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}}

Latest revision as of 19:21, 1 August 2025

← 24ed5 25ed5 26ed5 →
Prime factorization 52
Step size 111.453 ¢ 
Octave 11\25ed5 (1225.98 ¢)
Twelfth 17\25ed5 (1894.69 ¢)
Consistency limit 3
Distinct consistency limit 3

Division of the 5th harmonic into 25 equal parts (25ED5) was first used in Stockhausen’s Elektronische Studie II. The step size is about 111.4525 cents. This tuning is very similar to 17ED3 but compressed by several cents.

Intervals

degree cents value corresponding
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 65/32, 128/63,
132/65
12 1337.4306 13/6
13 1448.8831 30/13
14 1560.3357 32/13
15 1671.7882 21/8
16 1783.2408 14/5
17 1894.6933 224/75 pseudo-3/1
18 2006.1459 35/11, 51/16
19 2117.5984 17/5
20 2229.0510 29/8
21 2340.5035 58/15, 85/22
22 2451.9561 33/8, 70/17,
136/33
23 2563.4086 22/5
24 2674.8612 75/16
25 2786.3137 exact 5/1 just major third plus two octaves

Harmonics

Approximation of harmonics in 25ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +26.0 -7.3 +52.0 +0.0 +18.7 -25.2 -33.5 -14.5 +26.0 -27.6 +44.7
Relative (%) +23.3 -6.5 +46.6 +0.0 +16.8 -22.7 -30.1 -13.0 +23.3 -24.7 +40.1
Steps
(reduced) 		11
(11) 		17
(17) 		22
(22) 		25
(0) 		28
(3) 		30
(5) 		32
(7) 		34
(9) 		36
(11) 		37
(12) 		39
(14)
Approximation of harmonics in 25ed5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +17.6 +0.7 -7.3 -7.5 -1.0 +11.5 +29.3 +52.0 -32.5 -1.6 +32.9
Relative (%) +15.8 +0.7 -6.5 -6.8 -0.9 +10.3 +26.3 +46.6 -29.2 -1.4 +29.5
Steps
(reduced) 		40
(15) 		41
(16) 		42
(17) 		43
(18) 		44
(19) 		45
(20) 		46
(21) 		47
(22) 		47
(22) 		48
(23) 		49
(24)

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

Studie II - Karlheinz Stockhausen

Retrieved from "https://en.xen.wiki/index.php?title=25ed5&oldid=205975"