10/9
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author PiotrGrochowski and made on 2016-09-13 10:31:58 UTC.
- The original revision id was 591877702.
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Original Wikitext content:
**10/9** |1 -2 1> 182.40371 cents [[media type="file" key="jid_10_9_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_10_9_pluck_adu_dr220.mp3|sound sample]] 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 (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]]
Original HTML content:
<html><head><title>10_9</title></head><body><strong>10/9</strong><br />
|1 -2 1><br />
182.40371 cents<br />
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<br />
In <a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 10/9 is a small whole tone of about 182.4¢. It is a <a class="wiki_link" href="/superparticular">superparticular</a> 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 <a class="wiki_link" href="/9_8">9/8</a> (about 203.9¢), which is <a class="wiki_link" href="/81_80">81/80</a> (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to <a class="wiki_link" href="/12edo">12edo</a>'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.<br />
<br />
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, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/31edo">31edo</a> and other <a class="wiki_link" href="/meantone">meantone</a> 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.<br />
<br />
See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html>