37ed4: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>toddiharrop
**Imported revision 302975182 - Original comment: **
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,330 edits
m Removing from Category:Ed4 using Cat-a-lot
 
(7 intermediate revisions by 6 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
37ED4 is an [[equal]] tuning which divides the 4/1 double octave into 37 steps of approximately 64.865¢. As an [[ed4|ED4]] system, it is equivalent to taking every other tone of [[37edo]]. All the intervals of 37ED4 are thus the same as or an octave away from a corresponding interval in 37edo.
: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2012-02-18 10:43:29 UTC</tt>.<br>
: The original revision id was <tt>302975182</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">37ED4 is an [[equal]] tuning which divides the 4/1 double octave into 37 steps of approximately 64.865¢. As an [[ED4]] system, it is equivalent to taking every other tone of [[37edo]]. All the intervals of 37ED4 are thus the same as or an octave away from a corresponding interval in 37edo.


[[65cET]] is a slightly stretched version of 37ED4, in which the 37th degree is 5¢ sharp of 4/1.
[[65cET]] is a slightly stretched version of 37ED4, in which the 37th degree is 5¢ sharp of 4/1.


===Music===  
== Intervals ==
[[http://soundcloud.com/puffinwrangler/happy-birthday|Happy Birthday]] by Todd Harrop</pre></div>
{{Interval table}}
<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;37ED4&lt;/title&gt;&lt;/head&gt;&lt;body&gt;37ED4 is an &lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt; tuning which divides the 4/1 double octave into 37 steps of approximately 64.865¢. As an &lt;a class="wiki_link" href="/ED4"&gt;ED4&lt;/a&gt; system, it is equivalent to taking every other tone of &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt;. All the intervals of 37ED4 are thus the same as or an octave away from a corresponding interval in 37edo.&lt;br /&gt;
== Harmonics ==
&lt;br /&gt;
{{Harmonics in equal
&lt;a class="wiki_link" href="/65cET"&gt;65cET&lt;/a&gt; is a slightly stretched version of 37ED4, in which the 37th degree is 5¢ sharp of 4/1.&lt;br /&gt;
| steps = 37
&lt;br /&gt;
| num = 4
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h3&gt;
| denom = 1
&lt;a class="wiki_link_ext" href="http://soundcloud.com/puffinwrangler/happy-birthday" rel="nofollow"&gt;Happy Birthday&lt;/a&gt; by Todd Harrop&lt;/body&gt;&lt;/html&gt;</pre></div>
}}
{{Harmonics in equal
| steps = 37
| num = 4
| denom = 1
| start = 12
| collapsed = 1
}}
 
== Music ==
* [http://soundcloud.com/puffinwrangler/happy-birthday Happy Birthday] by [[Todd Harrop]]
 
[[Category:Equal-step tuning]]
[[Category:Nonoctave]]
{{todo|expand}}

Latest revision as of 21:18, 31 July 2025

← 35ed4 37ed4 39ed4 →
Prime factorization 37 (prime)
Step size 64.8649 ¢ 
Octave 19\37ed4 (1232.43 ¢)
Twelfth 29\37ed4 (1881.08 ¢)
Consistency limit 1
Distinct consistency limit 1

37ED4 is an equal tuning which divides the 4/1 double octave into 37 steps of approximately 64.865¢. As an ED4 system, it is equivalent to taking every other tone of 37edo. All the intervals of 37ED4 are thus the same as or an octave away from a corresponding interval in 37edo.

65cET is a slightly stretched version of 37ED4, in which the 37th degree is 5¢ sharp of 4/1.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 64.9 26/25
2 129.7
3 194.6 19/17, 29/26
4 259.5 7/6, 22/19, 29/25
5 324.3 23/19
6 389.2
7 454.1 22/17
8 518.9 23/17
9 583.8 7/5
10 648.6
11 713.5
12 778.4 11/7
13 843.2
14 908.1
15 973
16 1037.8
17 1102.7
18 1167.6
19 1232.4
20 1297.3
21 1362.2 11/5
22 1427 25/11
23 1491.9 26/11
24 1556.8
25 1621.6
26 1686.5
27 1751.4
28 1816.2
29 1881.1
30 1945.9
31 2010.8
32 2075.7
33 2140.5
34 2205.4 25/7
35 2270.3 26/7
36 2335.1
37 2400

Harmonics

Approximation of harmonics in 37ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +32.4 -20.9 +0.0 +2.9 +11.6 +4.1 +32.4 +23.1 -29.6 +0.0 -20.9
Relative (%) +50.0 -32.2 +0.0 +4.4 +17.8 +6.4 +50.0 +35.6 -45.6 +0.1 -32.2
Steps
(reduced) 		19
(19) 		29
(29) 		37
(0) 		43
(6) 		48
(11) 		52
(15) 		56
(19) 		59
(22) 		61
(24) 		64
(27) 		66
(29)
Approximation of harmonics in 37ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -29.7 -28.3 -18.0 +0.0 +24.8 -9.3 +26.8 +2.9 -16.7 -32.4 +20.4
Relative (%) -45.8 -43.6 -27.7 +0.0 +38.2 -14.4 +41.3 +4.4 -25.8 -49.9 +31.4
Steps
(reduced) 		68
(31) 		70
(33) 		72
(35) 		74
(0) 		76
(2) 		77
(3) 		79
(5) 		80
(6) 		81
(7) 		82
(8) 		84
(10)

Music

Retrieved from "https://en.xen.wiki/index.php?title=37ed4&oldid=205647"