Revision as of 00:00, 17 July 2018

Division of the sixth harmonic into n equal parts

The sixth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see 44ed6 and 49ed6). However, this is not to say of ed6s not supporting this important 13&18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.

4ed6 squares generator (with octaves)

5ed6 tritonic generator (with octaves)

6ed6 compare 7ed8

7ed6 sensi generator (with octaves)

8ed6 würschmidt generator (with octaves)

9ed6 compare 7ed4

10ed6 myna generator (with octaves)

11ed6 compare 17ed16

12ed6 compare 14ed8

13ed6 compare 5edo and 8edt

14ed6

15ed6

16ed6 hemiwuerschimdt generator (with octaves)

17ed6 Minortonic generator (with octaves)

18ed6 compare 7edo and 11edt

19ed6 Porcupine generator (with octaves)

20ed6

21ed6 progression generator (with octaves)

22ed6 compare 17ed4

23ed6 compare 9edo and 14edt

24ed6 twothirdtonic generator (with octaves)

25ed6

26ed6 compare 10edo and 16edt

27ed6

28ed6

29ed6

30ed6

31ed6 compare 12edo and 19edt

32ed6

33ed6

34ed6

35ed6 octacot generator (with octaves)

36ed6 compare 14edo and 22edt

37ed6

38ed6

39ed6 compare 15edo and 24edt

40ed6 valentine generator (with octaves)

41ed6 compare 16edo and 25edt

42ed6

43ed6

44ed6 compare 17edo and 27edt

45ed6

46ed6

47ed6

48ed6 compare 56ed8

49ed6 compare 19edo and 30edt

50ed6

51ed6

52ed6 compare 20edo and 32edt

53ed6

54ed6 compare 21edo and 33edt

55ed6

56ed6

57ed6 compare 22edo and 35edt

58ed6

59ed6

60ed6

61ed6

62ed6 compare 24edo and 38edt

63ed6

64ed6

65ed6 (compare 25edo and 40edt)

