15ed5: 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}}
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-01-04 04:06:40 UTC</tt>.<br>
A multiple of [[5ed5|5ed5]] It approximates the 7th, 12th, 13th, 18th, 31st and 43rd harmonics with some accuracy (but especially the 31st!). [[Hyperpyth]] analogues of [[blackwood]] of course are warranted.
: The original revision id was <tt>289440993</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">=15ed5=


A multiple of [[5ed5]] so its interesting. Indeed, it approximates the 7th, 12th, 13th, 18th, 31st and 43rd harmonics with some accuracy (but especially the 31st!). Hyperpyth analogues of blackwood of course are warranted.
== Intervals ==
.</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;15ed5&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="x15ed5"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;15ed5&lt;/h1&gt;
== Harmonics ==
&lt;br /&gt;
{{Harmonics in equal
A multiple of &lt;a class="wiki_link" href="/5ed5"&gt;5ed5&lt;/a&gt; so its interesting. Indeed, it approximates the 7th, 12th, 13th, 18th, 31st and 43rd harmonics with some accuracy (but especially the 31st!). Hyperpyth analogues of blackwood of course are warranted.&lt;br /&gt;
| steps = 15
.&lt;/body&gt;&lt;/html&gt;</pre></div>
| num = 5
| denom = 1
}}
{{Harmonics in equal
| steps = 15
| num = 5
| denom = 1
| start = 12
| collapsed = 1
}}

Latest revision as of 01:16, 6 October 2024

← 14ed5 15ed5 16ed5 →
Prime factorization 3 × 5
Step size 185.754 ¢ 
Octave 6\15ed5 (1114.53 ¢) (→ 2\5ed5)
Twelfth 10\15ed5 (1857.54 ¢) (→ 2\3ed5)
Consistency limit 3
Distinct consistency limit 3

15 equal divisions of the 5th harmonic (abbreviated 15ed5) is a nonoctave tuning system that divides the interval of 5/1 into 15 equal parts of about 186 ¢ each. Each step represents a frequency ratio of 51/15, or the 15th root of 5. A multiple of 5ed5 It approximates the 7th, 12th, 13th, 18th, 31st and 43rd harmonics with some accuracy (but especially the 31st!). Hyperpyth analogues of blackwood of course are warranted.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 185.8 10/9, 11/10, 19/17, 21/19
2 371.5 21/17
3 557.3 15/11
4 743 14/9, 17/11, 23/15
5 928.8 17/10, 19/11
6 1114.5 17/9, 19/10, 21/11
7 1300.3 15/7, 19/9, 21/10
8 1486 7/3
9 1671.8 13/5
10 1857.5
11 2043.3 23/7
12 2229.1 11/3
13 2414.8
14 2600.6 9/2
15 2786.3 5/1

Harmonics

Approximation of harmonics in 15ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -85.5 -44.4 +14.8 +0.0 +55.9 -25.2 -70.7 -88.8 -85.5 -64.7 -29.6
Relative (%) -46.0 -23.9 +8.0 +0.0 +30.1 -13.6 -38.0 -47.8 -46.0 -34.8 -15.9
Steps
(reduced) 		6
(6) 		10
(10) 		13
(13) 		15
(0) 		17
(2) 		18
(3) 		19
(4) 		20
(5) 		21
(6) 		22
(7) 		23
(8)
Approximation of harmonics in 15ed5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +17.6 +75.0 -44.4 +29.6 -75.3 +11.5 -82.1 +14.8 -69.7 +35.6 -41.4
Relative (%) +9.5 +40.4 -23.9 +15.9 -40.6 +6.2 -44.2 +8.0 -37.5 +19.1 -22.3
Steps
(reduced) 		24
(9) 		25
(10) 		25
(10) 		26
(11) 		26
(11) 		27
(12) 		27
(12) 		28
(13) 		28
(13) 		29
(14) 		29
(14)
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