10/9: Difference between revisions

Wikispaces>spt3125
**Imported revision 513197650 - Original comment: **
Wikispaces>PiotrGrochowski
**Imported revision 591877702 - 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:spt3125|spt3125]] and made on <tt>2014-06-07 16:46:10 UTC</tt>.<br>
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-13 10:31:58 UTC</tt>.<br>
: The original revision id was <tt>513197650</tt>.<br>
: The original revision id was <tt>591877702</tt>.<br>
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In [[5-limit]] [[Just Intonation]], 10/9 is a small whole tone of about 182.4¢. It is a [[superparticular]] interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is [[9_8|9/8]] (about 203.9¢), which is [[81_80|81/80]] (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to [[12edo]]'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.
In [[5-limit]] [[Just Intonation]], 10/9 is a small whole tone of about 182.4¢. It is a [[superparticular]] interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is [[9_8|9/8]] (about 203.9¢), which is [[81_80|81/80]] (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to [[12edo]]'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.


The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9. In systems where 81/80 is tempered out (in 12edo, [[19edo]], [[31edo]] and other [[meantone]] systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.
The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9 (or alternatively 1/1, 10/9, 5/4 -- move by a step of 10/9 followed by a step of 9/8). In systems where 81/80 is tempered out (in 12edo, [[19edo]], [[31edo]] and other [[meantone]] systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.


See: [[Gallery of Just Intervals]]</pre></div>
See: [[Gallery of Just Intervals]]</pre></div>
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In &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 10/9 is a small whole tone of about 182.4¢. It is a &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; (about 203.9¢), which is &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt; (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.&lt;br /&gt;
In &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 10/9 is a small whole tone of about 182.4¢. It is a &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; (about 203.9¢), which is &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt; (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9. In systems where 81/80 is tempered out (in 12edo, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; and other &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.&lt;br /&gt;
The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9 (or alternatively 1/1, 10/9, 5/4 -- move by a step of 10/9 followed by a step of 9/8). In systems where 81/80 is tempered out (in 12edo, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; and other &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>