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| <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 = large undevicesimal major third, Eratosthenes' major third |
| : This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on <tt>2016-11-21 19:34:08 UTC</tt>.<br>
| | | Color name = 19og4, nogu 4th |
| : The original revision id was <tt>600045888</tt>.<br>
| | | Sound = jid_19_15_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>
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| <h4>Original Wikitext content:</h4>
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| <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">**19/15**
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| |0 -1 -1 0 0 0 0 1> | |
| 409.2443 cents
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| [[media type="file" key="jid_19_15_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_19_15_pluck_adu_dr220.mp3|sound sample]]
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| **19/15** is a [[19-limit]] interval, 409.2 [[Cent|cents]] in size, that is sharper than the [[Pythagorean]] major third by the password (1216/1215), an unnoticeable comma of about 1.4243 cents.</pre></div>
| | '''19/15''', the '''large undevicesimal major third''' is a [[19-limit]] interval, 409.2 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished fourth'', obtained by adding [[81/80]] and [[513/512]] to the [[8192/6561|Pythagorean diminished fourth]], but it may be called the '''Eratosthenes' major third''' as it is sharper than the [[81/64|Pythagorean major third]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. |
| <h4>Original HTML content:</h4>
| | == Approximation == |
| <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>19_15</title></head><body><strong>19/15</strong><br />
| | {{Interval edo approximation|19/15}} |
| |0 -1 -1 0 0 0 0 1&gt;<br />
| | == See also == |
| 409.2443 cents<br />
| | * [[30/19]] – its [[octave complement]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_19_15_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_19_15_pluck_adu_dr220.mp3&amp;quot; width=&amp;quot;240&amp;quot; height=&amp;quot;20&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_19_15_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_19_15_pluck_adu_dr220.mp3/513250038/jid_19_15_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_19_15_pluck_adu_dr220.mp3/513250038/jid_19_15_pluck_adu_dr220.mp3');">sound sample</a><br />
| | * [[45/38]] – its [[fifth complement]] |
| <br />
| | * [[24/19]] – the small undevicesimal major third |
| <strong>19/15</strong> is a <a class="wiki_link" href="/19-limit">19-limit</a> interval, 409.2 <a class="wiki_link" href="/Cent">cents</a> in size, that is sharper than the <a class="wiki_link" href="/Pythagorean">Pythagorean</a> major third by the password (1216/1215), an unnoticeable comma of about 1.4243 cents.</body></html></pre></div>
| | * [[Gallery of just intervals]] |
| | |
| | [[Category:Major third]] |
| | [[Category:Third]] |
| | [[Category:Eratosthenes]] |
19/15, the large undevicesimal major third is a 19-limit interval, 409.2 cents in size. In the Functional Just System and Helmholtz-Ellis notation, it is a diminished fourth, obtained by adding 81/80 and 513/512 to the Pythagorean diminished fourth, but it may be called the Eratosthenes' major third as it is sharper than the Pythagorean major third by the password aka Eratosthenes' comma (1216/1215), an unnoticeable comma of about 1.4243 cents.
Approximation
Edo approximations for 19/15 (409.24 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 3 |
1\3 |
400.00 |
-9.24 |
-2.31
|
| 6 |
2\6 |
400.00 |
-9.24 |
-4.62
|
| 9 |
3\9 |
400.00 |
-9.24 |
-6.93
|
| 12 |
4\12 |
400.00 |
-9.24 |
-9.24
|
| 32 |
11\32 |
412.50 |
+3.26 |
+8.68
|
| 35 |
12\35 |
411.43 |
+2.18 |
+6.37
|
| 38 |
13\38 |
410.53 |
+1.28 |
+4.06
|
| 41 |
14\41 |
409.76 |
+0.51 |
+1.75
|
| 44 |
15\44 |
409.09 |
-0.15 |
-0.56
|
| 47 |
16\47 |
408.51 |
-0.73 |
-2.87
|
| 50 |
17\50 |
408.00 |
-1.24 |
-5.18
|
| 53 |
18\53 |
407.55 |
-1.70 |
-7.50
|
| 56 |
19\56 |
407.14 |
-2.10 |
-9.81
|
| 76 |
26\76 |
410.53 |
+1.28 |
+8.12
|
| 79 |
27\79 |
410.13 |
+0.88 |
+5.81
|
See also