18edt: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

18edt means the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference: ~~

~~: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-12 00:42:04 UTC</tt>. ~~

~~: The original revision id was <tt>591641538</tt>. ~~

~~: The revision comment was: <tt></tt> ~~

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. ~~

~~<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">18edt means the division of the tritave into 18 equal parts ~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.~~<~~/span~~>~~

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~As the double of [[@9edt]], it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like [[@8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.~~&lt~~;/span~~&gt~~;

As the double of [[9edt|9edt]], it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like [[8edt|8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

0: 1/1

1: 105.664 cents 16/15

2: 211.328 cents 9/8

~~0: 1/1~~

~~1: 105.664 cents 16/15~~

~~2: 211.328 cents 9/8~~

3: 316.993 cents 6/5

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~4: 422.657 cents 9/7~~<~~/span~~>~~

4: 422.657 cents 9/7

5: 528.321 cents 27/20

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~6: 633.985 cents 13/9~~<~~/span~~>~~

6: 633.985 cents 13/9

7: 739.649 cents 17/13

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~8: 845.313 cents 5/3~~<~~/span~~>~~

8: 845.313 cents 5/3

9: 950.9775 cents 19/11

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~10: 1056.642 cents 9/5~~<~~/span~~>~~

10: 1056.642 cents 9/5

11: 1162.306 cents 49/25

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~12: 1267.970 cents 27/13~~<~~/span~~>~~

12: 1267.970 cents 27/13

13: 1373.634 cents 20/9

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~14: 1479.298 cents 7/3~~<~~/span~~>~~

14: 1479.298 cents 7/3

15: 1584.963 cents 5/2

~~<~~span style="background-color: rgba(255,255,255,0);"~~>~~16: 1690.627 cents 8/3~~<~~/span~~>~~

16: 1690.627 cents 8/3

17: 1806.2905 cents 45/16

~~18: 3/1</pre></div>~~

<~~h4>Original HTML content:</h4>~~

18: 3/1

<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>18edt</title></head><body>18edt means the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.

~~ ~~

As the double of <a class="wiki_link" href="/9edt" target="_blank">9edt</a>, it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like <a class="wiki_link" href="/8edt" target="_blank">8edt</a>, is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

~~ ~~

~~0: 1/1 ~~

~~1: 105.664 cents 16/15 ~~

~~2: 211.328 cents 9/8 ~~

~~3: 316.993 cents 6/5 ~~

~~4: 422.657 cents 9/7 ~~

~~5: 528.321 cents 27/20 ~~

~~6: 633.985 cents 13/9 ~~

~~7: 739.649 cents 17/13 ~~

~~8: 845.313 cents 5/3 ~~

~~9: 950.9775 cents 19/11 ~~

~~10: 1056.642 cents 9/5 ~~

~~11: 1162.306 cents 49/25 ~~

~~12: 1267.970 cents 27/13 ~~

~~13: 1373.634 cents 20/9 ~~

~~14: 1479.298 cents 7/3 ~~

~~15: 1584.963 cents 5/2 ~~

~~16: 1690.627 cents 8/3 ~~

~~17: 1806.2905 cents 45/16 ~~

~~~~18: 3/1~~<~~/span~~></body></html></pre></div~~>

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+edt means the division of the tritave into 18 equal parts <span style="background-color: rgba(255,255,255,0);">of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.</span>
-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>2016-09-12 00:42:04 UTC</tt>.<br>
-: The original revision id was <tt>591641538</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">18edt means the division of the tritave into 18 equal parts &lt;span style="background-color: rgba(255,255,255,0);"&gt;of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;As the double of [[@9edt]], it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like [[@8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">As the double of [[9edt|9edt]], it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like [[8edt|8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.</span>
+<span style="background-color: rgba(255,255,255,0);">0: 1/1</span>
+<span style="background-color: rgba(255,255,255,0);">1: 105.664 cents 16/15</span>
+<span style="background-color: rgba(255,255,255,0);">2: 211.328 cents 9/8</span>
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;0: 1/1&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;1: 105.664 cents 16/15&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;2: 211.328 cents 9/8&lt;/span&gt;
 : 316.993 cents 6/5
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;4: 422.657 cents 9/7&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">4: 422.657 cents 9/7</span>
 : 528.321 cents 27/20
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;6: 633.985 cents 13/9&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">6: 633.985 cents 13/9</span>
 : 739.649 cents 17/13
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;8: 845.313 cents 5/3&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">8: 845.313 cents 5/3</span>
 : 950.9775 cents 19/11
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;10: 1056.642 cents 9/5&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">10: 1056.642 cents 9/5</span>
 : 1162.306 cents 49/25
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;12: 1267.970 cents 27/13&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">12: 1267.970 cents 27/13</span>
 : 1373.634 cents 20/9
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;14: 1479.298 cents 7/3&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">14: 1479.298 cents 7/3</span>
 : 1584.963 cents 5/2
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;16: 1690.627 cents 8/3&lt;/span&gt;
+<span style="background-color: rgba(255,255,255,0);">16: 1690.627 cents 8/3</span>
 : 1806.2905 cents 45/16
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;18: 3/1&lt;/span&gt;</pre></div>
-<h4>Original HTML content:</h4>
+<span style="background-color: rgba(255,255,255,0);">18: 3/1</span>
-<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;18edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;18edt means the division of the tritave into 18 equal parts &lt;span style="background-color: rgba(255,255,255,0);"&gt;of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.&lt;/span&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;As the double of &lt;a class="wiki_link" href="/9edt" target="_blank"&gt;9edt&lt;/a&gt;, it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like &lt;a class="wiki_link" href="/8edt" target="_blank"&gt;8edt&lt;/a&gt;, is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.&lt;/span&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;0: 1/1&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;1: 105.664 cents 16/15&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;2: 211.328 cents 9/8&lt;/span&gt;&lt;br /&gt;
-: 316.993 cents 6/5&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;4: 422.657 cents 9/7&lt;/span&gt;&lt;br /&gt;
-: 528.321 cents 27/20&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;6: 633.985 cents 13/9&lt;/span&gt;&lt;br /&gt;
-: 739.649 cents 17/13&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;8: 845.313 cents 5/3&lt;/span&gt;&lt;br /&gt;
-: 950.9775 cents 19/11&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;10: 1056.642 cents 9/5&lt;/span&gt;&lt;br /&gt;
-: 1162.306 cents 49/25&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;12: 1267.970 cents 27/13&lt;/span&gt;&lt;br /&gt;
-: 1373.634 cents 20/9&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;14: 1479.298 cents 7/3&lt;/span&gt;&lt;br /&gt;
-: 1584.963 cents 5/2&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;16: 1690.627 cents 8/3&lt;/span&gt;&lt;br /&gt;
-: 1806.2905 cents 45/16&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;18: 3/1&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>