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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-30 16:34:41 UTC</tt>.<br>
: The original revision id was <tt>239553053</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 Cube Root of the [[Perfect fourth]] ([[4_3|4:3]]) is a nonoctave scale which divides the just perfect fourth (frequency ratio 4:3) into three steps of approximately 166.015[[cent|¢]] each.


==Intervals==  
== Theory ==
=== Harmonics ===
{{Harmonics in equal|3|4|3|intervals=integer|columns=11}}
{{Harmonics in equal|3|4|3|intervals=integer|columns=11|start=12|collapsed=true|title=Approximation of harmonics in 3ed4/3 (continued)}}


|| degrees of CRP4 || cents value || cents value [[octave-reduce]]d ||
== Intervals ==
|| 0 || 0.00 ||  ||
{| class="wikitable"
|| 1 || 166.01 ||  ||
|-
|| 2 || 332.03 ||  ||
! #
|| 3 || 498.04 ||  ||
! Cents
|| 4 || 664.06 ||  ||
! Approximate ratios
|| 5 || 830.07 ||  ||
|-
|| 6 || 996.09 ||  ||
| 0
|| 7 || 1162.10 ||  ||
| 0.000
|| 8 || 1328.12 || 128.12 ||
| [[1/1]]
|| 9 || 1494.13 || 294.13 ||
|-
|| 10 || 1660.15 || 460.15 ||
| 1
|| 11 || 1826.16 || 626.16 ||
| 166.015
|| 12 || 1992.18 || 792.18 ||
| [[11/10]]
|| 13 || 2158.19 || 958.19 ||
|-
|| 14 || 2324.21 || 1124.21 ||
| 2
|| 15 || 2490.22 || 90.22 ||
| 332.030
|| 16 || 2656.24 || 256.24 ||
|  
|| 17 || 2822.25 || 422.25 ||
|-
|| 18 || 2988.27 || 588.27 ||
| 3
|| 19 || 3154.28 || 754.28 ||
| 498.045
|| 20 || 3320.30 || 920.30 ||
| [[4/3]]
|| 21 || 3486.31 || 1086.31 ||
|-
|| 22 || 3652.33 || 52.33 ||
| 4
|| 23 || 3818.34 || 218.34 ||</pre></div>
| 664.060
<h4>Original HTML content:</h4>
| [[22/15]]
<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;Cube Root of P4&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The Cube Root of the &lt;a class="wiki_link" href="/Perfect%20fourth"&gt;Perfect fourth&lt;/a&gt; (&lt;a class="wiki_link" href="/4_3"&gt;4:3&lt;/a&gt;) is a nonoctave scale which divides the just perfect fourth (frequency ratio 4:3) into three steps of approximately 166.015&lt;a class="wiki_link" href="/cent"&gt;¢&lt;/a&gt; each.&lt;br /&gt;
|-
&lt;br /&gt;
| 5
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals&lt;/h2&gt;
| 830.075
&lt;br /&gt;
| [[13/8]]
|-
| 6
| 996.090
| [[16/9]]
|-
| 7
| 1162.105
| 88/45
|-
| 8
| 1328.120
| [[13/6]]
|-
| 9
| 1494.135
| [[64/27]]
|-
| 10
| 1660.150
|  
|-
| 11
| 1826.165
| [[13/9]]
|-
| 12
| 1992.180
|  
|-
| 13
| 2158.195
|  
|-
| 14
| 2324.210
|  
|-
| 15
| 2490.225
| [[135/32]]
|-
| 16
| 2656.240
|  
|-
| 17
| 2822.255
|  
|-
| 18
| 2988.270
| [[45/8]]
|-
| 19
| 3154.285
|  
|-
| 20
| 3320.300
| [[17/5]]
|-
| 21
| 3486.315
| [[15/2]]
|-
| 22
| 3652.330
|  
|-
| 23
| 3818.345
| [[68/15]]
|-
| 24
| 3984.360
| [[10/1]]
|}


== Regular temperaments ==
3ed4/3 tuning is related to temperaments which temper out [[4000/3993]] (wizardharry temperament). The unit step of 3ed4/3 is approximately a cent sharp of [[11/10]]. Tempering out 4000/3993 leads equating three 11/10s with 4/3, hence wizardharry temperaments split the fourth in three.


&lt;table class="wiki_table"&gt;
Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads to [[porcupine]] (2.3.5.11 subgroup) or [[sonic]] (full 11-limit). Sonic temperaments include [[porcupine]], [[hystrix]], [[porky]], [[coendou]], [[hedgehog]], [[nautilus]], [[ammonite]], [[ceratitid]], and [[opossum]].
    &lt;tr&gt;
        &lt;td&gt;degrees of CRP4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value &lt;a class="wiki_link" href="/octave-reduce"&gt;octave-reduce&lt;/a&gt;d&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;0.00&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;166.01&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;332.03&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;498.04&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;664.06&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;830.07&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;996.09&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;1162.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1328.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128.12&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;1494.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;294.13&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;1660.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;460.15&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;1826.16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;626.16&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;1992.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;792.18&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;2158.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;958.19&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;2324.21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1124.21&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;2490.22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90.22&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;2656.24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;256.24&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;2822.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;422.25&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;2988.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;588.27&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;3154.28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;754.28&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;3320.30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;920.30&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;3486.31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1086.31&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;3652.33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;52.33&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;3818.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218.34&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[stearnscape]], [[pogo]], [[marvolo]], [[cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[escaped]], [[thuja]], and [[escapade]].
 
[[Category:Equal-step tuning]]
[[Category:Nonoctave]]
[[Category:Perfect fourth]]
Retrieved from "https://en.xen.wiki/w/3ed4/3"