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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the [[Pythagorean_comma|Pythagorean comma]], 531441/524288 = |-19 12&gt;. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports [[Magic|magic]], [[Compton|compton]] and [[Tritonic|tritonic]] temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic_pairs#Bleu|bleu temperament]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:x31eq|x31eq]] and made on <tt>2014-08-31 10:15:16 UTC</tt>.<br>
: The original revision id was <tt>520246508</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">
The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the [[Pythagorean comma]], 531441/524288 = |-19 12&gt;. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports [[magic]], [[compton]] and [[tritonic]] temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic pairs#Bleu|bleu temperament]].


=Intervals=  
=Intervals=
|| degrees of 60edo || cents value || approximate ratios in the 2.3.5.13 subgroup || additional ratios of 7 and 11 (assuming flat values for primes) ||
|| 0 || 0 ||  ||  ||
|| 1 || 20 ||  ||  ||
|| 2 || 40 ||  ||  ||
|| 3 || 60 ||  ||  ||
|| 4 || 80 ||  ||  ||
|| 5 || 100 ||  ||  ||
|| 6 || 120 || 16/15 ||  ||
|| 7 || 140 ||  ||  ||
|| 8 || 160 ||  || 12/11, 11/10 ||
|| 9 || 180 || 10/9 ||  ||
|| 10 || 200 || 9/8 ||  ||
|| 11 || 220 ||  ||  ||
|| 12 || 240 || 15/13 || 8/7 ||
|| 13 || 260 ||  || 7/6 ||
|| 14 || 280 ||  ||  ||
|| 15 || 300 ||  ||  ||
|| 16 || 320 ||  ||  ||
|| 17 || 340 ||  || 11/9 ||
|| 18 || 360 || 16/13 ||  ||
|| 19 || 380 ||  ||  ||
|| 20 || 400 ||  ||  ||
|| 21 || 420 ||  || 14/11 ||
|| 22 || 440 ||  || 9/7 ||
|| 23 || 460 || 13/10 ||  ||
|| 24 || 480 ||  ||  ||
|| 25 || 500 || 4/3 ||  ||
|| 26 || 520 ||  ||  ||
|| 27 || 540 ||  || 11/8, 15/11 ||
|| 28 || 560 || 18/13 ||  ||
|| 29 || 580 ||  || 7/5 ||
|| 30 || 600 ||  ||  ||
|| 31 || 620 ||  || 10/7 ||
|| 32 || 640 || 13/8 ||  ||
|| 33 || 660 ||  || 16/11, 22/15 ||
|| 34 || 680 ||  ||  ||
|| 35 || 700 || 3/2 ||  ||
|| 36 || 720 ||  ||  ||
|| 37 || 740 || 20/13 ||  ||
|| 38 || 760 ||  || 14/9 ||
|| 39 || 780 ||  || 11/7 ||
|| 40 || 800 ||  ||  ||
|| 41 || 820 ||  ||  ||
|| 42 || 840 || 13/8 ||  ||
|| 43 || 860 ||  || 18/11 ||
|| 44 || 880 ||  ||  ||
|| 45 || 900 ||  ||  ||
|| 46 || 920 ||  ||  ||
|| 47 || 940 ||  || 12/7 ||
|| 48 || 960 || 26/15 || 7/4 ||
|| 49 || 980 ||  ||  ||
|| 50 || 1000 || 16/9 ||  ||
|| 51 || 1020 || 9/5 ||  ||
|| 52 || 1040 ||  || 11/6, 20/11 ||
|| 53 || 1060 ||  ||  ||
|| 54 || 1080 || 15/8 ||  ||
|| 55 || 1100 ||  ||  ||
|| 56 || 1120 ||  ||  ||
|| 57 || 1140 ||  ||  ||
|| 58 || 1160 ||  ||  ||
|| 59 || 1180 ||  ||  ||
|| 60 || 1200 ||  ||  ||


