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25ed5: Difference between revisions

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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>
'''[[Ed5|Division of the 5th harmonic]] into 25 equal parts''' (25ED5) was first used in [[wikipedia:Karlheinz Stockhausen|Stockhausen’s]] [[wikipedia:Studie II|Elektronische Studie II]]. The step size is about 111.4525 cents. This tuning is very similar to [[17edt|17ED3]] but compressed by several cents.
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:54:55 UTC</tt>.<br>
: The original revision id was <tt>268462284</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">25ed5


The 25th root of 5 was first used in Stockhausen’s Elektronische Studie II. It is very similar to [[17edt]] but compressed by several cents.</pre></div>
== Intervals ==
<h4>Original HTML content:</h4>
{| class="wikitable"
<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;25ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;25ed5&lt;br /&gt;
|-
&lt;br /&gt;
! | degree
The 25th root of 5 was first used in Stockhausen’s Elektronische Studie II. It is very similar to &lt;a class="wiki_link" href="/17edt"&gt;17edt&lt;/a&gt; but compressed by several cents.&lt;/body&gt;&lt;/html&gt;</pre></div>
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.0000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 111.4525
| | [[16/15]]
| |
|-
| | 2
| | 222.9051
| | [[25/22]], 33/29
| |
|-
| | 3
| | 334.3576
| | [[17/14]], 40/33
| |
|-
| | 4
| | 445.8102
| | [[22/17]]
| |
|-
| | 5
| | 557.2627
| | 40/29
| |
|-
| | 6
| | 668.7153
| | [[25/17]]
| |
|-
| | 7
| | 780.1678
| | [[11/7]], 80/51
| |
|-
| | 8
| | 891.6204
| | 176/105
| | pseudo-[[5/3]]
|-
| | 9
| | 1003.0729
| | [[25/14]]
| |
|-
| | 10
| | 1114.5255
| | [[40/21]]
| |
|-
| | 11
| | 1225.9780
| | [[65/64|65/32]], [[64/63|128/63]], <br>[[66/65|132/65]]
| |
|-
| | 12
| | 1337.4306
| | [[13/6]]
| |
|-
| | 13
| | 1448.8831
| | [[15/13|30/13]]
| |
|-
| | 14
| | 1560.3357
| | [[16/13|32/13]]
| |
|-
| | 15
| | 1671.7882
| | [[21/16|21/8]]
| |
|-
| | 16
| | 1783.2408
| | [[7/5|14/5]]
| |
|-
| | 17
| | 1894.6933
| | 224/75
| | pseudo-[[3/1]]
|-
| | 18
| | 2006.1459
| | 35/11, 51/16
| |
|-
| | 19
| | 2117.5984
| | [[17/10|17/5]]
| |
|-
| | 20
| | 2229.0510
| | [[29/16|29/8]]
| |
|-
| | 21
| | 2340.5035
| | 58/15, 85/22
| |
|-
| | 22
| | 2451.9561
| | [[33/32|33/8]], [[35/34|70/17]], <br>[[34/33|136/33]]
| |
|-
| | 23
| | 2563.4086
| | [[11/10|22/5]]
| |
|-
| | 24
| | 2674.8612
| | [[75/64|75/16]]
| |
|-
| | 25
| | 2786.3137
| | '''exact [[5/1]]'''
| | just major third plus two octaves
|}
 
== Harmonics ==
{{Harmonics in equal
| steps = 25
| num = 5
| denom = 1
}}
{{Harmonics in equal
| steps = 25
| num = 5
| denom = 1
| start = 12
| collapsed = 1
}}
 
== Related temperament ==
25de5 is strongly related to the 140 & 183 temperament ([[stockhausenic]]), which tempers out 703125/702464 ([[meter]]) and 4096000/4084101 (hemfiness comma) in the 7-limit; 1375/1372, 5632/5625, and 35937/35840 in the 11-limit; 676/675, 1001/1000, 1573/1568, and 4096/4095 in the 13-limit.
 
== Etymology ==
25ed5 is sometimes called "McLaren" or "Stockhausen" according to the main [[Ed5]] article. Stockhausen is named for Karlheinz Stockhausen who used this scale. McLaren might be named after [[Brian McLaren]].
 
== Music ==
[https://www.youtube.com/watch?v=bwj6ZptPnDo Studie II] - [[wikipedia:Karlheinz Stockhausen|Karlheinz Stockhausen]]
 
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/25ed5"