54/49: Difference between revisions

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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>
<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**
|1 3 0 -2&gt;
168.2132 cents
[[media type="file" key="jid_54_49_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_54_49_pluck_adu_dr220.mp3|sound sample]]


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">&lt;html&gt;&lt;head&gt;&lt;title&gt;54_49&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;54/49&lt;/strong&gt;&lt;br /&gt;
 
|1 3 0 -2&amp;gt;&lt;br /&gt;
== Temperaments ==
168.2132 cents&lt;br /&gt;
[[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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&lt;br /&gt;
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 &lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt; and 245/243 flat of &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;. It is the interval between &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; and &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;. Tempering out 540/539 equates it with 11/10 and leads to &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into 7-limit scales.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
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.
 
== See also ==
* [[49/27]] – its [[octave complement]]
* [[Gallery of just intervals]]
 
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Equable heptatonic]]

Latest revision as of 09:14, 30 May 2026

Interval information
Ratio 54/49
Factorization 2 × 33 × 7-2
Monzo [1 3 0 -2
Size in cents 168.2132¢
Names Zalzal's mujannab,
superpythagorean chroma
Color name rr1, ruru unison
FJS name [math]\displaystyle{ \text{A1}_{7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 11.3696
Weil norm (log2 max(n, d)) 11.5098
Wilson norm (sopfr(nd)) 25

[sound info]
Open this interval in xen-calc

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