28edt: Difference between revisions

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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>
'''28edt''' divides the [[3/1|third harmonic]] into 28 [[equal]] parts of 67.9 [[cent]]s each. It is the simplest [[edt]] which intelligibly doubles the Anti-BP harmonic chain{{clarify}}. One step is very close to every third step of [[53edo]]. It tempers out the [[schisma]] in the 8.3.5 subgroup, albeit a really strange tuning due to being a multiple of 4edt and being index-2 in BP.  It also supports [[deneb]] temperament in the 3.5.11 subgroup, equating 4 [[11/9]]s with [[11/5]].
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-15 09:25:39 UTC</tt>.<br>
: The original revision id was <tt>602230286</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 simplest edt which intelligibly doubles the Anti-BP harmonic chain. It is a schismatic temperament, albeit a really strange one due to being a multiple of 4edt and being index-2 in BP.


||~ Degree ||~ cents ||~ notation ||
== Harmonics ==
|| 1/28 || 67.93 || Cq/D@y ||
{{Harmonics in equal
|| 2/28 || 135.85 || Cp/D@ ||
| steps = 28
|| 3/28 || 203.78 || Cp/Dy ||
| num = 3
|| 4/28 || 271.71 || D ||
| denom = 1
|| 5/28 || 339.635 || Dp/Ey ||
| intervals = integer
|| 6/28 || 407.56 || E ||
}}
|| 7/28 || 475.49 || Epq/F@y ||
{{Harmonics in equal
|| 8/28 || 543.42 || Ep/F@ ||
| steps = 28
|| 9/28 || 611.34 || Eq/Fy ||
| num = 3
|| 10/28 || 679.27 || F ||
| denom = 1
|| 11/28 || 747.2 || Fq/Gy ||
| start = 12
|| 12/28 || 815.12 || G ||
| collapsed = 1
|| 13/28 || 883.05 || Gq/Hy ||
| intervals = integer
|| 14/28 || 950.98 || Gp/H@ ||
}}
|| 15/28 || 1018.9 || Gpq/H@y ||
|| 16/28 || 1086.83 || H ||
|| 17/28 || 1154.76 || Hq/Jy ||
|| 18/28 || 1222.685 || J ||
|| 19/28 || 1290.61 || Jq/A@y ||
|| 20/28 || 1358.54 || Jp/A@ ||
|| 21/28 || 1426.47 || Jpq/Ay ||
|| 22/28 || 1494.39 || A ||
|| 23/28 || 1562.32 || Aq/B@y ||
|| 24/28 || 1630.25 || Ap/B@ ||
|| 25/28 || 1698.17 || Apq/By ||
|| 26/28 || 1766.1 || B ||
|| 27/28 || 1834.03 || Bq/Cy ||
|| 28/28 || 1901.955 || C ||</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;28edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the simplest edt which intelligibly doubles the Anti-BP harmonic chain. It is a schismatic temperament, albeit a really strange one due to being a multiple of 4edt and being index-2 in BP.&lt;br /&gt;
&lt;br /&gt;


== Intervals ==
{| class="wikitable right-all left-4"
|-
! Steps
! [[cent]]s
! [[hekt]]s
! notation
|-
| 1
| 67.927
| 46.429
| Cq/D\\y
|-
| 2
| 135.854
| 92.857
| Cp/D\\
|-
| 3
| 203.781
| 139.286
| Cpq/Dy
|-
| 4
| 271.708
| 185.714
| D
|-
| 5
| 339.635
| 232.143
| Dp/Ey
|-
| 6
| 407.562
| 278.571
| E
|-
| 7
| 475.489
| 325.000
| Epq/F\\y
|-
| 8
| 543.416
| 371.429
| Ep/F\\
|-
| 9
| 611.343
| 417.857
| Eq/Fy
|-
| 10
| 679.270
| 464.286
| F
|-
| 11
| 747.197
| 510.714
| Fq/Gy
|-
| 12
| 815.124
| 557.143
| G
|-
| 13
| 883.051
| 603.571
| Gq/H\\y
|-
| 14
| 950.978
| 650.000
| Gp/H\\
|-
| 15
| 1018.904
| 696.429
| Gpq/Hy
|-
| 16
| 1086.831
| 742.857
| H
|-
| 17
| 1154.758
| 789.286
| Hq/Jy
|-
| 18
| 1222.685
| 835.714
| J
|-
| 19
| 1290.612
| 882.143
| Jq/A\\y
|-
| 20
| 1358.539
| 928.571
| Jp/A\\
|-
| 21
| 1426.466
| 975.000
| Jpq/Ay
|-
| 22
| 1494.393
| 1021.429
| A
|-
| 23
| 1562.320
| 1067.857
| Aq/B\\y
|-
| 24
| 1630.247
| 1114.286
| Ap/B\\
|-
| 25
| 1698.174
| 1160.714
| Apq/By
|-
| 26
| 1766.101
| 1207.143
| B
|-
| 27
| 1834.028
| 1253.571
| Bq/Cy
|-
| 28
| 1901.955
| 1300.000
| C
|}


&lt;table class="wiki_table"&gt;
== Music ==
    &lt;tr&gt;
* [http://www.seraph.it/dep/det/NonOctaveMelancholic.mp3 NonOctave Melancholic] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/06940a530481965d791c521ea45012f2-267.html blog entry])
        &lt;th&gt;Degree&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notation&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;67.93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cq/D@y&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;135.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cp/D@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.78&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cp/Dy&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;339.635&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dp/Ey&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;407.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;475.49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Epq/F@y&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ep/F@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;611.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Eq/Fy&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;679.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;747.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Fq/Gy&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;815.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;883.05&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gq/Hy&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;950.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gp/H@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1018.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gpq/H@y&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1086.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1154.76&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hq/Jy&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1222.685&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1290.61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jq/A@y&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1358.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jp/A@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1426.47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jpq/Ay&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1494.39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1562.32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Aq/B@y&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1630.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ap/B@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1698.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Apq/By&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1766.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1834.03&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Bq/Cy&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
{{todo|expand}}