1236edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-15 12:11:29 UTC</tt>.<br>
 
: The original revision id was <tt>556730349</tt>.<br>
1236edo is a [[zeta peak edo]], though not [[zeta integral edo|zeta integral]] nor [[zeta gap edo|zeta gap]]. It is a strong 17-limit system and [[consistency|distinctly consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.  
: 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>
=== Prime harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|1236|columns=11}}
<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">The 1236 division of the octave divides it into 1236 equal parts of 0.9709 cents each. It is a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely consistent through the 17-limit, with a 17-limit comma basis of 2601/2600, 5832/5831, 9801/9800, 10648/10647, 14875/14872 and 105644/105625. It is divisible by 12 (12 * 103 = 1236).</pre></div>
 
<h4>Original HTML content:</h4>
=== Subsets and supersets ===
<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;1236edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 1236 division of the octave divides it into 1236 equal parts of 0.9709 cents each. It is a  &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta peak edo&lt;/a&gt;, though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely consistent through the 17-limit, with a 17-limit comma basis of 2601/2600, 5832/5831, 9801/9800, 10648/10647, 14875/14872 and 105644/105625. It is divisible by 12 (12 * 103 = 1236).&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 1236 factors into {{factorization|1236}}, 1236edo has subset edos {{EDOs| 2, 3, 6, 12, 103, 206, 309, and 618 }}. It is divisible by 12, and is an [[atomic]] system.

Latest revision as of 16:58, 18 February 2025

← 1235edo 1236edo 1237edo →
Prime factorization 22 × 3 × 103
Step size 0.970874 ¢ 
Fifth 723\1236 (701.942 ¢) (→ 241\412)
Semitones (A1:m2) 117:93 (113.6 ¢ : 90.29 ¢)
Consistency limit 17
Distinct consistency limit 17

1236 equal divisions of the octave (abbreviated 1236edo or 1236ed2), also called 1236-tone equal temperament (1236tet) or 1236 equal temperament (1236et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1236 equal parts of about 0.971 ¢ each. Each step represents a frequency ratio of 21/1236, or the 1236th root of 2.

1236edo is a zeta peak edo, though not zeta integral nor zeta gap. It is a strong 17-limit system and distinctly consistent through the 17-odd-limit, with a 17-limit comma basis of {2601/2600, 4096/4095, 5832/5831, 6656/6655, 9801/9800, 105644/105625}.

Prime harmonics

Approximation of prime harmonics in 1236edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.013 +0.094 +0.106 +0.138 +0.249 -0.101 -0.426 -0.119 -0.451 -0.375
Relative (%) +0.0 -1.4 +9.7 +10.9 +14.3 +25.7 -10.4 -43.8 -12.3 -46.5 -38.7
Steps
(reduced) 		1236
(0) 		1959
(723) 		2870
(398) 		3470
(998) 		4276
(568) 		4574
(866) 		5052
(108) 		5250
(306) 		5591
(647) 		6004
(1060) 		6123
(1179)

Subsets and supersets

Since 1236 factors into 22 × 3 × 103, 1236edo has subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an atomic system.

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