|
|
| (19 intermediate revisions by 7 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 = large tridecimal third tone |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-30 20:49:14 UTC</tt>.<br>
| | | Color name = 3ogg2, thogugu 2nd |
| : The original revision id was <tt>515316730</tt>.<br>
| | | Sound = jid_26_25_pluck_adu_dr220.mp3 |
| : The revision comment was: <tt></tt><br>
| | | Comma = yes |
| 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>
| | In [[13-limit]] [[just intonation]], '''26/25''', the '''large tridecimal third tone''' appears as the difference between the 26th and 25th [[harmonic]]s. Thus it makes the difference between [[13/8]] and [[25/16]] (a stack of two [[5/4]]'s). If it is treated as a comma, then [[5/4]] and [[13/10]] both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢. |
| <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">**26/25**
| |
| |1 0 -2 0 0 1>
| |
| 67.9002 cents
| |
| [[media type="file" key="jid_26_25_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_26_25_pluck_adu_dr220.mp3|sound sample]] | |
|
| |
|
| In [[13-limit]] [[Just Intonation]], 26/25 appears as the difference between the 26th harmonic and the 25th. Thus it makes the difference between [[13_8|13/8]] and [[25_16|25/16]] (a stack of two [[5_4|5/4]]'s). It measures about 67.9¢.
| | == Approximation == |
| | 26/25 is very well approximated in [[53edo]] as 3\53 (+0.024{{cent}}), and in [[28edt]] as 1\28edt (+0.027{{cent}}). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt. |
| | {{interval edo approximation}} |
| | == See also == |
| | * [[25/13]] - its [[octave complement]] |
| | * [[27/26]] - the small tridecimal third tone |
| | * [[Gallery of just intervals]] |
| | * [[List of superparticular intervals]] |
|
| |
|
| See: [[Gallery of Just Intervals]], [[List of Superparticular Intervals]]</pre></div>
| | [[Category:Third tone]] |
| <h4>Original HTML content:</h4>
| | [[Category:Commas named after their interval size]] |
| <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>26_25</title></head><body><strong>26/25</strong><br />
| |
| |1 0 -2 0 0 1&gt;<br />
| |
| 67.9002 cents<br />
| |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_26_25_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_26_25_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_26_25_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_26_25_pluck_adu_dr220.mp3/515315642/jid_26_25_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_26_25_pluck_adu_dr220.mp3/515315642/jid_26_25_pluck_adu_dr220.mp3');">sound sample</a><br />
| |
| <br />
| |
| In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 26/25 appears as the difference between the 26th harmonic and the 25th. Thus it makes the difference between <a class="wiki_link" href="/13_8">13/8</a> and <a class="wiki_link" href="/25_16">25/16</a> (a stack of two <a class="wiki_link" href="/5_4">5/4</a>'s). It measures about 67.9¢.<br />
| |
| <br />
| |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>, <a class="wiki_link" href="/List%20of%20Superparticular%20Intervals">List of Superparticular Intervals</a></body></html></pre></div>
| |
In 13-limit just intonation, 26/25, the large tridecimal third tone appears as the difference between the 26th and 25th harmonics. Thus it makes the difference between 13/8 and 25/16 (a stack of two 5/4's). If it is treated as a comma, then 5/4 and 13/10 both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢.
Approximation
26/25 is very well approximated in 53edo as 3\53 (+0.024 ¢), and in 28edt as 1\28edt (+0.027 ¢). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt.
Edo approximations for 26/25 (67.90 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 16 |
1\16 |
75.00 |
+7.10 |
+9.47
|
| 17 |
1\17 |
70.59 |
+2.69 |
+3.81
|
| 18 |
1\18 |
66.67 |
-1.23 |
-1.85
|
| 19 |
1\19 |
63.16 |
-4.74 |
-7.51
|
| 34 |
2\34 |
70.59 |
+2.69 |
+7.62
|
| 35 |
2\35 |
68.57 |
+0.67 |
+1.96
|
| 36 |
2\36 |
66.67 |
-1.23 |
-3.70
|
| 37 |
2\37 |
64.86 |
-3.04 |
-9.36
|
| 52 |
3\52 |
69.23 |
+1.33 |
+5.77
|
| 53 |
3\53 |
67.92 |
+0.02 |
+0.11
|
| 54 |
3\54 |
66.67 |
-1.23 |
-5.55
|
| 69 |
4\69 |
69.57 |
+1.66 |
+9.57
|
| 70 |
4\70 |
68.57 |
+0.67 |
+3.92
|
| 71 |
4\71 |
67.61 |
-0.29 |
-1.74
|
| 72 |
4\72 |
66.67 |
-1.23 |
-7.40
|
See also