31ed8: 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>
{{ED intro}} It is identical to every third step of [[31edo]].
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-01-13 06:01:38 UTC</tt>.<br>
 
: The original revision id was <tt>537096370</tt>.<br>
== Intervals ==
: The revision comment was: <tt></tt><br>
{{Interval table}}
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>
== Harmonics ==
<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">Music:
{{Harmonics in equal|31|8|1}}
[[https://soundcloud.com/jdfreivald/a-call-in-summer-60-by-60|A Call in Summer]] by Jake Freivald</pre></div>
{{Harmonics in equal|31|8|1|collapsed=1|start=12}}
<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;31ed8&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Music:&lt;br /&gt;
== Music ==
&lt;a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/a-call-in-summer-60-by-60" rel="nofollow"&gt;A Call in Summer&lt;/a&gt; by Jake Freivald&lt;/body&gt;&lt;/html&gt;</pre></div>
* [https://soundcloud.com/jdfreivald/a-call-in-summer-60-by-60 A Call in Summer] by [[Jake Freivald]]
 
 
{{stub}}
[[Category:31edo]]
[[Category:Listen]]

Latest revision as of 19:21, 1 August 2025

← 30ed8 31ed8 32ed8 →
Prime factorization 31 (prime)
Step size 116.129 ¢ 
Octave 10\31ed8 (1161.29 ¢)
Twelfth 16\31ed8 (1858.06 ¢)
Consistency limit 3
Distinct consistency limit 3

31 equal divisions of the 8th harmonic (abbreviated 31ed8) is a nonoctave tuning system that divides the interval of 8/1 into 31 equal parts of about 116 ¢ each. Each step represents a frequency ratio of 81/31, or the 31st root of 8. It is identical to every third step of 31edo.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 116.1 15/14
2 232.3
3 348.4
4 464.5 17/13
5 580.6 7/5
6 696.8 3/2
7 812.9
8 929
9 1045.2
10 1161.3
11 1277.4 21/10, 23/11
12 1393.5
13 1509.7
14 1625.8
15 1741.9
16 1858.1
17 1974.2 22/7
18 2090.3 10/3
19 2206.5 25/7
20 2322.6
21 2438.7
22 2554.8
23 2671 14/3
24 2787.1 5/1
25 2903.2
26 3019.4
27 3135.5
28 3251.6
29 3367.7 7/1
30 3483.9 15/2
31 3600

Harmonics

Approximation of harmonics in 31ed8
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -38.7 -43.9 +38.7 +0.8 +33.5 -1.1 +0.0 +28.3 -37.9 +29.3 -5.2
Relative (%) -33.3 -37.8 +33.3 +0.7 +28.9 -0.9 +0.0 +24.4 -32.7 +25.3 -4.5
Steps
(reduced) 		10
(10) 		16
(16) 		21
(21) 		24
(24) 		27
(27) 		29
(29) 		31
(0) 		33
(2) 		34
(3) 		36
(5) 		37
(6)
Approximation of harmonics in 31ed8
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -27.6 -39.8 -43.1 -38.7 -27.5 -10.4 +12.2 +39.5 -45.0 -9.4 +29.8
Relative (%) -23.8 -34.3 -37.1 -33.3 -23.7 -8.9 +10.5 +34.0 -38.7 -8.1 +25.7
Steps
(reduced) 		38
(7) 		39
(8) 		40
(9) 		41
(10) 		42
(11) 		43
(12) 		44
(13) 		45
(14) 		45
(14) 		46
(15) 		47
(16)

Music


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