60edo: Difference between revisions

Wikispaces>x31eq
**Imported revision 520246508 - Original comment: **
Notation: SZG notation
 
(107 intermediate revisions by 26 users not shown)
Line 1: Line 1:
<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: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=  
== Theory ==
|| 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) ||
Since {{nowrap| 60 {{=}} 5 × 12 }}, 60edo belongs to the family of edos which contain [[12edo]], and like the other small edos of this kind, it [[tempering out|tempers out]] the [[Pythagorean comma]], 531441/524288 ({{monzo| -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]]. In the [[7-limit]] it tempers out [[225/224]], [[245/243]], [[875/864]], and [[10976/10935]], and [[support]]s [[magic]], [[compton]] and [[tritonic]] temperaments. In the [[11-limit]], the 60e [[val]] {{val| 60 95 139 168 '''207''' }} scores lower in [[badness]] than the [[patent val]] {{val| 60 95 139 168 '''208''' }} 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 [[subgroup temperament]], it is also excellent for the 2.3.7.11.13-subgroup [[bleu]] temperament, using the 60d val.
|| 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 ||  ||  ||


=== Odd harmonics ===
{{Harmonics in equal|60}}


=Compositions=  
=== Subsets and supersets ===
[[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
60edo is the 9th [[highly composite edo]], with subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 }}. In addition, it is of largest consistency among highly composite edos for its size, being consistent in the 9-odd-limit, and all such edos all the way to [[27720edo]] are consistent in only at most 7-odd-limit.
[[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
[[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


=Images=
A step of 60edo is exactly 9 [[dexl]]s, or exactly 41 [[mina]]s.
[[image:60edo wheel with cents values.png width="560" height="560"]]
[[image:blue_60edo.png]]


[[image:60edoguitar.jpg]]
== Intervals ==
Robin Perry guitar</pre></div>
{| class="wikitable center-all right-2 left-3 left-4"
<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;
! Degrees
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;
! Cents
&lt;br /&gt;
! Approximate ratios<br>in the 2.3.5.7.13.17 subgroup
&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;
! Additional ratios<br>of 11 (tending flat, 60e val)
|-
| 0
| 0
| [[1/1]]
|
|-
| 1
| 20
| [[81/80]], ''[[49/48]]''
|
|-
| 2
| 40
| [[50/49]], ''[[64/63]]''
| ''[[33/32]]''
|-
| 3
| 60
| ''[[25/24]]'', [[28/27]], ''[[36/35]]''
|
|-
| 4
| 80
| [[21/20]]
|
|-
| 5
| 100
| [[17/16]], [[18/17]]
|
|-
| 6
| 120
| [[16/15]], [[15/14]], [[14/13]]
|
|-
| 7
| 140
| [[13/12]]
|
|-
| 8
| 160
|
| [[12/11]], [[11/10]]
|-
| 9
| 180
| [[10/9]]
|
|-
| 10
| 200
| [[9/8]]
|
|-
| 11
| 220
| [[17/15]]
|
|-
| 12
| 240
| [[8/7]], [[15/13]]
|
|-
| 13
| 260
| [[7/6]]
|
|-
| 14
| 280
| [[20/17]]
| [[33/28]]
|-
| 15
| 300
| [[32/27]]
| ''[[13/11]]''
|-
| 16
| 320
| [[6/5]]
|
|-
| 17
| 340
| [[39/32]], [[17/14]]
| [[11/9]]
|-
| 18
| 360
| [[16/13]], [[21/17]]
| [[27/22]]
|-
| 19
| 380
| [[5/4]]
|
|-
| 20
| 400
| [[81/64]]
| ''[[33/26]]''
|-
| 21
| 420
|
| [[14/11]]
|-
| 22
| 440
| [[9/7]]
| [[22/17]]
|-
| 23
| 460
| ''[[21/16]]'', [[13/10]], [[17/13]]
|
|-
| 24
| 480
|
|
|-
| 25
| 500
| [[4/3]]
|
|-
| 26
| 520
| [[27/20]]
|
|-
| 27
| 540
|
| ''[[11/8]]'', [[15/11]]
|-
| 28
| 560
| [[18/13]]
|
|-
| 29
| 580
| [[7/5]]
|
|-
| 30
| 600
| [[17/12]], [[24/17]]
|
|-
| 31
| 620
| [[10/7]]
|
|-
| 32
| 640
| [[13/9]]
|
|-
| 33
| 660
|
| ''[[16/11]]'', [[22/15]]
|-
| 34
| 680
| [[40/27]]
|
|-
| 35
| 700
| [[3/2]]
|
|-
| 36
| 720
|
|
|-
| 37
| 740
| ''[[32/21]]'', [[20/13]], [[26/17]]
|
|-
| 38
| 760
| [[14/9]]
| [[17/11]]
|-
| 39
| 780
|
| [[11/7]]
|-
| 40
| 800
| [[128/81]]
| ''[[52/33]]''
|-
| 41
| 820
| [[8/5]]
|
|-
| 42
| 840
| [[13/8]], [[34/21]]
| [[44/27]]
|-
| 43
| 860
| [[64/39]], [[28/17]]
| [[18/11]]
|-
| 44
| 880
| [[5/3]]
|
|-
| 45
| 900
| [[27/16]]
| ''[[22/13]]''
|-
| 46
| 920
| [[17/10]]
| [[56/33]]
|-
| 47
| 940
| [[12/7]]
|
|-
| 48
| 960
| [[7/4]], [[26/15]]
|
|-
| 49
| 980
| [[30/17]]
|
|-
| 50
| 1000
| [[16/9]]
|
|-
| 51
| 1020
| [[9/5]]
|
|-
| 52
| 1040
|
| [[11/6]], [[20/11]]
|-
| 53
| 1060
| [[24/13]]
|
|-
| 54
| 1080
| [[15/8]], [[28/15]], [[13/7]]
|
|-
| 55
| 1100
| [[17/9]], [[32/17]]
|
|-
| 56
| 1120
| [[40/21]]
|
|-
| 57
| 1140
| ''[[48/25]]'', [[27/14]], ''[[35/18]]''
|
|-
| 58
| 1160
| [[49/25]], ''[[63/32]]''
| ''[[64/33]]''
|-
| 59
| 1180
| [[160/81]], ''[[96/49]]''
|
|-
| 60
| 1200
| [[2/1]]
|
|}


