Xenharmonic Wiki

43edt: Difference between revisions

← Older editNewer edit →
VisualWikitext
Wikispaces>xenwolf
**Imported revision 602918480 - Original comment: **
Wikispaces>FREEZE
No edit summary
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
=43 EDT=
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-30 15:56:09 UTC</tt>.<br>
: The original revision id was <tt>602918480</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">=43 EDT=  


This tuning is related to [[27edo]] having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).
This tuning is related to [[27edo|27edo]] having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).


However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt]] is not. The 4L+5s MOS has L=7 s=3.
However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt|13edt]] is not. The 4L+5s MOS has L=7 s=3.


||~ Degrees ||~ Cents ||
{| class="wikitable"
|| 1 || 44.2315 ||
|-
|| 2 || 88.463 ||
! | Degrees
|| 3 || 132.6945 ||
! | Cents
|| 4 || 176.926 ||
|-
|| 5 || 221.158 ||
| | 1
|| 6 || 265.389 ||
| | 44.2315
|| 7 || 309.621 ||
|-
|| 8 || 353.852 ||
| | 2
|| 9 || 398.084 ||
| | 88.463
|| 10 || 442.315 ||
|-
|| 11 || 486.547 ||
| | 3
|| 12 || 530.778 ||
| | 132.6945
|| 13 || 575.01 ||
|-
|| 14 || 619.241 ||
| | 4
|| 15 || 663.473 ||
| | 176.926
|| 16 || 707.704 ||
|-
|| 17 || 751.936 ||
| | 5
|| 18 || 796.167 ||
| | 221.158
|| 19 || 840.399 ||
|-
|| 20 || 884.63 ||
| | 6
|| 21 || 928.862 ||
| | 265.389
|| 22 || 973.093 ||
|-
|| 23 || 1017.325 ||
| | 7
|| 24 || 1061.556 ||
| | 309.621
|| 25 || 1105.788 ||
|-
|| 26 || 1150.019 ||
| | 8
|| 27 || 1194.251 ||
| | 353.852
|| 28 || 1238.482 ||
|-
|| 29 || 1282.713 ||
| | 9
|| 30 || 1326.946 ||
| | 398.084
|| 31 || 1371.177 ||
|-
|| 32 || 1415.408 ||
| | 10
|| 33 || 1459.64 ||
| | 442.315
|| 34 || 1503.871 ||
|-
|| 35 || 1548.193 ||
| | 11
|| 36 || 1592.334 ||
| | 486.547
|| 37 || 1636.566 ||
|-
|| 38 || 1680.797 ||
| | 12
|| 39 || 1725.029 ||
| | 530.778
|| 40 || 1769.2605 ||
|-
|| 41 || 1813.492 ||
| | 13
|| 42 || 1857.7235 ||
| | 575.01
|| 43 || 1901.955 ||</pre></div>
|-
<h4>Original HTML content:</h4>
| | 14
<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;43edt&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="x43 EDT"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;43 EDT&lt;/h1&gt;
| | 619.241
&lt;br /&gt;
|-
This tuning is related to &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt; having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a &amp;quot;sharp tending&amp;quot; system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).&lt;br /&gt;
| | 15
&lt;br /&gt;
| | 663.473
However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt; is not. The 4L+5s MOS has L=7 s=3.&lt;br /&gt;
|-
&lt;br /&gt;
| | 16
 
| | 707.704
 
|-
&lt;table class="wiki_table"&gt;
| | 17
    &lt;tr&gt;
| | 751.936
        &lt;th&gt;Degrees&lt;br /&gt;
|-
&lt;/th&gt;
| | 18
        &lt;th&gt;Cents&lt;br /&gt;
| | 796.167
&lt;/th&gt;
|-
    &lt;/tr&gt;
| | 19
    &lt;tr&gt;
| | 840.399
        &lt;td&gt;1&lt;br /&gt;
|-
&lt;/td&gt;
| | 20
        &lt;td&gt;44.2315&lt;br /&gt;
| | 884.63
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 21
    &lt;tr&gt;
| | 928.862
        &lt;td&gt;2&lt;br /&gt;
|-
&lt;/td&gt;
| | 22
        &lt;td&gt;88.463&lt;br /&gt;
| | 973.093
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 23
    &lt;tr&gt;
| | 1017.325
        &lt;td&gt;3&lt;br /&gt;
|-
&lt;/td&gt;
| | 24
        &lt;td&gt;132.6945&lt;br /&gt;
| | 1061.556
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 25
    &lt;tr&gt;
| | 1105.788
        &lt;td&gt;4&lt;br /&gt;
|-
&lt;/td&gt;
| | 26
        &lt;td&gt;176.926&lt;br /&gt;
| | 1150.019
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 27
    &lt;tr&gt;
| | 1194.251
        &lt;td&gt;5&lt;br /&gt;
|-
&lt;/td&gt;
| | 28
        &lt;td&gt;221.158&lt;br /&gt;
| | 1238.482
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 29
    &lt;tr&gt;
| | 1282.713
        &lt;td&gt;6&lt;br /&gt;
|-
&lt;/td&gt;
| | 30
        &lt;td&gt;265.389&lt;br /&gt;
| | 1326.946
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 31
    &lt;tr&gt;
| | 1371.177
        &lt;td&gt;7&lt;br /&gt;
|-
&lt;/td&gt;
| | 32
        &lt;td&gt;309.621&lt;br /&gt;
| | 1415.408
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 33
    &lt;tr&gt;
| | 1459.64
        &lt;td&gt;8&lt;br /&gt;
|-
&lt;/td&gt;
| | 34
        &lt;td&gt;353.852&lt;br /&gt;
| | 1503.871
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 35
    &lt;tr&gt;
| | 1548.193
        &lt;td&gt;9&lt;br /&gt;
|-
&lt;/td&gt;
| | 36
        &lt;td&gt;398.084&lt;br /&gt;
| | 1592.334
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 37
    &lt;tr&gt;
| | 1636.566
        &lt;td&gt;10&lt;br /&gt;
|-
&lt;/td&gt;
| | 38
        &lt;td&gt;442.315&lt;br /&gt;
| | 1680.797
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 39
    &lt;tr&gt;
| | 1725.029
        &lt;td&gt;11&lt;br /&gt;
|-
&lt;/td&gt;
| | 40
        &lt;td&gt;486.547&lt;br /&gt;
| | 1769.2605
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 41
    &lt;tr&gt;
| | 1813.492
        &lt;td&gt;12&lt;br /&gt;
|-
&lt;/td&gt;
| | 42
        &lt;td&gt;530.778&lt;br /&gt;
| | 1857.7235
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 43
    &lt;tr&gt;
| | 1901.955
        &lt;td&gt;13&lt;br /&gt;
|}
&lt;/td&gt;
[[Category:edt]]
        &lt;td&gt;575.01&lt;br /&gt;
[[Category:todo:unify_precision]]
&lt;/td&gt;
[[Category:tritave]]
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;619.241&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;663.473&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;707.704&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;751.936&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;796.167&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840.399&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884.63&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;928.862&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;973.093&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1017.325&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1061.556&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1105.788&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1150.019&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1194.251&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1238.482&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1282.713&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1326.946&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1371.177&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1415.408&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1459.64&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1503.871&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1548.193&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1592.334&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1636.566&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1680.797&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1725.029&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1769.2605&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1813.492&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1857.7235&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/43edt"