Xenharmonic Wiki

Superfourth: Difference between revisions

VisualWikitext
Wikispaces>Andrew_Heathwaite
**Imported revision 262968896 - Original comment: **
 
m Style
 
(20 intermediate revisions by 11 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''superfourth''', '''ultrafourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization|neutralized]] diatonic scales as exactly one half of a [[major seventh]].  
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-09 10:55:36 UTC</tt>.<br>
: The original revision id was <tt>262968896</tt>.<br>
: 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>
<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">A "superfourth" is an interval too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]], proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in [[Just Intonation]] are [[11_8|11/8]] (about 551.3¢) and [[15_11|15/11]] (about 537¢), both undecimal (11-based) superfourths, and [[48_35|48/35]] (about 546.8¢), a septimal superfourth.


Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are "fuzzy". Other description are possible and legitimate.
In [[just intonation]], an interval may be classified as a superfourth if it is reasonably mapped to [[7edo|3\7]] and [[24edo|11\24]] (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).


See: [[Interval Category]], [[Gallery of Just Intervals]]</pre></div>
As a concrete [[interval region]], it is typically near 550{{cent}} in size. It is too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Superfourth&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &amp;quot;superfourth&amp;quot; is an interval too wide to sound like a &lt;a class="wiki_link" href="/perfect%20fourth"&gt;perfect fourth&lt;/a&gt; and too narrow to sound like a &lt;a class="wiki_link" href="/tritone"&gt;tritone&lt;/a&gt;. &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;, in her article &lt;a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow"&gt;Regions of the Interval Spectrum&lt;/a&gt;, proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt; are &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; (about 551.3¢) and &lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt; (about 537¢), both undecimal (11-based) superfourths, and &lt;a class="wiki_link" href="/48_35"&gt;48/35&lt;/a&gt; (about 546.8¢), a septimal superfourth.&lt;br /&gt;
Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 547{{c}}) and [[49/36]] (about 534{{c}}), both septimal (7-based) superfourths.
&lt;br /&gt;
 
Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are &amp;quot;fuzzy&amp;quot;. Other description are possible and legitimate.&lt;br /&gt;
The inversion of a superfourth is a [[subfifth]].
&lt;br /&gt;
 
See: &lt;a class="wiki_link" href="/Interval%20Category"&gt;Interval Category&lt;/a&gt;, &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Information about superfourths in the conventional interval-region format may be found at [[Tritone]].
 
== Examples ==
Below is a list of some intervals in the superfourth range, both just and tempered.
 
{| class="wikitable center-1 right-2"
|-
! Interval
! Cents
! Prime limit<br>(if applicable)
|-
| [[88cET|6\88cET]]<br>or [[25edo|11\25]]
| 528.000
| —
|-
| [[19/14]]
| 528.687
| 19
|-
| 87/64
| 531.532
| 29
|-
| 34/25
| 532.328
| 17
|-
| [[9edo|4\9]]
| 533.333
| —
|-
| [[49/36]]
| 533.742
| 7
|-
| 64/47
| 534.493
| 47
|-
| [[15/11]]
| 536.951
| 11
|-
| [[29edo|13\29]]
| 537.931
| —
|-
| 56/41
| 539.764
| 41
|-
| [[20edo|9\20]]
| 540.000
| —
|-
| 41/30
| 540.794
| 41
|-
| 175/128
| 541.453
| 7
|-
| [[31edo|14\31]]
| 541.935
| —
|-
| [[26/19]]
| 543.015
| 19
|-
| [[11edo|5\11]]
| 545.455
| —
|-
| 37/27
| 545.479
| 37
|-
| [[48/35]]
| 546.815
| 7
|-
| [[24edo|11\24]]
| 550.000
| —
|-
| [[11/8]]
| 551.318
| 11
|-
| [[13edo|6\13]]
| 553.846
| —
|-
| 62/45
| 554.812
| 31
|-
| 40/29
| 556.737
| 29
|-
| [[28edo|13\28]]
| 557.143
| —
|-
| 243/176
| 558.457
| 11
|-
| 29/21
| 558.796
| 29
|-
| 47/34
| 560.551
| 47
|-
| [[15edo|7\15]]
| 560.000
| —
|}
 
== See also ==
* [[43/31]] – a tritone with a "superfourth-ish" taste
* [[Gallery of just intervals]]
* [[Subfifth]] – the [[octave complement]] region
 
{{Navbox intervals}}
 
[[Category:Superfourth| ]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/Superfourth"