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| <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 = small whole tone, classic(al) whole tone, ptolemaic whole tone |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 12:34:00 UTC</tt>.<br>
| | | Color name = y2, yo 2nd |
| : The original revision id was <tt>513184890</tt>.<br>
| | | Sound = jid_10_9_pluck_adu_dr220.mp3 |
| : 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>
| | {{Wikipedia|Major second}} |
| <h4>Original Wikitext content:</h4>
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| <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">**10/9**
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| 182.40371 cents
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| [[media type="file" key="jid_10_9_pluck_adu_dr220.mp3"]]
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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 the '''small''', '''classic(al)''', or '''ptolemaic whole tone'''<ref>For reference, see [[5-limit]]. </ref> 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]] (about 203.9¢), which is [[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. |
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| 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 may be hard to notice at first. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | == Temperaments == |
| <h4>Original HTML content:</h4>
| | The following [[linear temperament]]s are [[generate]]d by a [[~]]10/9: |
| <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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>10_9</title></head><body><strong>10/9</strong><br />
| | * [[Porcupine]] |
| |1 -2 1&gt;<br /> | | * [[Minortone]] |
| 182.40371 cents<br />
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| | {{todo|complete list}} |
| <br />
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| 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 />
| | == See also == |
| <br />
| | * [[Decaononic]] - temperament which sets the tone to this interval, instead of to 9/8 |
| 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, <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 />
| | * [[9/5]] – its [[octave complement]] |
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| | * [[27/20]] – its [[fifth complement]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | * [[6/5]] – its [[fourth complement]] |
| | * [[Gallery of just intervals]] |
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| | == Notes == |
| | <references/> |
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| | [[Category:Second]] |
| | [[Category:Whole tone]] |
| | [[Category:Tritave-reduced harmonics]] |
In 5-limit just intonation, 10/9 is the small, classic(al), or ptolemaic whole tone[1] 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 (about 203.9¢), which is 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 may be hard to notice at first.
Temperaments
The following linear temperaments are generated by a ~10/9:
See also
Notes
