Wikispaces>Andrew_Heathwaite |
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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 11:52:38 UTC</tt>.<br>
| | 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). |
| : The original revision id was <tt>262976924</tt>.<br>
| | |
| : The revision comment was: <tt></tt><br>
| | 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. |
| 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>
| | 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. |
| <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.
| |
|
| |
|
| The inversion of a superfourth is a [[subfifth]]. | | 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.
| | Information about superfourths in the conventional interval-region format may be found at [[Tritone]]. |
|
| |
|
| ==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 center-1 right-2" |
| || 6\[[88cET]] or 11\[[25edo]] || 528.000 || - || | | |- |
| || [[19_14|19/14]] || 528.687 || 19 ||
| | ! Interval |
| || 34/25 || 532.328 || 17 || | | ! Cents |
| || 4\[[9edo]] || 533.333 || - || | | ! Prime limit<br>(if applicable) |
| || 64/47 || 534.493 || 47 || | | |- |
| || [[15_11|15/11]] || 536.951 || 11 ||
| | | [[88cET|6\88cET]]<br>or [[25edo|11\25]] |
| || 13\[[29edo]] || 537.931 || - || | | | 528.000 |
| || 56/41 || 539.764 || 41 ||
| | | — |
| || 9\[[20edo]] || 540.000 || - || | | |- |
| || 41/30 || 540.794 || 41 ||
| | | [[19/14]] |
| || 14\[[31edo]] || 541.935 || - || | | | 528.687 |
| || [[26_19|26/19]] || 543.015 || 19 ||
| | | 19 |
| || 5\[[11edo]] || 545.455 || - || | | |- |
| || 37/27 || 545.479 || 37 ||
| | | 87/64 |
| || [[48_35|48/35]] || 546.815 || 7 ||
| | | 531.532 |
| || 11\[[24edo]] || 550.000 || - || | | | 29 |
| || [[11_8|11/8]] || 551.318 || 11 ||
| | |- |
| || 6\[[13edo]] || 553.846 || - || | | | 34/25 |
| || 62/45 || 554.812 || 31 ||
| | | 532.328 |
| || 40/29 || 556.737 || 29 ||
| | | 17 |
| || 13\[[28edo]] || 557.143 || - || | | |- |
| || 29/21 || 558.796 || 29 || | | | [[9edo|4\9]] |
| || 47/34 || 560.551 || 47 ||
| | | 533.333 |
| || 7\[[15edo]] || 560.000 || - || | | | — |
| | | |- |
| | | | [[49/36]] |
| See: [[Interval Category]], [[Gallery of Just Intervals]]</pre></div>
| | | 533.742 |
| <h4>Original HTML content:</h4>
| | | 7 |
| <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"><html><head><title>Superfourth</title></head><body>A &quot;superfourth&quot; is an interval too wide to sound like a <a class="wiki_link" href="/perfect%20fourth">perfect fourth</a> and too narrow to sound like a <a class="wiki_link" href="/tritone">tritone</a>. <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, in her article <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>, proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> are <a class="wiki_link" href="/11_8">11/8</a> (about 551.3¢) and <a class="wiki_link" href="/15_11">15/11</a> (about 537¢), both undecimal (11-based) superfourths, and <a class="wiki_link" href="/48_35">48/35</a> (about 546.8¢), a septimal superfourth.<br />
| | |- |
| <br />
| | | 64/47 |
| The inversion of a superfourth is a <a class="wiki_link" href="/subfifth">subfifth</a>.<br />
| | | 534.493 |
| <br />
| | | 47 |
| Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are &quot;fuzzy&quot;. Other description are possible and legitimate.<br />
| | |- |
| <br />
| | | [[15/11]] |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2>
| | | 536.951 |
| Below is a list of some intervals in the superfourth range, both just and tempered.<br />
| | | 11 |
| <br />
| | |- |
| | | [[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 |
|
| |
|
| <table class="wiki_table">
| | {{Navbox intervals}} |
| <tr>
| |
| <th>Interval<br />
| |
| </th>
| |
| <th>Cents Value<br />
| |
| </th>
| |
| <th>Prime Limit (if applicable)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>6\<a class="wiki_link" href="/88cET">88cET</a> or 11\<a class="wiki_link" href="/25edo">25edo</a><br />
| |
| </td>
| |
| <td>528.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/19_14">19/14</a><br />
| |
| </td>
| |
| <td>528.687<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/25<br />
| |
| </td>
| |
| <td>532.328<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4\<a class="wiki_link" href="/9edo">9edo</a><br />
| |
| </td>
| |
| <td>533.333<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>64/47<br />
| |
| </td>
| |
| <td>534.493<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/15_11">15/11</a><br />
| |
| </td>
| |
| <td>536.951<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\<a class="wiki_link" href="/29edo">29edo</a><br />
| |
| </td>
| |
| <td>537.931<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56/41<br />
| |
| </td>
| |
| <td>539.764<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9\<a class="wiki_link" href="/20edo">20edo</a><br />
| |
| </td>
| |
| <td>540.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/30<br />
| |
| </td>
| |
| <td>540.794<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14\<a class="wiki_link" href="/31edo">31edo</a><br />
| |
| </td>
| |
| <td>541.935<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/26_19">26/19</a><br />
| |
| </td>
| |
| <td>543.015<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5\<a class="wiki_link" href="/11edo">11edo</a><br />
| |
| </td>
| |
| <td>545.455<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/27<br />
| |
| </td>
| |
| <td>545.479<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/48_35">48/35</a><br />
| |
| </td>
| |
| <td>546.815<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11\<a class="wiki_link" href="/24edo">24edo</a><br />
| |
| </td>
| |
| <td>550.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/11_8">11/8</a><br />
| |
| </td>
| |
| <td>551.318<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6\<a class="wiki_link" href="/13edo">13edo</a><br />
| |
| </td>
| |
| <td>553.846<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>62/45<br />
| |
| </td>
| |
| <td>554.812<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/29<br />
| |
| </td>
| |
| <td>556.737<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\<a class="wiki_link" href="/28edo">28edo</a><br />
| |
| </td>
| |
| <td>557.143<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29/21<br />
| |
| </td>
| |
| <td>558.796<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/34<br />
| |
| </td>
| |
| <td>560.551<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\<a class="wiki_link" href="/15edo">15edo</a><br />
| |
| </td>
| |
| <td>560.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | [[Category:Superfourth| ]] <!-- main article --> |
| <br />
| |
| See: <a class="wiki_link" href="/Interval%20Category">Interval Category</a>, <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| |
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