{| class="wikitable"
|-
| | degrees of 60edo
| | cents value
| | approximate ratios in the 2.3.5.13 subgroup
| | additional ratios of 7 and 11 (assuming flat values for primes)
|-
| | 0
| | 0
| |
| |
|-
| | 1
| | 20
| |
| |
|-
| | 2
| | 40
| |
| |
|-
| | 3
| | 60
| |
| |
|-
| | 4
| | 80
| |
| |
|-
| | 5
| | 100
| |
| |
|-
| | 6
| | 120
| | 16/15
| |
|-
| | 7
| | 140
| |
| |
|-
| | 8
| | 160
| |
| | 12/11, 11/10
|-
| | 9
| | 180
| | 10/9
| |
|-
| | 10
| | 200
| | 9/8
| |
|-
| | 11
| | 220
| |
| |
|-
| | 12
| | 240
| | 15/13
| | 8/7
|-
| | 13
| | 260
| |
| | 7/6
|-
| | 14
| | 280
| |
| |
|-
| | 15
| | 300
| |
| |
|-
| | 16
| | 320
| |
| |
|-
| | 17
| | 340
| |
| | 11/9
|-
| | 18
| | 360
| | 16/13
| |
|-
| | 19
| | 380
| |
| |
|-
| | 20
| | 400
| |
| |
|-
| | 21
| | 420
| |
| | 14/11
|-
| | 22
| | 440
| |
| | 9/7
|-
| | 23
| | 460
| | 13/10
| |
|-
| | 24
| | 480
| |
| |
|-
| | 25
| | 500
| | 4/3
| |
|-
| | 26
| | 520
| |
| |
|-
| | 27
| | 540
| |
| | 11/8, 15/11
|-
| | 28
| | 560
| | 18/13
| |
|-
| | 29
| | 580
| |
| | 7/5
|-
| | 30
| | 600
| |
| |
|-
| | 31
| | 620
| |
| | 10/7
|-
| | 32
| | 640
| | 13/8
| |
|-
| | 33
| | 660
| |
| | 16/11, 22/15
|-
| | 34
| | 680
| |
| |
|-
| | 35
| | 700
| | 3/2
| |
|-
| | 36
| | 720
| |
| |
|-
| | 37
| | 740
| | 20/13
| |
|-
| | 38
| | 760
| |
| | 14/9
|-
| | 39
| | 780
| |
| | 11/7
|-
| | 40
| | 800
| |
| |
|-
| | 41
| | 820
| |
| |
|-
| | 42
| | 840
| | 13/8
| |
|-
| | 43
| | 860
| |
| | 18/11
|-
| | 44
| | 880
| |
| |
|-
| | 45
| | 900
| |
| |
|-
| | 46
| | 920
| |
| |
|-
| | 47
| | 940
| |
| | 12/7
|-
| | 48
| | 960
| | 26/15
| | 7/4
|-
| | 49
| | 980
| |
| |
|-
| | 50
| | 1000
| | 16/9
| |
|-
| | 51
| | 1020
| | 9/5
| |
|-
| | 52
| | 1040
| |
| | 11/6, 20/11
|-
| | 53
| | 1060
| |
| |
|-
| | 54
| | 1080
| | 15/8
| |
|-
| | 55
| | 1100
| |
| |
|-
| | 56
| | 1120
| |
| |
|-
| | 57
| | 1140
| |
| |
|-
| | 58
| | 1160
| |
| |
|-
| | 59
| | 1180
| |
| |
|-
| | 60
| | 1200
| |
| |
|}
=Compositions=
[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html Rojqoq (So-Called Peace)] [http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3 play] by William Sethares
[http://youtu.be/1rrgmP9VYQU Skating On Thin Ice] [http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3 play]
[http://youtu.be/5GIZOYMkkJ0 My Mother Said So] [http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3 play]
[http://www.macjams.com/song/62273 Black Salt - White Pepper] [http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3 play]
[http://www.macjams.com/song/64413 NGC 300][http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3 play]


=Compositions=
[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html|Rojqoq (So-Called Peace)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3|play]] by William Sethares
[[http://youtu.be/1rrgmP9VYQU|Skating On Thin Ice]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3|play]]
[[http://youtu.be/5GIZOYMkkJ0|My Mother Said So]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3|play]]
[[http://www.macjams.com/song/62273|Black Salt - White Pepper]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3|play]]
[[http://www.macjams.com/song/64413|NGC 300]][[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3|play]]
all by Robin Perry
all by Robin Perry
[[http://x31eq.com/music/dingshi.mp3|Dingshi]] and
 
[[http://x31eq.com/music/jitter.ogg|Gene's Jitterbug (ogg)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3|Gene's Jitterbug (mp3)]] [[http://x31eq.com/music/jitter60.pdf|Score]]
[http://x31eq.com/music/dingshi.mp3 Dingshi] and
 
[http://x31eq.com/music/jitter.ogg Gene's Jitterbug (ogg)] [http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3 Gene's Jitterbug (mp3)] [http://x31eq.com/music/jitter60.pdf Score]
 
by Graham Breed
by Graham Breed


=Images=  
=Images=
[[image:60edo wheel with cents values.png width="560" height="560"]]
[[File:60edo_wheel_with_cents_values.png|alt=60edo wheel with cents values.png|560x560px|60edo wheel with cents values.png]]
[[image:blue_60edo.png]]