&lt;table class="wiki_table"&gt;
== Notation ==
    &lt;tr&gt;
=== Stein–Zimmermann–Gould notation ===
        &lt;td&gt;degrees of 60edo&lt;br /&gt;
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
&lt;/td&gt;
{{Sharpness-sharp5-szg|60}}
        &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;
=== Kite's ups and downs notation ===
&lt;br /&gt;
60edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
&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;
{{Sharpness-sharp5a}}
&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;
 
&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;
=== Sagittal notation ===
&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;
This notation is a superset of the notations for edos [[12edo #Sagittal notation|12]] and [[6edo #Sagittal notation|6]].
&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;
==== Evo flavor ====
all by Robin Perry&lt;br /&gt;
<imagemap>
&lt;a class="wiki_link_ext" href="http://x31eq.com/music/dingshi.mp3" rel="nofollow"&gt;Dingshi&lt;/a&gt; and&lt;br /&gt;
File:60-EDO_Evo_Sagittal.svg
&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;
desc none
by Graham Breed&lt;br /&gt;
rect 80 0 300 50 [[Sagittal_notation]]
&lt;br /&gt;
rect 300 0 655 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
&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;
rect 20 80 190 106 [[45927/45056]]
&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;
rect 190 80 310 106 [[46/45]]
&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;
default [[File:60-EDO_Evo_Sagittal.svg]]
&lt;br /&gt;
</imagemap>
&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>
==== Revo flavor ====
<imagemap>
File:60-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 628 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 190 106 [[45927/45056]]
rect 190 80 310 106 [[46/45]]
default [[File:60-EDO_Revo_Sagittal.svg]]
</imagemap>
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals|60}}
{{Q-odd-limit intervals|59.9|apx=val|header=none|tag=none|title=15-odd-limit intervals by 60e val mapping}}
 
== Regular temperament properties ==
Multiple vals are listed since they all provide good temperaments.
 
{| 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
| 3125/3072, 531441/524288
| {{mapping| 60 95 139 }}
| +1.32
| 1.11
| 5.56
|-
| 2.3.5.7
| 225/224, 245/243, 64827/64000
| {{mapping| 60 95 139 168 }}
| +1.78
| 1.25
| 6.23
|-
| 2.3.5.7.13
| 105/104, 196/195, 245/243, 8281/8192
| {{mapping| 60 95 139 168 222 }}
| +1.45
| 1.29
| 6.46
|-style="border-top: double;"
| 2.3.5.7.11
| 121/120, 225/224, 245/243, 441/440
| {{mapping| 60 95 139 168 207 }} (60e)
| +2.08
| 1.27
| 6.33
|-
| 2.3.5.7.11.13
| 105/104, 121/120, 196/195, 275/273, 325/324
| {{mapping| 60 95 139 168 207 222 }} (60e)
| +1.75
| 1.36
| 6.80
|-style="border-top: double;"
| 2.3.5.7.11
| 100/99, 225/224, 385/384, 3087/3025
| {{mapping| 60 95 139 168 208 }} (60)
| +0.91
| 2.05
| 10.22
|-
| 2.3.5.7.11.13
| 100/99, 105/104, 144/143, 196/195, 1352/1331
| {{mapping| 60 95 139 168 208 222 }} (60)
| +0.79
| 1.89
| 9.44
|}
 
