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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 = Zalzal's mujannab, superpythagorean chroma |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-28 14:09:43 UTC</tt>.<br>
| | | Color name = rr1, ruru unison |
| : The original revision id was <tt>515170254</tt>.<br>
| | | Sound = jid_54_49_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>
| | '''54/49''', '''Zalzal's mujannab''', is an interval introduced by {{w|Mansour Zalzal}}. It is between [[11/10]] and [[10/9]] in size, being [[540/539]] sharp of 11/10 and [[245/243]] flat of 10/9. It is the interval between [[7/6]] and [[9/7]]. |
| <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">**54/49**
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| |1 3 0 -2>
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| 168.2132 cents
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| [[media type="file" key="jid_54_49_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_54_49_pluck_adu_dr220.mp3|sound sample]] | |
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| Zalzal's mujannab, the interval of 54/49 introduced by Mansour Zalzal, is between 11/10 and 10/9 in size, being 540/539 sharp of [[11_10|11/10]] and 245/243 flat of [[10_9|10/9]]. It is the interval between [[7_6|7/6]] and [[9_7|9/7]]. Tempering out 540/539 equates it with 11/10 and leads to [[swetismic chords]]. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into 7-limit scales.</pre></div>
| | == Approximation == |
| <h4>Original HTML content:</h4>
| | {{Interval edo approximation|54/49}} |
| <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>54_49</title></head><body><strong>54/49</strong><br />
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| |1 3 0 -2&gt;<br /> | | == Temperaments == |
| 168.2132 cents<br />
| | [[Tempering out]] [[540/539]] equates 54/49 with 11/10 and leads to [[swetismic chords]]. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into [[7-limit]] scales. |
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| <br />
| | It is also called the '''superpythagorean chromatic semitone''' or '''superpythagorean chroma'''{{idio}} since, in [[superpyth]] temperament, the minor third is 7/6, the major third is 9/7, and the difference between the two is 54/49. |
| Zalzal's mujannab, the interval of 54/49 introduced by Mansour Zalzal, is between 11/10 and 10/9 in size, being 540/539 sharp of <a class="wiki_link" href="/11_10">11/10</a> and 245/243 flat of <a class="wiki_link" href="/10_9">10/9</a>. It is the interval between <a class="wiki_link" href="/7_6">7/6</a> and <a class="wiki_link" href="/9_7">9/7</a>. Tempering out 540/539 equates it with 11/10 and leads to <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a>. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into 7-limit scales.</body></html></pre></div>
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| | Moving to [[exotemperament|exotempering]], the interval can be tempered out, leading to the [[2.3.7 subgroup|2.3.7-subgroup]] version of the [[mujannabic]] temperament equating 7/6 and 9/7. However, it is usually better to temper out [[25/24]] instead for a similar structural effect. |
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| | == See also == |
| | * [[49/27]] – its [[octave complement]] |
| | * [[Gallery of just intervals]] |
| | |
| | [[Category:Second]] |
| | [[Category:Neutral second]] |
| | [[Category:Equable heptatonic]] |
54/49, Zalzal's mujannab, is an interval introduced by Mansour Zalzal. It is between 11/10 and 10/9 in size, being 540/539 sharp of 11/10 and 245/243 flat of 10/9. It is the interval between 7/6 and 9/7.
Approximation
Edo approximations for 54/49 (168.21 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 7 |
1\7 |
171.43 |
+3.22 |
+1.88
|
| 14 |
2\14 |
171.43 |
+3.22 |
+3.75
|
| 21 |
3\21 |
171.43 |
+3.22 |
+5.63
|
| 22 |
3\22 |
163.64 |
-4.58 |
-8.39
|
| 28 |
4\28 |
171.43 |
+3.22 |
+7.50
|
| 29 |
4\29 |
165.52 |
-2.70 |
-6.52
|
| 35 |
5\35 |
171.43 |
+3.22 |
+9.38
|
| 36 |
5\36 |
166.67 |
-1.55 |
-4.64
|
| 43 |
6\43 |
167.44 |
-0.77 |
-2.76
|
| 50 |
7\50 |
168.00 |
-0.21 |
-0.89
|
| 57 |
8\57 |
168.42 |
+0.21 |
+0.99
|
| 64 |
9\64 |
168.75 |
+0.54 |
+2.86
|
| 71 |
10\71 |
169.01 |
+0.80 |
+4.74
|
| 72 |
10\72 |
166.67 |
-1.55 |
-9.28
|
| 78 |
11\78 |
169.23 |
+1.02 |
+6.61
|
| 79 |
11\79 |
167.09 |
-1.12 |
-7.40
|
Temperaments
Tempering out 540/539 equates 54/49 with 11/10 and leads to swetismic chords. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into 7-limit scales.
It is also called the superpythagorean chromatic semitone or superpythagorean chroma[idiosyncratic term] since, in superpyth temperament, the minor third is 7/6, the major third is 9/7, and the difference between the two is 54/49.
Moving to exotempering, the interval can be tempered out, leading to the 2.3.7-subgroup version of the mujannabic temperament equating 7/6 and 9/7. However, it is usually better to temper out 25/24 instead for a similar structural effect.
See also