[[image:60edoguitar.jpg]]
[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]
Robin Perry guitar</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;60edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the &lt;a class="wiki_link" href="/Pythagorean%20comma"&gt;Pythagorean comma&lt;/a&gt;, 531441/524288 = |-19 12&amp;gt;. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports &lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt;, &lt;a class="wiki_link" href="/compton"&gt;compton&lt;/a&gt; and &lt;a class="wiki_link" href="/tritonic"&gt;tritonic&lt;/a&gt; temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 &lt;a class="wiki_link" href="/Chromatic%20pairs#Bleu"&gt;bleu temperament&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
[[File:60edoguitar.jpg|alt=60edoguitar.jpg|60edoguitar.jpg]]
    &lt;tr&gt;
        &lt;td&gt;degrees of 60edo&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;approximate ratios in the 2.3.5.13 subgroup&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;additional ratios of 7 and 11 (assuming flat values for primes)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;140&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;160&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11, 11/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;180&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;220&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;240&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;260&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;280&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;340&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;360&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;400&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;420&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;460&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;480&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;500&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;520&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8, 15/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;580&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;620&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;640&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;660&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11, 22/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;680&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;700&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;720&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;740&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;760&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;780&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;800&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;820&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;860&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;880&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;900&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;920&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;940&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;960&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;980&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1020&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1040&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6, 20/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1060&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1080&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1140&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1160&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1180&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
Robin Perry guitar
&lt;br /&gt;
[[Category:60edo]]
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Compositions&lt;/h1&gt;
[[Category:edo]]
&lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html" rel="nofollow"&gt;Rojqoq (So-Called Peace)&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3" rel="nofollow"&gt;play&lt;/a&gt; by William Sethares&lt;br /&gt;
[[Category:listen]]
&lt;a class="wiki_link_ext" href="http://youtu.be/1rrgmP9VYQU" rel="nofollow"&gt;Skating On Thin Ice&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://youtu.be/5GIZOYMkkJ0" rel="nofollow"&gt;My Mother Said So&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.macjams.com/song/62273" rel="nofollow"&gt;Black Salt - White Pepper&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.macjams.com/song/64413" rel="nofollow"&gt;NGC 300&lt;/a&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
all by Robin Perry&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://x31eq.com/music/dingshi.mp3" rel="nofollow"&gt;Dingshi&lt;/a&gt; and&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://x31eq.com/music/jitter.ogg" rel="nofollow"&gt;Gene's Jitterbug (ogg)&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3" rel="nofollow"&gt;Gene's Jitterbug (mp3)&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/music/jitter60.pdf" rel="nofollow"&gt;Score&lt;/a&gt;&lt;br /&gt;
by Graham Breed&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Images"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Images&lt;/h1&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:628:&amp;lt;img src=&amp;quot;/file/view/60edo%20wheel%20with%20cents%20values.png/516676902/560x560/60edo%20wheel%20with%20cents%20values.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 560px; width: 560px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/60edo%20wheel%20with%20cents%20values.png/516676902/560x560/60edo%20wheel%20with%20cents%20values.png" alt="60edo wheel with cents values.png" title="60edo wheel with cents values.png" style="height: 560px; width: 560px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:628 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:629:&amp;lt;img src=&amp;quot;/file/view/blue_60edo.png/284591332/blue_60edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/blue_60edo.png/284591332/blue_60edo.png" alt="blue_60edo.png" title="blue_60edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:629 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:630:&amp;lt;img src=&amp;quot;/file/view/60edoguitar.jpg/312533826/60edoguitar.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/60edoguitar.jpg/312533826/60edoguitar.jpg" alt="60edoguitar.jpg" title="60edoguitar.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:630 --&gt;&lt;br /&gt;
Robin Perry guitar&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the Pythagorean comma, 531441/524288 = |-19 12>. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 bleu temperament.

Intervals

degrees of 60edo cents value approximate ratios in the 2.3.5.13 subgroup additional ratios of 7 and 11 (assuming flat values for primes)
0 0
1 20
2 40
3 60
4 80
5 100
6 120 16/15
7 140
8 160 12/11, 11/10
9 180 10/9
10 200 9/8
11 220
12 240 15/13 8/7
13 260 7/6
14 280
15 300
16 320
17 340 11/9
18 360 16/13
19 380
20 400
21 420 14/11
22 440 9/7
23 460 13/10
24 480
25 500 4/3
26 520
27 540 11/8, 15/11
28 560 18/13
29 580 7/5
30 600
31 620 10/7
32 640 13/8
33 660 16/11, 22/15
34 680
35 700 3/2
36 720
37 740 20/13
38 760 14/9
39 780 11/7
40 800
41 820
42 840 13/8
43 860 18/11
44 880
45 900
46 920
47 940 12/7
48 960 26/15 7/4
49 980
50 1000 16/9
51 1020 9/5
52 1040 11/6, 20/11
53 1060
54 1080 15/8
55 1100
56 1120
57 1140
58 1160
59 1180
60 1200

Compositions

Rojqoq (So-Called Peace) play by William Sethares

Skating On Thin Ice play

My Mother Said So play

Black Salt - White Pepper play

NGC 300play

all by Robin Perry

Dingshi and

Gene's Jitterbug (ogg) Gene's Jitterbug (mp3) Score

by Graham Breed

Images

60edo wheel with cents values.png

blue_60edo.png

60edoguitar.jpg

Robin Perry guitar

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