25edo: Difference between revisions
Wikispaces>spt3125 **Imported revision 489052564 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 489080882 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-02-12 13:16:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>489080882</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> | ||
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=<span style="color: #006b2e; font-family: 'Times New Roman',Times,serif; font-size: 113%;">25 tone equal temperament</span>= | =<span style="color: #006b2e; font-family: 'Times New Roman',Times,serif; font-size: 113%;">25 tone equal temperament</span>= | ||
25EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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 ([[5_4|5/4]]) and 7 ([[7_4|7/4]] | 25EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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 ([[5_4|5/4]]) and 7 ([[7_4|7/4]]). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65. | ||
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit icluding the 3, it is not [[consistent]]. 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_7|8/7]]s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a [[128_125|128/125]] [[diesis]] and two [[septimal tritones]] of [[7_5|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]]. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[mavila]] temperament. | 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit icluding the 3, it is not [[consistent]]. 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_7|8/7]]s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a [[128_125|128/125]] [[diesis]] and two [[septimal tritones]] of [[7_5|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]]. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[mavila]] temperament. | ||
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<!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:3 --><span style="color: #006b2e; font-family: 'Times New Roman',Times,serif; font-size: 113%;">25 tone equal temperament</span></h1> | <!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:3 --><span style="color: #006b2e; font-family: 'Times New Roman',Times,serif; font-size: 113%;">25 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, 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 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a> | 25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, 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 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a>). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&amp;25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65.<br /> | ||
<br /> | <br /> | ||
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit icluding the 3, it is not <a class="wiki_link" href="/consistent">consistent</a>. 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 <a class="wiki_link" href="/8_7">8/7</a>s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a <a class="wiki_link" href="/128_125">128/125</a> <a class="wiki_link" href="/diesis">diesis</a> and two <a class="wiki_link" href="/septimal%20tritones">septimal tritones</a> of <a class="wiki_link" href="/7_5">7/5</a> 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>. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for <a class="wiki_link" href="/mavila">mavila</a> temperament.<br /> | 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit icluding the 3, it is not <a class="wiki_link" href="/consistent">consistent</a>. 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 <a class="wiki_link" href="/8_7">8/7</a>s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a <a class="wiki_link" href="/128_125">128/125</a> <a class="wiki_link" href="/diesis">diesis</a> and two <a class="wiki_link" href="/septimal%20tritones">septimal tritones</a> of <a class="wiki_link" href="/7_5">7/5</a> 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>. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for <a class="wiki_link" href="/mavila">mavila</a> temperament.<br /> | ||