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21edt: Difference between revisions

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Wikispaces>Kosmorsky
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-08-16 01:18:12 UTC</tt>.<br>
 
: The original revision id was <tt>246175817</tt>.<br>
== Intervals ==
: The revision comment was: <tt></tt><br>
{| class="wikitable"
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>
! Degrees
<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">Before I forget, 21 edt, important. BP family L=4 s=1, quite exaggerated from the optimal 2:1. With a step size of about 90 cents. Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 19th (-24 c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.</pre></div>
! Cents
<h4>Original HTML content:</h4>
! Hekts
<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;21edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Before I forget, 21 edt, important. BP family L=4 s=1, quite exaggerated from the optimal 2:1. With a step size of about 90 cents. Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 19th (-24 c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.&lt;/body&gt;&lt;/html&gt;</pre></div>
! Approximate Ratio
|-
| colspan="3" style="text-align: center;" | 0
| [[1/1|1/1]]
|-
| 1
| 90.569
| 61.905
| [[21/20|21/20]], [[135/128|135/128]]
|-
| 2
| 181.139
| 123.81
| [[10/9|10/9]]
|-
| 3
| 271.708
| 185.714
| [[7/6|7/6]]
|-
| 4
| 362.277
| 247.619
| [[16/13|16/13]]
|-
| 5
| 452.846
| 309.524
| [[13/10|13/10]]
|-
| 6
| 543.416
| 371.429
| [[15/11|15/11]], [[11/8|11/8]]
|-
| 7
| 633.985
| 433.333
| [[13/9|13/9]]
|-
| 8
| 724.554
| 495.238
| 35/23
|-
| 9
| 815.124
| 557.143
| [[8/5|8/5]]
|-
| 10
| 905.693
| 619.048
| 27/16
|-
| 11
| 996.262
| 680.952
| 16/9
|-
| 12
| 1086.831
| 742.857
| [[15/8|15/8]]
|-
| 13
| 1177.401
| 804.762
| 69/35
|-
| 14
| 1267.97
| 866.667
| 27/13
|-
| 15
| 1358.539
| 928.571
| 11/5 ([[11/10|11/10]] plus an octave), 24/11 (12/11 plus an octave)
|-
| 16
| 1449.109
| 990.476
| 30/13 ([[15/13|15/13]] plus an octave)
|-
| 17
| 1539.678
| 1052.381
| 39/16
|-
| 18
| 1630.247
| 1114.286
| 18/7 ([[9/7|9/7]] plus an octave)
|-
| 19
| 1720.816
| 1076.19
| 27/10
|-
| 20
| 1811.386
| 1238.095
| 20/7, 128/45
|-
| 21
| 1901.955
| 1300
| 3/1
|}
 
21edt contains 6 intervals from [[7edt|7edt]] and 2 intervals from [[3edt|3edt]], meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...
 
21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.
 
21edt also contains a 4L5s MOS similar to [[BP|BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt|3edt]] essentially tempered chord).
 
== Harmonics==
Not the best approximations but all within 20 cents: it has 5th&nbsp;(+20¢), 7th&nbsp;(&minus;16¢), 10th&nbsp;(+2¢), 11th&nbsp;(+15¢), 13th&nbsp;(&minus;3¢), 17th&nbsp;(&minus;14¢), 23rd&nbsp;(+6¢), and 37th&nbsp;(&minus;2¢) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.
 
{{Harmonics in equal
| steps = 21
| num = 3
| denom = 1
| intervals = integer
}}
{{Harmonics in equal
| steps = 21
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
 
[[Category:tritave]]
{{todo|expand|improve synopsis}}
Retrieved from "https://en.xen.wiki/w/21edt"