|
|
| (19 intermediate revisions by 8 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 = septimal acute major seventh, small septimal diminished octave |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:40:06 UTC</tt>.<br>
| | | Color name = ry7, ruyo 7th |
| : The original revision id was <tt>513546128</tt>.<br>
| | | Sound = jid_40_21_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>
| | '''40/21''', the '''septimal acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. |
| <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">**40/21**
| | |
| |3 -1 1 -1>
| | == Terminology == |
| 1115.5328 cents
| | Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by [[5120/5103]]. |
| [[media type="file" key="jid_40_21_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_40_21_pluck_adu_dr220.mp3|sound sample]] | | == Approximation == |
| </pre></div>
| | {{Interval edo approximation|40/21}} |
| <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"><html><head><title>40_21</title></head><body><strong>40/21</strong><br />
| | == See also == |
| |3 -1 1 -1&gt;<br />
| | * [[21/20]] – its [[octave complement]] |
| 1115.5328 cents<br />
| | * [[Gallery of just intervals]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_40_21_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_40_21_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_40_21_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_40_21_pluck_adu_dr220.mp3/513545608/jid_40_21_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_40_21_pluck_adu_dr220.mp3/513545608/jid_40_21_pluck_adu_dr220.mp3');">sound sample</a></body></html></pre></div>
| | |
| | [[Category:Seventh]] |
| | [[Category:Major seventh]] |
40/21, the septimal acute major seventh, is a 7-limit interval measuring about 1115.5 cents.
Terminology
Despite being approximated by the diminished octave in systems like septimal meantone, and even being called the small septimal diminished octave by some musicians due to analogy with 21/20 being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and Functional Just System, viewed as the Pythagorean major seventh (243/128) altered by 5120/5103.
Approximation
Edo approximations for 40/21 (1115.53 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 13 |
12\13 |
1107.69 |
-7.84 |
-8.49
|
| 14 |
13\14 |
1114.29 |
-1.25 |
-1.45
|
| 15 |
14\15 |
1120.00 |
+4.47 |
+5.58
|
| 27 |
25\27 |
1111.11 |
-4.42 |
-9.95
|
| 28 |
26\28 |
1114.29 |
-1.25 |
-2.91
|
| 29 |
27\29 |
1117.24 |
+1.71 |
+4.13
|
| 42 |
39\42 |
1114.29 |
-1.25 |
-4.36
|
| 43 |
40\43 |
1116.28 |
+0.75 |
+2.67
|
| 44 |
41\44 |
1118.18 |
+2.65 |
+9.71
|
| 56 |
52\56 |
1114.29 |
-1.25 |
-5.82
|
| 57 |
53\57 |
1115.79 |
+0.26 |
+1.22
|
| 58 |
54\58 |
1117.24 |
+1.71 |
+8.26
|
| 70 |
65\70 |
1114.29 |
-1.25 |
-7.27
|
| 71 |
66\71 |
1115.49 |
-0.04 |
-0.24
|
| 72 |
67\72 |
1116.67 |
+1.13 |
+6.80
|
See also