User:Moremajorthanmajor/15edX: Difference between revisions

Wikispaces>JosephRuhf
**Imported revision 601980492 - Original comment: **
 
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''15edX''' is the scale which occurs as the dominant minor edX (equal division of a tenth interval). It also gives the period of the 15th-decade Alfincavallo branch of the Carrera temperament family.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-12 10:58:03 UTC</tt>.<br>
: The original revision id was <tt>601980492</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">This is the scale which occurs as the dominant minor edX.


==Intervals==  
== Intervals ==
||~ Degrees ||~ Enneatonic ||~ Minimum ||~ ed(7/3) ||~ Mean/Median ||~ Golden ||~ Maximum ||
{| class="wikitable"
|| 1 || G#/Hb || 96 || 97.791 || 104 || 105.8885/1 || 112 ||
|+
|| 2 || H || 192 || 195.582 || 208 || 211.777 || 224 ||
!Decade
|| 3 || H#/Jb || 288 || 293.374 || 312 || 317.666 || 336 ||
!Period
|| 4 || J || 384 || 391.166 || 416 || 423.554 || 448 ||
!Notes
|| 5 || A || 480 || 488.957 || 520 || 529.443 || 560 ||
|-
|| 6 || A#/Bb || 576 || 586.748 || 624 || 635.331 || 672 ||
|6\5
|| 7 || B || 672 || 684.54 || 728 || 741.22 || 784 ||
|96.000
|| 8 || B#/Cb || 768 || 782.331 || 832 || 847.108 || 896 ||
|Intense Aeolian-Subpental Dorian mode begins
|| 9 || C || 864 || 880.1225/1 || 936 || 952.997 || 1008 ||
|-
|| 10 || D || 960 || 977.913 || 1040 || 1058.885 || 1120 ||
|17\14
|| 11 || D#/Eb || 1056 || 1075.705 || 1144 || 1164.774 || 1232 ||
|97.143
|| 12 || E || 1152 || 1173.497 || 1248 || 1270.6625 || 1344 ||
|
|| 13 || E#/Fb || 1248 || 1271.288 || 1352 || 1376.551 || 1456 ||
|-
|| 14 || F || 1344 || 1369.0795 || 1456 || 1482.44 || 1568 ||</pre></div>
|11\9
<h4>Original HTML content:</h4>
|97.778
<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;15edX&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the scale which occurs as the dominant minor edX.&lt;br /&gt;
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals&lt;/h2&gt;
|16\13
|98.462
|
|-
|21\17
|98.824
|
|-
|26\21
|99.048
|
|-
|5\4
|100.000
|Subpental Dorian mode ends, Pental Dorian mode begins
|-
|19\15
|101.333
|
|-
|14\11
|101.818
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|23\18
|102.222
|
|-
|9\7
|102.857
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|31\24
|103.333
|
|-
|22\17
|103.529
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|35\27
|103.704
|
|-
|13\10
|104.000
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|104.615
|
|-
|21\16
|105.000
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|25\19
|105.263
|
|-
|4\3
|106.667
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|31\23
|107.826
|
|-
|27\20
|108.000
|
|-
|23\17
|108.235
|
|-
|19\14
|108.571
|
|-
|15\11
|109.091
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|26\19
|109.474
|
|-
|11\8
|110.000
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|18\13
|110.769
|
|-
|25\18
|111.111
|
|-
|7\5
|112.500
|Mixolydian-Ionian mode ends
|}
Relative cents
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="2" |Enneatonic
!Intense Aeolian-Subpental Dorian
!Dorian
!Dorian-Mixolydian
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
| |1
|G#/Jb
|''G#/Ab''
|96.{{Overline|6}}
|100
|103.{{Overline|3}}
|106.{{Overline|6}}
|110
|-
| |2
|J
|''A''
|193.{{Overline|3}}
|200
|206.{{Overline|6}}
|213.{{Overline|3}}
|220
|-
| |3
|J#/Ab
|''A#/Bb''
|290
|300
|310
|320
|330
|-
| |4
|A
|''B''
|386.{{Overline|6}}
|400
|413.{{Overline|3}}
|426.{{Overline|6}}
|440
|-
| |5
|B
|''C''
|483.{{Overline|3}}
|500
|516.{{Overline|6}}
|533.{{Overline|3}}
|550
|-
| |6
|B#/Cb
|''C#/Qb''
|580
|600
|620
|640
|660
|-
| |7
|C
|''Q''
|676.{{Overline|6}}
|700
|723.{{Overline|3}}
|746.{{Overline|6}}
|770
|-
|8
|C#/Qb
|''Q#/Db''
|773.{{Overline|3}}
|800
|826.{{Overline|6}}
|853.{{Overline|3}}
|880
|-
|9
|Q
|''D''
|870
|900
|930
|960
|990
|-
|10
|D
|''S''
|966.{{Overline|6}}
|1000
|1033.{{Overline|3}}
|1066.{{Overline|6}}
|1100
|-
|11
|D#/Eb
|''S#/Eb''
|1063.{{Overline|3}}
|1100
|1136.{{Overline|6}}
|1173.{{Overline|3}}
|1210
|-
|12
| colspan="2" |E
|1160
|1200
|1240
|1280
|1320
|-
|13
| colspan="2" |E#/Fb
|1256.{{Overline|6}}
|1300
|1343.{{Overline|3}}
|1386.{{Overline|6}}
|1430
|-
|14
| colspan="2" |F
|1353.{{Overline|3}}
|1400
|1446.{{Overline|6}}
|1493.{{Overline|3}}
|1540
|-
|15
| colspan="2" |G
|1450
|1500
|1550
|1600
|1650
|}


&lt;table class="wiki_table"&gt;
By a surprising coincidence, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of [[34edo]]. Additionally, those of the modal Golden and Pyrite tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Intense Aeolian-Subpental Dorian), [[9ed5/3|9ed(5/3)]]/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), 4ed(9/7)/+1/36-syntonic comma 14ed(12/5) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.
    &lt;tr&gt;
== See also ==
        &lt;th&gt;Degrees&lt;br /&gt;
* [[15ed5/2]] - equal division of the classic major tenth
&lt;/th&gt;
* [[15ed7/3]] - equal division of the septimal minor tenth
        &lt;th&gt;Enneatonic&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Minimum&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;ed(7/3)&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Mean/Median&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Golden&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Maximum&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G#/Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;96&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;97.791&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105.8885/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;192&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;195.582&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;208&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;211.777&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H#/Jb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;288&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;293.374&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;312&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;317.666&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;336&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;391.166&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;423.554&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;448&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;480&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;488.957&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;520&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;529.443&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A#/Bb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;576&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;586.748&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;624&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;635.331&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;672&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;672&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;684.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;728&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;741.22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;784&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B#/Cb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;768&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;782.331&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;832&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;847.108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;896&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;864&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;880.1225/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;936&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;952.997&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1008&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;960&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;977.913&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1040&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1058.885&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1120&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D#/Eb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1056&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1075.705&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1144&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1164.774&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1232&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1152&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1173.497&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1248&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1270.6625&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1344&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E#/Fb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1248&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1271.288&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1376.551&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1456&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1344&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1369.0795&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1456&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1482.44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1568&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:15-tone scales]]
[[Category:EdX]]