66ed6 compare 51ed4

67ed6 compare 26edo and 41edt

68ed6

69ed6

70ed6 compare 27edo and 43edt

71ed6 compare 55ed4

72ed6 compare 28edo and 44edt

73ed6

74ed6

75ed6 compare 29edo and 46edt

Ed6: Difference between revisions

Revision as of 00:00, 17 July 2018

Division of the sixth harmonic into n equal parts

Navigation menu

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+=Division of the sixth harmonic into n equal parts=
-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>2016-11-29 23:42:21 UTC</tt>.<br>
-: The original revision id was <tt>600976038</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">=Division of the sixth harmonic into n equal parts=
-The sixth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, &lt;/span&gt;this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6]] and [[49ed6]]). However, this is not to say of ed6s not supporting this important 13&amp;18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.
+The sixth harmonic is particularly wide as far as equivalences go.<span style=""> There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, </span>this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6|44ed6]] and [[49ed6|49ed6]]). However, this is not to say of ed6s not supporting this important 13&amp;18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.
 ed6 [[Squares|squares]] generator (with octaves)
 ed6 [[Tritonic|tritonic]] generator (with octaves)
 ed6 compare 7ed8
 ed6 [[Sensi|sensi]] generator (with octaves)
 ed6 [[Würschmidt|würschmidt]] generator (with octaves)
 ed6 compare 7ed4
 ed6 [[Myna|myna]] generator (with octaves)
 ed6 compare 17ed16
 ed6 compare 14ed8
-ed6 compare [[5edo]] and [[8edt]]
+ed6 compare [[5edo|5edo]] and [[8edt|8edt]]
 ed6
 ed6
 ed6 [[Hemiwuerschmidt|hemiwuerschimdt]] generator (with octaves)
-ed6 [[Minortonic family|Minortonic]] generator (with octaves)
-ed6 compare [[7edo]] and [[11edt]]
+ed6 [[Minortonic_family|Minortonic]] generator (with octaves)
-ed6 [[Porcupine]] generator (with octaves)
+ed6 compare [[7edo|7edo]] and [[11edt|11edt]]
+ed6 [[Porcupine|Porcupine]] generator (with octaves)
 ed6
 ed6 [[Progression|progression]] generator (with octaves)
 ed6 compare 17ed4
-ed6 compare [[9edo]] and [[14edt]]
+ed6 compare [[9edo|9edo]] and [[14edt|14edt]]
 ed6 [[Twothirdtonic|twothirdtonic]] generator (with octaves)
 ed6
-ed6 compare [[10edo]] and [[16edt]]
+ed6 compare [[10edo|10edo]] and [[16edt|16edt]]
 ed6
 ed6
 ed6
 ed6
-ed6 compare [[12edo]] and [[19edt]]
+ed6 compare [[12edo|12edo]] and [[19edt|19edt]]
 ed6
 ed6
 ed6
 ed6 [[Octacot|octacot]] generator (with octaves)
-ed6 compare [[14edo]] and [[22edt]]
+ed6 compare [[14edo|14edo]] and [[22edt|22edt]]
 ed6
 ed6
-ed6 compare [[15edo]] and [[24edt]]
+ed6 compare [[15edo|15edo]] and [[24edt|24edt]]
 ed6 [[Valentine|valentine]] generator (with octaves)
-ed6 compare [[16edo]] and [[25edt]]
+ed6 compare [[16edo|16edo]] and [[25edt|25edt]]
 ed6
 ed6
-[[44ed6]] compare [[17edo]] and [[27edt]]
+[[44ed6|44ed6]] compare [[17edo|17edo]] and [[27edt|27edt]]
 ed6
 ed6
 ed6
 ed6 compare 56ed8
-[[49ed6]] compare [[19edo]] and [[30edt]]
+[[49ed6|49ed6]] compare [[19edo|19edo]] and [[30edt|30edt]]
 ed6
 ed6
-ed6 compare [[20edo]] and [[32edt]]
+ed6 compare [[20edo|20edo]] and [[32edt|32edt]]
 ed6
-ed6 compare [[21edo]] and [[33edt]]
+ed6 compare [[21edo|21edo]] and [[33edt|33edt]]
 ed6
 ed6
-ed6 compare [[22edo]] and [[35edt]]
+ed6 compare [[22edo|22edo]] and [[35edt|35edt]]
 ed6
 ed6
 ed6
 ed6
-ed6 compare [[24edo]] and [[38edt]]
+ed6 compare [[24edo|24edo]] and [[38edt|38edt]]
 ed6
 ed6
-ed6 (compare [[25edo]] and [[40edt]])
+ed6 (compare [[25edo|25edo]] and [[40edt|40edt]])
 ed6 compare 51ed4
-ed6 compare [[26edo]] and [[41edt]]
+ed6 compare [[26edo|26edo]] and [[41edt|41edt]]
 ed6
 ed6
-ed6 compare [[27edo]] and [[43edt]]
+ed6 compare [[27edo|27edo]] and [[43edt|43edt]]
 ed6 compare 55ed4
-ed6 compare [[28edo]] and [[44edt]]
+ed6 compare [[28edo|28edo]] and [[44edt|44edt]]
 ed6
 ed6
-ed6 compare [[29edo]] and 46edt</pre></div>
-<h4>Original HTML content:</h4>
+ed6 compare [[29edo|29edo]] and 46edt
-<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;ed6&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Division of the sixth harmonic into n equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Division of the sixth harmonic into n equal parts&lt;/h1&gt;
- &lt;br /&gt;
-The sixth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, &lt;/span&gt;this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see &lt;a class="wiki_link" href="/44ed6"&gt;44ed6&lt;/a&gt; and &lt;a class="wiki_link" href="/49ed6"&gt;49ed6&lt;/a&gt;). However, this is not to say of ed6s not supporting this important 13&amp;amp;18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.&lt;br /&gt;
-&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Squares"&gt;squares&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Tritonic"&gt;tritonic&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare 7ed8&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Sensi"&gt;sensi&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/W%C3%BCrschmidt"&gt;würschmidt&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare 7ed4&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Myna"&gt;myna&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare 17ed16&lt;br /&gt;
-ed6 compare 14ed8&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; and &lt;a class="wiki_link" href="/8edt"&gt;8edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Hemiwuerschmidt"&gt;hemiwuerschimdt&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Minortonic%20family"&gt;Minortonic&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt; and &lt;a class="wiki_link" href="/11edt"&gt;11edt&lt;/a&gt;&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Progression"&gt;progression&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare 17ed4&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; and &lt;a class="wiki_link" href="/14edt"&gt;14edt&lt;/a&gt;&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Twothirdtonic"&gt;twothirdtonic&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt; and &lt;a class="wiki_link" href="/16edt"&gt;16edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/19edt"&gt;19edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Octacot"&gt;octacot&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edt"&gt;22edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; and &lt;a class="wiki_link" href="/24edt"&gt;24edt&lt;/a&gt;&lt;br /&gt;
-ed6 &lt;a class="wiki_link" href="/Valentine"&gt;valentine&lt;/a&gt; generator (with octaves)&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; and &lt;a class="wiki_link" href="/25edt"&gt;25edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-&lt;a class="wiki_link" href="/44ed6"&gt;44ed6&lt;/a&gt; compare &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt; and &lt;a class="wiki_link" href="/27edt"&gt;27edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare 56ed8&lt;br /&gt;
-&lt;a class="wiki_link" href="/49ed6"&gt;49ed6&lt;/a&gt; compare &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; and &lt;a class="wiki_link" href="/30edt"&gt;30edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt; and &lt;a class="wiki_link" href="/32edt"&gt;32edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt; and &lt;a class="wiki_link" href="/33edt"&gt;33edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; and &lt;a class="wiki_link" href="/35edt"&gt;35edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; and &lt;a class="wiki_link" href="/38edt"&gt;38edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 (compare &lt;a class="wiki_link" href="/25edo"&gt;25edo&lt;/a&gt; and &lt;a class="wiki_link" href="/40edt"&gt;40edt&lt;/a&gt;)&lt;br /&gt;
-ed6 compare 51ed4&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt; and &lt;a class="wiki_link" href="/41edt"&gt;41edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt; and &lt;a class="wiki_link" href="/43edt"&gt;43edt&lt;/a&gt;&lt;br /&gt;
-ed6 compare 55ed4&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/28edo"&gt;28edo&lt;/a&gt; and &lt;a class="wiki_link" href="/44edt"&gt;44edt&lt;/a&gt;&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6&lt;br /&gt;
-ed6 compare &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; and 46edt&lt;/body&gt;&lt;/html&gt;</pre></div>

Ed6: Difference between revisions

Revision as of 00:00, 17 July 2018

Division of the sixth harmonic into n equal parts

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