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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>
'''23EDF''' is the [[EDF|equal division of the just perfect fifth]] into 23 parts of 30.5198 [[cents]] each, corresponding to 39.3188 [[edo]] (similar to every third step of [[118edo]]).
: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2015-06-13 05:23:10 UTC</tt>.<br>
: The original revision id was <tt>553808036</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">Twenty-three equal divisions of the perfect fifth (23ed3/2)


Rank 1 scale with step size of 30.52 cents.
==History==
Close to 39ed2 and/or 62ed3, however, the respective
A proponent of 23edf is [[Petr Pařízek]]. The first to write about 23edf on this wiki was [[Todd Harrop]] in 2015.
octave and twelfth would need to be nearly 10 cents flat.
A proponent of this scale is Petr Pařízek.


Some intervals in table below, selected on the basis of
==Theory==
single-use of primes (for most cases):
23edf is close to [[39edo]] and/or [[62edt]], however, the respective [[octave]] and [[tritave|twelfth]] would need to be nearly 10 cents flat.
||= **Step** ||= **Size**
**(cents)** ||= **Approx.**
**(JI) ratio** ||= **Error from**
**ratio (cents)** ||
||= 19 ||= 579.9 ||= 7/5 ||= –2.6¢ ||
||= 23 ||= 702 ||= 3/2 ||=  ||
||= 24 ||= 732.5 ||= 29/19 ||= +0.4¢ ||
||= 29 ||= 885.1 ||= 5/3 ||= +0.7¢ ||
||= 31 ||= 946.1 ||= 19/11 ||= –0.1¢ ||
||= 35 ||= 1068 ||= 13/7 ||= –3.5¢ ||
||= 46 ||= 1404 ||= 9/4 ||=  ||
||= 48 ||= 1465 ||= 7/3 ||= –1.9¢ ||
||= 52 ||= 1587 ||= 5/2 ||= +0.7¢ ||
||= 55 ||= 1679 ||= 29/11 ||= +0.3¢ ||
||= 58 ||= 1770 ||= 25/9 ||= +1.4¢ ||
||= 71 ||= 2167 ||= 7/2 ||= –1.9¢ ||
||=  ||=  ||=  ||=  ||
–Todd Harrop (June 2015)</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;23edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Twenty-three equal divisions of the perfect fifth (23ed3/2)&lt;br /&gt;
&lt;br /&gt;
Rank 1 scale with step size of 30.52 cents.&lt;br /&gt;
Close to 39ed2 and/or 62ed3, however, the respective&lt;br /&gt;
octave and twelfth would need to be nearly 10 cents flat.&lt;br /&gt;
A proponent of this scale is Petr Pařízek.&lt;br /&gt;
&lt;br /&gt;
Some intervals in table below, selected on the basis of&lt;br /&gt;
single-use of primes (for most cases):&lt;br /&gt;


Some intervals in table below, selected on the basis of single-use of [[prime]]s (for most cases):


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Step&lt;/strong&gt;&lt;br /&gt;
| style="text-align:center;" | '''Step'''
&lt;/td&gt;
| style="text-align:center;" | '''Size'''
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Size&lt;/strong&gt; &lt;br /&gt;
&lt;strong&gt;(cents)&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approx.&lt;/strong&gt; &lt;br /&gt;
&lt;strong&gt;(JI) ratio&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Error from&lt;/strong&gt; &lt;br /&gt;
&lt;strong&gt;ratio (cents)&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;579.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–2.6¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;702&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;732.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;+0.4¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;885.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;+0.7¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;946.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;19/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–0.1¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1068&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–3.5¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1404&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1465&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–1.9¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;52&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1587&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;+0.7¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1679&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;+0.3¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;58&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1770&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;25/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;+1.4¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2167&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–1.9¢&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


–Todd Harrop (June 2015)&lt;/body&gt;&lt;/html&gt;</pre></div>
'''(cents)'''
| style="text-align:center;" | '''Approx.'''
 
'''(JI) ratio'''
| style="text-align:center;" | '''Error from'''
 
'''ratio (cents)'''
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 579.9
| style="text-align:center;" | 7/5
| style="text-align:center;" | –2.6¢
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 702
| style="text-align:center;" | 3/2
| style="text-align:center;" |
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 732.5
| style="text-align:center;" | 29/19
| style="text-align:center;" | +0.4¢
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 885.1
| style="text-align:center;" | 5/3
| style="text-align:center;" | +0.7¢
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 946.1
| style="text-align:center;" | 19/11
| style="text-align:center;" | –0.1¢
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 1068
| style="text-align:center;" | 13/7
| style="text-align:center;" | –3.5¢
|-
| style="text-align:center;" | 46
| style="text-align:center;" | 1404
| style="text-align:center;" | 9/4
| style="text-align:center;" |
|-
| style="text-align:center;" | 48
| style="text-align:center;" | 1465
| style="text-align:center;" | 7/3
| style="text-align:center;" | –1.9¢
|-
| style="text-align:center;" | 52
| style="text-align:center;" | 1587
| style="text-align:center;" | 5/2
| style="text-align:center;" | +0.7¢
|-
| style="text-align:center;" | 55
| style="text-align:center;" | 1679
| style="text-align:center;" | 29/11
| style="text-align:center;" | +0.3¢
|-
| style="text-align:center;" | 58
| style="text-align:center;" | 1770
| style="text-align:center;" | 25/9
| style="text-align:center;" | +1.4¢
|-
| style="text-align:center;" | 71
| style="text-align:center;" | 2167
| style="text-align:center;" | 7/2
| style="text-align:center;" | –1.9¢
|}
 
=== Harmonics ===
{{Harmonics in equal|23|3|2}}
{{Harmonics in equal|23|3|2|start=12|collapsed=1}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 23edf
|-
!Step number
!Size (cents)
|-
|1
|30.5198
|-
|2
|61.0296
|-
|3
|91.55935
|-
|4
|122.0791
|-
|5
|152.5989
|-
|6
|183.1187
|-
|7
|213.6385
|-
|8
|244.1583
|-
|9
|274.678
|-
|10
|305.1978
|-
|11
|335.7176
|-
|12
|366.2374
|-
|13
|396.7572
|-
|14
|427.277
|-
|15
|457.7967
|-
|16
|488.3165
|-
|17
|518.8363
|-
|18
|549.3561
|-
|19
|579.8759
|-
|20
|610.39565
|-
|21
|640.9154
|-
|22
|671.4352
|-
|23
|701.955
|-
|24
|732.4748
|-
|25
|762.9946
|-
|26
|793.51435
|-
|27
|824.0341
|-
|28
|854.5539
|-
|29
|885.0737
|-
|30
|915.5935
|-
|31
|946.1133
|-
|32
|976.633
|-
|33
|1007.1529
|-
|34
|1037.6726
|-
|35
|1068.1924
|-
|36
|1098.7122
|-
|37
|1129.232
|-
|38
|1159.7517
|-
|39
|1190.2715
|-
|40
|1220.7913
|-
|41
|1251.3111
|-
|42
|1281.8309
|-
|43
|1312.35065
|-
|44
|1342.8704
|-
|45
|1373.3902
|-
|46
|1403.91
|}
{{todo|inline=1|complete table|text=Add at least one more column, showing what the notes are named, what JI they approximate, or anything else interesting about them individually.}}
 
 
{{todo|expand}}
[[Category:nonoctave]]
Retrieved from "https://en.xen.wiki/w/23edf"