birdshite stalactite]] |
| | * [https://www.youtube.com/watch?v=q41n5XI6YA4 ''wazzock''] (2024) |
| | |
| | ; [[Sevish]] |
| | * [https://www.youtube.com/watch?v=30UQVYWnsDU Narrative Wars] |
| | |
| | ; [[Gene Ward Smith]] |
| | * [https://www.archive.org/details/TheParadiseOfCantor ''The Paradise of Cantor''] [https://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] (2006) |
| | |
| | [[Category:Harry]] |
| | [[Category:Hemischis]] |
| | [[Category:Hemiwürschmidt]] |
| | [[Category:Listen]] |
| | [[Category:Sesquiquartififths]] |
| Prime factorization
|
2 × 5 × 13
|
| Step size
|
9.23077 ¢
|
| Fifth
|
76\130 (701.538 ¢) (→ 38\65)
|
| Semitones (A1:m2)
|
12:10 (110.8 ¢ : 92.31 ¢)
|
| Consistency limit
|
15
|
| Distinct consistency limit
|
15
|
130 equal divisions of the octave (abbreviated 130edo or 130ed2), also called 130-tone equal temperament (130tet) or 130 equal temperament (130et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 130 equal parts of about 9.23 ¢ each. Each step represents a frequency ratio of 21/130, or the 130th root of 2.
Theory
130edo is a zeta peak edo, a zeta peak integer edo, and a zeta integral edo but not a gap edo. It is distinctly consistent to the 15-odd-limit and is the first nontrivial edo to be consistent in the 14-odd-prime-sum-limit. It is also almost consistent in the no-29 31-odd-limit, missing 19/11 (50.5%), 25/19 (52.9%), 17/11 (64,4%), 25/17 (66.8%), and octave complements.
As an equal temperament, it tempers out 2401/2400, 3136/3125, 6144/6125, and 19683/19600 in the 7-limit; 243/242, 441/440, 540/539, and 4000/3993 in the 11-limit; and 351/350, 364/363, 676/675, 729/728, 1001/1000, 1575/1573, 1716/1715, 2080/2079, 4096/4095, and 4225/4224 in the 13-limit. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischis. It also can be used to tune the rank-3 temperament jove, tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and 595/594 for the 17-limit. It gives the optimal patent val for 11-limit hemiwürschmidt and sesquart and 13-limit harry.
Prime harmonics
Approximation of prime harmonics in 130edo
| Harmonic
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
19
|
23
|
| Error
|
Absolute (¢)
|
+0.00
|
-0.42
|
+1.38
|
+0.40
|
+2.53
|
-0.53
|
-3.42
|
-2.13
|
-0.58
|
| Relative (%)
|
+0.0
|
-4.5
|
+14.9
|
+4.4
|
+27.4
|
-5.7
|
-37.0
|
-23.1
|
-6.3
|
Steps
(reduced)
|
130
(0)
|
206
(76)
|
302
(42)
|
365
(105)
|
450
(60)
|
481
(91)
|
531
(11)
|
552
(32)
|
588
(68)
|
Approximation of prime harmonics in 130edo (continued)
| Harmonic
|
29
|
31
|
37
|
41
|
43
|
47
|
53
|
59
|
61
|
| Error
|
Absolute (¢)
|
+4.27
|
-0.42
|
-2.11
|
-4.45
|
-3.83
|
-0.89
|
+3.42
|
+2.37
|
+0.04
|
| Relative (%)
|
+46.2
|
-4.6
|
-22.9
|
-48.2
|
-41.4
|
-9.7
|
+37.0
|
+25.6
|
+0.4
|
Steps
(reduced)
|
632
(112)
|
644
(124)
|
677
(27)
|
696
(46)
|
705
(55)
|
722
(72)
|
745
(95)
|
765
(115)
|
771
(121)
|
Subsets and supersets
Since 130 factors into 2 × 5 × 13, 130edo has subset edos 2, 5, 10, 13, 26, and 65.
260edo, which divides the edostep in two, provides a strong correction for the 29th harmonic.
