25edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 144461681 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 179204617 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-11-13 15:42:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>179204617</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7. | <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">=25 tone equal temperament= | ||
25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7. | |||
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]]. | 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]]. | ||
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.</pre></div> | If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. | ||
Some example of a keyboard in 25-EDO | |||
[[image:mm25.PNG]]</pre></div> | |||
<h4>Original HTML content:</h4> | <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>25edo</title></head><body>25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.<br /> | <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>25edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->25 tone equal temperament</h1> | ||
<br /> | |||
25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.<br /> | |||
<br /> | <br /> | ||
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.<br /> | 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.<br /> | ||
<br /> | <br /> | ||
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.</body></html></pre></div> | If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.<br /> | ||
<br /> | |||
Some example of a keyboard in 25-EDO<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:2:&lt;img src=&quot;/file/view/mm25.PNG/179204243/mm25.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /><!-- ws:end:WikiTextLocalImageRule:2 --></body></html></pre></div> | |||
Revision as of 15:42, 13 November 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Osmiorisbendi and made on 2010-11-13 15:42:35 UTC.
- The original revision id was 179204617.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=25 tone equal temperament= 25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7. 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]]. If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. Some example of a keyboard in 25-EDO [[image:mm25.PNG]]
Original HTML content:
<html><head><title>25edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->25 tone equal temperament</h1> <br /> 25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.<br /> <br /> 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.<br /> <br /> If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.<br /> <br /> Some example of a keyboard in 25-EDO<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:2:<img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="" title="" /> --><img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /><!-- ws:end:WikiTextLocalImageRule:2 --></body></html>