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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 = supermajor third, septimal major third |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 14:22:15 UTC</tt>.<br>
| | | Color name = r3, ru 3rd |
| : The original revision id was <tt>513190816</tt>.<br>
| | | Sound = jid_9_7_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|Septimal major third}} |
| <h4>Original Wikitext content:</h4>
| | In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The [[9-odd-limit]] harmonic ninth chord, a [[pentad]] with ratios [[4:5:6:7:9]], includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way [[9/8]] behaves as ratios of [[9/1|9]] all share this quality. |
| <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">**9/7**
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| |0 2 0 -1>
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| 435.08410 cents
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| [[media type="file" key="jid_9_7_pluck_adu_dr220.mp3" width="240" height="20"]]
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| [[file/view/jid_9_7_pluck_adu_dr220.mp3|audio sample]] | |
| [[http://micro.soonlabel.com/gene_ward_smith/intervals/jid_9_7_pluck_adu_dr220.mp3|9/7]] | |
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| In [[Just Intonation]], 9/7 is a supermajor third of approximately 435.1¢, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit hexad 4:5:6:7:8:9 includes a septimal supermajor third between the 7th and the 9th.
| | A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be [[14:18:21]]. This triad can be very effective in music, but in this context, the modern ear accustomed to [[12edo]] thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant. |
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| A just chord can be built with this wide third in place of the more traditional [[5_4|5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400¢ is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Chords such as the [[9-limit]] hexad above and subsets of it give more opportunity for 9/7 to be heard as consonant.
| | In [[Ancient Greek music]], {{w|Archytas}} used the 9/7 interval in his [[tetrachord]] tunings (in all three genera), for the interval between the ''parhypate'' (second degree) and ''mese'' (fourth degree). |
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| See also:
| | == Approximation == |
| [[Gallery of Just Intervals]] | | In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7. |
| [[http://en.wikipedia.org/wiki/Septimal_major_third|Septimal major third]] (Wikipedia)</pre></div>
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| <h4>Original HTML content:</h4>
| | {{Interval edo approximation|9/7}} |
| <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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>9_7</title></head><body><strong>9/7</strong><br />
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| |0 2 0 -1&gt;<br />
| | == See also == |
| 435.08410 cents<br />
| | * [[14/9]] – its [[octave complement]] |
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| | * [[7/6]] – its [[fifth complement]] |
| [[file/view/jid_9_7_pluck_adu_dr220.mp3|audio sample]]<br /> | | * [[28/27]] – its [[fourth complement]] |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/intervals/jid_9_7_pluck_adu_dr220.mp3" rel="nofollow">9/7</a><br />
| | * [[Gallery of just intervals]] |
| <br />
| | |
| In <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 9/7 is a supermajor third of approximately 435.1¢, characteristic of <a class="wiki_link" href="/7-limit">7-limit</a> and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit hexad 4:5:6:7:8:9 includes a septimal supermajor third between the 7th and the 9th.<br />
| | == References == |
| <br />
| | <references /> |
| A just chord can be built with this wide third in place of the more traditional <a class="wiki_link" href="/5_4">5/4</a>. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400¢ is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Chords such as the <a class="wiki_link" href="/9-limit">9-limit</a> hexad above and subsets of it give more opportunity for 9/7 to be heard as consonant.<br />
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| <br />
| | [[Category:Third]] |
| See also:<br />
| | [[Category:Major third]] |
| <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a><br />
| | [[Category:Supermajor third]] |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_major_third" rel="nofollow">Septimal major third</a> (Wikipedia)</body></html></pre></div>
| | [[Category:Over-7 intervals]] |
In just intonation, 9/7 is the supermajor third[1] or septimal major third of approximately 435.1 ¢, characteristic of 7-limit and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-odd-limit harmonic ninth chord, a pentad with ratios 4:5:6:7:9, includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way 9/8 behaves as ratios of 9 all share this quality.
A just chord can be built with this wide third in place of the more traditional 5/4. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400 ¢ is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.
In Ancient Greek music, Archytas used the 9/7 interval in his tetrachord tunings (in all three genera), for the interval between the parhypate (second degree) and mese (fourth degree).
Approximation
In 11edo, 4\11 is about 1.3 ¢ sharp of 9/7.
Edo approximations for 9/7 (435.08 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 3 |
1\3 |
400.00 |
-35.08 |
-8.77
|
| 8 |
3\8 |
450.00 |
+14.92 |
+9.94
|
| 11 |
4\11 |
436.36 |
+1.28 |
+1.17
|
| 14 |
5\14 |
428.57 |
-6.51 |
-7.60
|
| 22 |
8\22 |
436.36 |
+1.28 |
+2.35
|
| 25 |
9\25 |
432.00 |
-3.08 |
-6.43
|
| 33 |
12\33 |
436.36 |
+1.28 |
+3.52
|
| 36 |
13\36 |
433.33 |
-1.75 |
-5.25
|
| 44 |
16\44 |
436.36 |
+1.28 |
+4.69
|
| 47 |
17\47 |
434.04 |
-1.04 |
-4.08
|
| 55 |
20\55 |
436.36 |
+1.28 |
+5.86
|
| 58 |
21\58 |
434.48 |
-0.60 |
-2.91
|
| 66 |
24\66 |
436.36 |
+1.28 |
+7.04
|
| 69 |
25\69 |
434.78 |
-0.30 |
-1.73
|
| 77 |
28\77 |
436.36 |
+1.28 |
+8.21
|
| 80 |
29\80 |
435.00 |
-0.08 |
-0.56
|
See also
References