=== 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
| 7\60
| 140.0
| 13/12
| [[Quintannic]] (60e)
|-
| 1
| 13\60
| 260.0
| 7/6
| [[Superpelog]] (7-limit, 60bbccdd)
|-
| 1
| 17\60
| 340.0
| 39/32
| [[Houborizic]] (60) / [[houbor]] (60e)
|-
| 1
| 19\60
| 380.0
| 5/4
| [[Magic]] (60) / [[Magic_extensions#Witchcraft|witchcraft]] (60e)
|-
| 1
| 29\60
| 580.0
| 7/5
| [[Tritonic]] (60e) / [[tritoni]] (60)
|-
| 2
| 1\60
| 20.0
| 81/80
| [[Bicommatic]] (60e)
|-
| 2
| 7\60
| 140.0
| 13/12
| [[Fifive]] / [[fifives]] (60)
|-
| 2
| 19\60<br>(11\60)
| 380.0<br>(220.0)
| 5/4<br>(25/22)
| [[Astrology]] (60de) / [[divination]] (60e)
|-
| 2
| 13\60
| 260.0
| 7/6
| [[Bamity]] (11-limit, 60e)
|-
| 3
| 7\60
| 140.0
| 243/224
| [[Septichrome]]
|-
| 5
| 19\60<br>(5\60)
| 380.0<br>(100.0)
| 5/4<br>(256/245)
| [[Warlock]]
|-
| 5
| 25\60<br>(1\60)
| 500.0<br>(20.0)
| 4/3<br>(81/80)
| [[Quintile]] (60)
|-
| 6
| 17\60<br>(3\60)
| 340.0<br>(60.0)
| 375/308<br>(1760/1701)
| [[Semiseptichrome]] (11-limit, 60e)
|-
| 10
| 25\60<br>(1\60)
| 500.0<br>(20.0)
| 4/3<br>(91/90)
| [[Decile]] (60e)<br>[[Decic]] (60) / [[splendecic]] (60e) / [[prodecic]] (60e)
|-
| 12
| 19\60<br>(1\60)
| 380.0<br>(20.0)
| 5/4<br>(81/80)
| [[Compton]] / [[comptone]] (60e)
|-
| 12
| 12\60<br>(2\60)
| 240.0<br>(40.0)
| 8/7<br>(40/39)
| [[Catnip]] (60cf)
|-
| 15
| 25\60<br>(3\60)
| 500.0<br>(20.0)
| 4/3<br>(126/125)
| [[Pentadecal]] (60) / [[Cloudy_clan#Quindeca|quindecal]] (60e)
|-
| 20
| 25\60<br>(2\60)
| 500.0<br>(20.0)
| 4/3<br>(99/98)
| [[Degrees]] (60e)
|}
<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
 
== Diagrams ==
[[File:60edo_wheel_with_cents_values.png|alt=60edo wheel with cents values.png|560x560px|60edo wheel with cents values.png]] {{todo|annotate}}
 
[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]
 
== Octave stretch or compression ==
What follows is a comparison of compressed- and stretched-octave 60edo tunings.
 
60edo can benefit from slightly [[stretched and compressed tuning|stretching the octave]], especially when using it as a no-11 17-limit equal temperament. With the right amount of stretch we can find better harmonics 3, 5, and 7 at the expense of somewhat less accurate approximations of 2 and 13. Tunings such as [[155ed6]], [[95edt]] or [[zpi|301zpi]] make good options for this.
 
== Scales ==
* [[5- to 10-tone scales in 60edo]]
* Amulet{{idiosyncratic}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5
* Approximations of [[gamelan]] scales:
** 5-tone pelog: 6 8 20 5 21
** 7-tone pelog: 6 8 12 8 5 14 7
** 5-tone slendro: 12 12 12 12 12
 
== Instruments ==
Due to its highly composite nature, 60edo has an unusually high number of ways it can be subdivided. This means it has multiple good [[skip-fretting]] systems which can be used to create stringed instruments with playable fret spacings that still span the full gamut. Probably the best of these is tuning a 20edo guitar to major thirds, as demonstrated by Robin Perry in the image below. This is very closely related to the [[Kite Guitar]], with tuning accuracy slightly worse in the 11-limit, but far better when ratios of 13, 17 & 19 are added.
 
[[File:60edoguitar.jpg|alt=60edoguitar.jpg|60edoguitar.jpg]]
 
* [[Skip fretting system 60 2 29]]
* [[Skip fretting system 60 3 19]]
* [[Skip fretting system 60 4 17]]
 
* [[Lumatone mapping for 60edo]]
 
== Music ==
; [[Graham Breed]]
* [http://x31eq.com/music/dingshi.mp3 ''Dingshi'']
* ''Gene's Jitterbug'' [http://x31eq.com/music/jitter.ogg (ogg)] [http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3 (mp3)] [http://x31eq.com/music/jitter60.pdf Score]
 
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/nlKHUDCR3pI ''60edo improv''] (2025-05-16)
* [https://www.youtube.com/shorts/VA_P26_3dTk ''60edo improv''] (2025-11-22)
 
; [[Robin Perry]]
* [https://youtu.be/1rrgmP9VYQU ''Skating On Thin Ice''] [http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3 play]
* [https://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]
 
; [[William Sethares]]
* [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]
 
; [[Randy Wells]]
* [https://www.youtube.com/watch?v=MuLl0UUhUK0 ''Absinthe Green'']
* [https://www.youtube.com/watch?v=CNkg1rQE8Zk ''The Well of Sensitivity'']
 
[[Category:Listen]]
[[Category:Catnip]]