Superfourth: Difference between revisions

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<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 -->

Latest revision as of 08:57, 6 March 2025

A superfourth, ultrafourth or semi-augmented fourth is an interval that spans three steps of the diatonic scale with a quality between augmented and perfect. It exists in neutralized diatonic scales as exactly one half of a major seventh.

In just intonation, an interval may be classified as a superfourth if it is reasonably mapped to 3\7 and 11\24 (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).

As a concrete interval region, it is typically near 550 ¢ 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 Regions of the Interval Spectrum, proposes an approximate range for a superfourth to be from 528 ¢ to 560 ¢. 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.

Some of the simplest superfourths in just intonation are 11/8 (about 551 ¢) and 15/11 (about 537 ¢), both undecimal (11-based) superfourths; and 48/35 (about 547 ¢) and 49/36 (about 534 ¢), both septimal (7-based) superfourths.

The inversion of a superfourth is a subfifth.

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.

Interval Cents Prime limit
(if applicable)
6\88cET
or 11\25 		528.000 —
19/14 528.687 19
87/64 531.532 29
34/25 532.328 17
4\9 533.333 —
49/36 533.742 7
64/47 534.493 47
15/11 536.951 11
13\29 537.931 —
56/41 539.764 41
9\20 540.000 —
41/30 540.794 41
175/128 541.453 7
14\31 541.935 —
26/19 543.015 19
5\11 545.455 —
37/27 545.479 37
48/35 546.815 7
11\24 550.000 —
11/8 551.318 11
6\13 553.846 —
62/45 554.812 31
40/29 556.737 29
13\28 557.143 —
243/176 558.457 11
29/21 558.796 29
47/34 560.551 47
7\15 560.000 —

See also


View • Talk • EditInterval classification
Interval regions
Unison and octave Unison • Comma and diesis • Octave
Seconds Minor second • Neutral second • Major second
Thirds Minor third • Neutral third • Major third
Fourths and fifths Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth
Sixths Minor sixth • Neutral sixth • Major sixth
Sevenths Minor seventh • Neutral seventh • Major seventh
Interseptimal intervals Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th
Interval qualities
Diatonic qualities Diminished • Minor • Perfect • Major • Augmented
Tuning ranges Neutral (interval quality) • Submajor and supraminor • Pental major and minor • Novamajor and novaminor • Neogothic major and minor • Supermajor and subminor • Ultramajor and inframinor
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