93ed30: Difference between revisions

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**Imported revision 603346338 - Original comment: 30:1 is an example where the cent value gives a worse impression than using microoctaves would.**
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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:xenwolf|xenwolf]] and made on <tt>2017-01-09 03:31:15 UTC</tt>.<br>
: The original revision id was <tt>603346338</tt>.<br>
: The revision comment was: <tt>30:1 is an example where the cent value gives a worse impression than using microoctaves would.</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">**93ed30** is the division of [[30_1|30:1]] into 93 equal parts of 63.3147 cents each. It's a variant of [[19edo]] with a stretched [[octave]] of about 1203 cents.


todo: expand</pre></div>
== Theory ==
<h4>Original HTML content:</h4>
93ed30 is a variant of [[19edo]] with a stretched [[2/1|octave]] of about 1203 cents. Like 19edo, 93ed30 is [[consistent]] to the [[integer limit|10-integer-limit]]. It optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp.
<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;93ed30&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;93ed30&lt;/strong&gt; is the division of &lt;a class="wiki_link" href="/30_1"&gt;30:1&lt;/a&gt; into 93 equal parts of 63.3147 cents each. It's a variant of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; with a stretched &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; of about 1203 cents.&lt;br /&gt;
 
&lt;br /&gt;
=== Harmonics ===
todo: expand&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Harmonics in equal|93|30|1|intervals=integer|columns=11}}
{{Harmonics in equal|93|30|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 93ed30 (continued)}}
 
=== Subsets and supersets ===
Since 93 factors into primes as {{nowrap| 3 × 31 }}, 93ed30 contains [[3ed30]] and [[31ed30]] as subset ed30's.
 
== See also ==
* [[11edf]] – relative edf
* [[19edo]] – relative edo
* [[30edt]] – relative edt
* [[49ed6]] – relative ed6
* [[53ed7]] – relative ed7
* [[68ed12]] – relative ed12
 
[[Category:19edo]]

Latest revision as of 13:13, 30 March 2025

← 92ed30 93ed30 94ed30 →
Prime factorization 3 × 31
Step size 63.3147 ¢ 
Octave 19\93ed30 (1202.98 ¢)
Twelfth 30\93ed30 (1899.44 ¢) (→ 10\31ed30)
Consistency limit 10
Distinct consistency limit 7

93 equal divisions of the 30th harmonic (abbreviated 93ed30) is a nonoctave tuning system that divides the interval of 30/1 into 93 equal parts of about 63.3 ¢ each. Each step represents a frequency ratio of 301/93, or the 93rd root of 30.

Theory

93ed30 is a variant of 19edo with a stretched octave of about 1203 cents. Like 19edo, 93ed30 is consistent to the 10-integer-limit. It optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp.

Harmonics

Approximation of harmonics in 93ed30
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.0 -2.5 +6.0 -0.5 +0.5 -13.1 +8.9 -5.0 +2.5 +27.5 +3.4
Relative (%) +4.7 -4.0 +9.4 -0.7 +0.7 -20.8 +14.1 -7.9 +4.0 +43.4 +5.4
Steps
(reduced) 		19
(19) 		30
(30) 		38
(38) 		44
(44) 		49
(49) 		53
(53) 		57
(57) 		60
(60) 		63
(63) 		66
(66) 		68
(68)
Approximation of harmonics in 93ed30 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -8.5 -10.2 -3.0 +11.9 -29.7 -2.0 +31.0 +5.5 -15.7 +30.4 +16.8 +6.4
Relative (%) -13.4 -16.1 -4.7 +18.8 -46.9 -3.2 +48.9 +8.7 -24.7 +48.1 +26.5 +10.1
Steps
(reduced) 		70
(70) 		72
(72) 		74
(74) 		76
(76) 		77
(77) 		79
(79) 		81
(81) 		82
(82) 		83
(83) 		85
(85) 		86
(86) 		87
(87)

Subsets and supersets

Since 93 factors into primes as 3 × 31, 93ed30 contains 3ed30 and 31ed30 as subset ed30's.

See also

Retrieved from "https://en.xen.wiki/index.php?title=93ed30&oldid=188922"