49/36: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 301091130 - Original comment: **
Overthink (talk | contribs)
autopatrolled
2,763 edits
+ note; approximation template
 
(13 intermediate revisions by 9 users not shown)
Line 1: Line 1:
<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 = Arabic lute acute fourth
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 22:59:42 UTC</tt>.<br>
| Color name = zz5, zozo 5th
: The original revision id was <tt>301091130</tt>.<br>
| Sound = jid_49_36_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>
'''49/36''', the '''Arabic lute acute fourth''', is composed of two subminor thirds of [[7/6]], and is the interval between [[9/7]] and [[7/4]]. It is [[540/539]] (~4{{cent}}) flat of [[15/11]]. Tempering out 540/539 leads to 11-limit [[swetismic chords]], such as the tempering of <span style="white-space:nowrap">[[28:36:42:49|1–9/7–3/2–7/4]]</span> (note that this chord is [[15-odd-limit]]).
<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">49/36, the Arabic lute acute fourth, is composed of two subminor thirds of [[7_6|7/6]], and is the interval between [[9_7|9/7]] and [[7_4|7/4]]. It is 540/539 flat of [[15_11|15/11]]. Tempering out 540/539 leads to 15-limit [[swetismic chords]] such as the tempering of 1-9/7-3/2-7/4.</pre></div>
== Approximation ==
<h4>Original HTML content:</h4>
This interval is especially near the 4th step of [[9edo]].
<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;49_36&lt;/title&gt;&lt;/head&gt;&lt;body&gt;49/36, the Arabic lute acute fourth, is composed of two subminor thirds of &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, and is the interval between &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; and &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;. It is 540/539 flat of &lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;. Tempering out 540/539 leads to 15-limit &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt; such as the tempering of 1-9/7-3/2-7/4.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Interval edo approximation}}
 
[[Category:Fourth]]
[[Category:Superfourth]]

Latest revision as of 18:21, 14 March 2026

Interval information
Ratio 49/36
Factorization 2-2 × 3-2 × 72
Monzo [-2 -2 0 2⟩
Size in cents 533.7418¢
Name Arabic lute acute fourth
Color name zz5, zozo 5th
FJS name [math]\displaystyle{ \text{d5}^{7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 10.7846
Weil norm (log2 max(n, d)) 11.2294
Wilson norm (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc

49/36, the Arabic lute acute fourth, is composed of two subminor thirds of 7/6, and is the interval between 9/7 and 7/4. It is 540/539 (~4 ¢) flat of 15/11. Tempering out 540/539 leads to 11-limit swetismic chords, such as the tempering of 1–9/7–3/2–7/4 (note that this chord is 15-odd-limit).

Approximation

This interval is especially near the 4th step of 9edo.

Edo approximations for 49/36 (533.74 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
9 4\9 533.33 -0.41 -0.31
18 8\18 533.33 -0.41 -0.61
27 12\27 533.33 -0.41 -0.92
36 16\36 533.33 -0.41 -1.23
38 17\38 536.84 +3.10 +9.82
45 20\45 533.33 -0.41 -1.53
47 21\47 536.17 +2.43 +9.51
54 24\54 533.33 -0.41 -1.84
56 25\56 535.71 +1.97 +9.20
63 28\63 533.33 -0.41 -2.14
65 29\65 535.38 +1.64 +8.90
72 32\72 533.33 -0.41 -2.45
74 33\74 535.14 +1.39 +8.59
Retrieved from "https://en.xen.wiki/index.php?title=49/36&oldid=226067"