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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A "superfourth" is an interval too wide to sound like a [[Perfect_fourth|perfect fourth]] and too narrow to sound like a [[tritone|tritone]]. [[Margo_Schulter|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|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¢) and [[49/36|49/36]] (about 533.7¢), both septimal (7-based) superfourths.
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>2011-10-10 14:13:58 UTC</tt>.<br>
: The original revision id was <tt>263315524</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¢) and [[49_36|49/36]] (about 533.7¢), both septimal (7-based) superfourths.


The inversion of a superfourth is a [[subfifth]].
The inversion of a superfourth is a [[Subfifth|subfifth]].


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.
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.


==Examples==  
==Examples==
Below is a list of some intervals in the superfourth range, both just and tempered.
Below is a list of some intervals in the superfourth range, both just and tempered.


||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) ||
{| class="wikitable"
|| 6\[[88cET]] or 11\[[25edo]] || 528.000 || - ||
|-
|| [[19_14|19/14]] || 528.687 || 19 ||
! | Interval
|| 87/64 || 531.532 || 29 ||
! | Cents Value
|| 34/25 || 532.328 || 17 ||
! | Prime Limit (if applicable)
|| 4\[[9edo]] || 533.333 || - ||
|-
|| [[49_36|49/36]] || 533.742 || 7 ||
| | 6\[[88cET|88cET]] or 11\[[25edo|25edo]]
|| 64/47 || 534.493 || 47 ||
| | 528.000
|| [[15_11|15/11]] || 536.951 || 11 ||
| | -
|| 13\[[29edo]] || 537.931 || - ||
|-
|| 56/41 || 539.764 || 41 ||
| | [[19/14|19/14]]
|| 9\[[20edo]] || 540.000 || - ||
| | 528.687
|| 41/30 || 540.794 || 41 ||
| | 19
|| 175/128 || 541.453 || 7 ||
|-
|| 14\[[31edo]] || 541.935 || - ||
| | 87/64
|| [[26_19|26/19]] || 543.015 || 19 ||
| | 531.532
|| 5\[[11edo]] || 545.455 || - ||
| | 29
|| 37/27 || 545.479 || 37 ||
|-
|| [[48_35|48/35]] || 546.815 || 7 ||
| | 34/25
|| 11\[[24edo]] || 550.000 || - ||
| | 532.328
|| [[11_8|11/8]] || 551.318 || 11 ||
| | 17
|| 6\[[13edo]] || 553.846 || - ||
|-
|| 62/45 || 554.812 || 31 ||
| | 4\[[9edo|9edo]]
|| 40/29 || 556.737 || 29 ||
| | 533.333
|| 13\[[28edo]] || 557.143 || - ||
| | -
|| 243/176 || 558.457 || 11 ||
|-
|| 29/21 || 558.796 || 29 ||
| | [[49/36|49/36]]
|| 47/34 || 560.551 || 47 ||
| | 533.742
|| 7\[[15edo]] || 560.000 || - ||
| | 7
|-
| | 64/47
| | 534.493
| | 47
|-
| | [[15/11|15/11]]
| | 536.951
| | 11
|-
| | 13\[[29edo|29edo]]
| | 537.931
| | -
|-
| | 56/41
| | 539.764
| | 41
|-
| | 9\[[20edo|20edo]]
| | 540.000
| | -
|-
| | 41/30
| | 540.794
| | 41
|-
| | 175/128
| | 541.453
| | 7
|-
| | 14\[[31edo|31edo]]
| | 541.935
| | -
|-
| | [[26/19|26/19]]
| | 543.015
| | 19
|-
| | 5\[[11edo|11edo]]
| | 545.455
| | -
|-
| | 37/27
| | 545.479
| | 37
|-
| | [[48/35|48/35]]
| | 546.815
| | 7
|-
| | 11\[[24edo|24edo]]
| | 550.000
| | -
|-
| | [[11/8|11/8]]
| | 551.318
| | 11
|-
| | 6\[[13edo|13edo]]
| | 553.846
| | -
|-
| | 62/45
| | 554.812
| | 31
|-
| | 40/29
| | 556.737
| | 29
|-
| | 13\[[28edo|28edo]]
| | 557.143
| | -
|-
| | 243/176
| | 558.457
| | 11
|-
| | 29/21
| | 558.796
| | 29
|-
| | 47/34
| | 560.551
| | 47
|-
| | 7\[[15edo|15edo]]
| | 560.000
| | -
|}


 
See: [[interval_category|Interval Category]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]     [[Category:superfourth]]
See: [[Interval Category]], [[Gallery of Just Intervals]]</pre></div>
<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¢) and &lt;a class="wiki_link" href="/49_36"&gt;49/36&lt;/a&gt; (about 533.7¢), both septimal (7-based) superfourths.&lt;br /&gt;
&lt;br /&gt;
The inversion of a superfourth is a &lt;a class="wiki_link" href="/subfifth"&gt;subfifth&lt;/a&gt;.&lt;br /&gt;
&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;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Examples&lt;/h2&gt;
Below is a list of some intervals in the superfourth range, both just and tempered.&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Interval&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents Value&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Prime Limit (if applicable)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\&lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt; or 11\&lt;a class="wiki_link" href="/25edo"&gt;25edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;528.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/19_14"&gt;19/14&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;528.687&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;87/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;531.532&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;532.328&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4\&lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;533.333&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/49_36"&gt;49/36&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;533.742&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;534.493&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;536.951&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\&lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;537.931&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;56/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539.764&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9\&lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41/30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540.794&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;175/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;541.453&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14\&lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;541.935&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/26_19"&gt;26/19&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.015&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5\&lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;545.455&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;545.479&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/48_35"&gt;48/35&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;546.815&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\&lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;550.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;551.318&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\&lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;553.846&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;62/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;554.812&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;556.737&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\&lt;a class="wiki_link" href="/28edo"&gt;28edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;557.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;243/176&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;558.457&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;558.796&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47/34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560.551&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\&lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&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>

Revision as of 00:00, 17 July 2018

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 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 (about 551.3¢) and 15/11 (about 537¢), both undecimal (11-based) superfourths; and 48/35 (about 546.8¢) and 49/36 (about 533.7¢), both septimal (7-based) superfourths.

The inversion of a superfourth is a subfifth.

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.

Examples

Below is a list of some intervals in the superfourth range, both just and tempered.

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

See: Interval Category, Gallery of Just Intervals

Retrieved from "https://en.xen.wiki/index.php?title=Superfourth&oldid=3588"