|
|
| (12 intermediate revisions by 11 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = wolf fourth, classic acute fourth |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:48:49 UTC</tt>.<br>
| | | Color name = g4, gu 4th |
| : The original revision id was <tt>513256328</tt>.<br>
| | | Sound = jid_27_20_pluck_adu_dr220.mp3 |
| : 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">**27/20**
| |
| |-2 3 -1> | |
| 519.5513 cents
| |
| [[media type="file" key="jid_27_20_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_27_20_pluck_adu_dr220.mp3|sound sample]]
| |
|
| |
|
| In [[5-limit]] [[Just Intonation]], 27/20 is an interval measuring about 519.6¢. It differs from the [[4_3|4/3]] perfect fourth by [[81_80|81/80]] (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3_2|3/2]] perfect fifths, or as the interval between [[10_9|10/9]] and [[3_2|3/2]]. In [[12edo]] and [[meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls," as compared to simpler intervals within the 5-limit such as [[5_4|5/4]] and [[9_8|9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3. | | In [[5-limit]] [[just intonation]], '''27/20''', the '''classic acute fourth''', is an interval measuring about 519.6{{cent}}. It differs from the [[4/3]] perfect fourth by [[81/80]] (about 21.5{{cent}}), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3/2]] perfect fifths, or as the interval between [[10/9]] and [[3/2]]. In [[12edo]] and [[meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls", as compared to simpler intervals within the 5-limit such as [[5/4]] and [[9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3. |
| | == Approximation == |
| | {{Interval edo approximation|27/20}} |
|
| |
|
| See: [[Gallery of Just Intervals]]</pre></div>
| | == Trivia == |
| <h4>Original HTML content:</h4>
| | This ratio is the difference between two common record speeds (45 rpm and "33" rpm). As such, alterations by this interval often occur when a record is played at the wrong speed. |
| <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"><html><head><title>27_20</title></head><body><strong>27/20</strong><br />
| | |
| |-2 3 -1&gt;<br />
| | == See also == |
| 519.5513 cents<br />
| | * [[40/27]] – its [[octave complement]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_27_20_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_27_20_pluck_adu_dr220.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_27_20_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_27_20_pluck_adu_dr220.mp3/513250140/jid_27_20_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_27_20_pluck_adu_dr220.mp3/513250140/jid_27_20_pluck_adu_dr220.mp3');">sound sample</a><br />
| | * [[10/9]] – its [[fifth complement]] |
| <br />
| | * [[Gallery of just intervals]] |
| In <a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 27/20 is an interval measuring about 519.6¢. It differs from the <a class="wiki_link" href="/4_3">4/3</a> perfect fourth by <a class="wiki_link" href="/81_80">81/80</a> (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five <a class="wiki_link" href="/3_2">3/2</a> perfect fifths, or as the interval between <a class="wiki_link" href="/10_9">10/9</a> and <a class="wiki_link" href="/3_2">3/2</a>. In <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/meantone">meantone</a> systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a &quot;wolf&quot; interval, implying that it &quot;howls,&quot; as compared to simpler intervals within the 5-limit such as <a class="wiki_link" href="/5_4">5/4</a> and <a class="wiki_link" href="/9_8">9/8</a>. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.<br />
| | |
| <br />
| | [[Category:Fourth]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| |
In 5-limit just intonation, 27/20, the classic acute fourth, is an interval measuring about 519.6 ¢. It differs from the 4/3 perfect fourth by 81/80 (about 21.5 ¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five 3/2 perfect fifths, or as the interval between 10/9 and 3/2. In 12edo and meantone systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls", as compared to simpler intervals within the 5-limit such as 5/4 and 9/8. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.
Approximation
Edo approximations for 27/20 (519.55 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 7 |
3\7 |
514.29 |
-5.27 |
-3.07
|
| 14 |
6\14 |
514.29 |
-5.27 |
-6.14
|
| 16 |
7\16 |
525.00 |
+5.45 |
+7.26
|
| 21 |
9\21 |
514.29 |
-5.27 |
-9.21
|
| 23 |
10\23 |
521.74 |
+2.19 |
+4.19
|
| 30 |
13\30 |
520.00 |
+0.45 |
+1.12
|
| 37 |
16\37 |
518.92 |
-0.63 |
-1.95
|
| 44 |
19\44 |
518.18 |
-1.37 |
-5.02
|
| 46 |
20\46 |
521.74 |
+2.19 |
+8.39
|
| 51 |
22\51 |
517.65 |
-1.90 |
-8.09
|
| 53 |
23\53 |
520.75 |
+1.20 |
+5.32
|
| 60 |
26\60 |
520.00 |
+0.45 |
+2.24
|
| 67 |
29\67 |
519.40 |
-0.15 |
-0.83
|
| 74 |
32\74 |
518.92 |
-0.63 |
-3.90
|
| 76 |
33\76 |
521.05 |
+1.50 |
+9.51
|
Trivia
This ratio is the difference between two common record speeds (45 rpm and "33" rpm). As such, alterations by this interval often occur when a record is played at the wrong speed.
See also