Intervals
| Degree
|
Cents
|
Approximate ratios
|
| 0
|
0.00
|
1/1
|
| 1
|
9.23
|
126/125, 144/143, 169/168, 176/175, 196/195, 225/224
|
| 2
|
18.46
|
78/77, 81/80, 91/90, 99/98, 100/99, 105/104, 121/120
|
| 3
|
27.69
|
56/55, 64/63, 65/64, 66/65
|
| 4
|
36.92
|
45/44, 49/48, 50/49, 55/54
|
| 5
|
46.15
|
36/35, 40/39
|
| 6
|
55.38
|
33/32
|
| 7
|
64.62
|
27/26, 28/27
|
| 8
|
73.85
|
25/24, 26/25
|
| 9
|
83.08
|
21/20, 22/21
|
| 10
|
92.31
|
135/128
|
| 11
|
101.54
|
35/33
|
| 12
|
110.77
|
16/15
|
| 13
|
120.00
|
15/14
|
| 14
|
129.23
|
14/13
|
| 15
|
138.46
|
13/12
|
| 16
|
147.69
|
12/11
|
| 17
|
156.92
|
35/32
|
| 18
|
166.15
|
11/10
|
| 19
|
175.38
|
72/65
|
| 20
|
184.62
|
10/9
|
| 21
|
193.85
|
28/25
|
| 22
|
203.08
|
9/8
|
| 23
|
212.31
|
44/39
|
| 24
|
221.54
|
25/22
|
| 25
|
230.77
|
8/7
|
| 26
|
240.00
|
55/48
|
| 27
|
249.23
|
15/13
|
| 28
|
258.46
|
64/55
|
| 29
|
267.69
|
7/6
|
| 30
|
276.92
|
75/64
|
| 31
|
286.15
|
13/11
|
| 32
|
295.38
|
32/27
|
| 33
|
304.62
|
25/21
|
| 34
|
313.85
|
6/5
|
| 35
|
323.08
|
65/54
|
| 36
|
332.31
|
40/33
|
| 37
|
341.54
|
39/32
|
| 38
|
350.77
|
11/9, 27/22
|
| 39
|
360.00
|
16/13
|
| 40
|
369.23
|
26/21
|
| 41
|
378.46
|
56/45
|
| 42
|
387.69
|
5/4
|
| 43
|
396.92
|
44/35
|
| 44
|
406.15
|
81/64
|
| 45
|
415.38
|
14/11
|
| 46
|
424.62
|
32/25
|
| 47
|
433.85
|
9/7
|
| 48
|
443.08
|
84/65, 128/99
|
| 49
|
452.31
|
13/10
|
| 50
|
461.54
|
64/49, 72/55
|
| 51
|
470.77
|
21/16
|
| 52
|
480.00
|
33/25
|
| 53
|
489.23
|
65/49
|
| 54
|
498.46
|
4/3
|
| 55
|
507.69
|
75/56
|
| 56
|
516.92
|
27/20
|
| 57
|
526.15
|
65/48
|
| 58
|
535.38
|
15/11
|
| 59
|
544.62
|
48/35
|
| 60
|
553.85
|
11/8
|
| 61
|
563.08
|
18/13
|
| 62
|
572.31
|
25/18
|
| 63
|
581.54
|
7/5
|
| 64
|
590.77
|
45/32
|
| 65
|
600.00
|
99/70, 140/99
|
| …
|
…
|
…
|
Notation
Ups and downs notation
130edo can be notated using ups and downs and quarter-tone accidentals:
| Step offset
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25
|
| Sharp symbol
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Flat symbol
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sagittal notation
130edo can be notated in Sagittal using the Spartan extension, with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the rastma is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
| Steps
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Symbol
|
Evo+SZ
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Evo
|
|
|
|
|
|
|
| Revo
|
|
|
|
|
|
|
Because it uses the entire Spartan extension, it allows no accidental enharmonic respellings.
Approximation to JI
Zeta peak index
| Tuning
|
Strength
|
Octave (cents)
|
Integer limit
|
| ZPI
|
Steps
per 8ve
|
Step size
(cents)
|
Height
|
Integral
|
Gap
|
Size
|
Stretch
|
Consistent
|
Distinct
|
| Tempered
|
Pure
|
| 796zpi
|
130.00391
|
9.230492
|
10.355108
|
10.339572
|
1.634018
|
19.594551
|
1199.963905
|
−0.036095
|
16
|
16
|
Regular temperament properties
| Subgroup
|
Comma list
|
Mapping
|
Optimal
8ve stretch (¢)
|
Tuning error
|
| Absolute (¢)
|
Relative (%)
|
| 2.3.5.7
|
2401/2400, 3136/3125, 19683/19600
|
[⟨130 206 302 365]]
|
−0.119
|
0.311
|
3.37
|
| 2.3.5.7.11
|
243/242, 441/440, 3136/3125, 4000/3993
|
[⟨130 206 302 365 450]]
|
−0.241
|
0.370
|
4.02
|
| 2.3.5.7.11.13
|
243/242, 351/350, 364/363, 441/440, 3136/3125
|
[⟨130 206 302 365 450 481]]
|
−0.177
|
0.367
|
3.98
|
Rank-2 temperaments
Note: temperaments supported by 65et are not included.
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct
Scales
14-tone temperament of "Narrative Wars"
as an example of using 130edo:
| Step
|
Cents
|
Distance to the nearest JI interval
(selected ratios)
|
| 13 (13/130)
|
120.000
|
15/14 (+0.557 ¢)
|
| 7 (20/130)
|
184.615
|
10/9 (+2.211 ¢)
|
| 9 (29/130)
|
267.692
|
7/6 (+0,821 ¢)
|
| 9 (38/130)
|
350.769
|
11/9 (+3.361 ¢)
|
| 9 (47/130)
|
433.846
|
9/7 (−1.238 ¢)
|
| 7 (54/130)
|
498.462
|
4/3 (+0.417 ¢)
|
| 13 (67/130)
|
618.462
|
10/7 (+0.974 ¢)
|
| 9 (76/130)
|
701.538
|
3/2 (−0.417 ¢)
|
| 7 (83/130)
|
766.154
|
14/9 (+1.238 ¢)
|
| 13 (96/130)
|
886.154
|
5/3 (+1.795 ¢)
|
| 5 (101/130)
|
932.308
|
12/7 (−0.821 ¢)
|
| 13 (114/130)
|
1052.308
|
11/6 (+2.945 ¢)
|
| 7 (121/130)
|
1116.923
|
21/11 (−2.540 ¢)
|
| 9 (130/130)
|
1200.000
|
Octave (2/1, 0 ¢)
|
Instruments
Lumatone mapping for 130edo
Music
- See also: Category:130edo tracks
- birdshite stalactite
- Sevish
- Gene Ward Smith
