2100edo: 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:genewardsmith|genewardsmith]] and made on <tt>2011-10-25 14:13:56 UTC</tt>.<br>
 
: The original revision id was <tt>268443454</tt>.<br>
The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit [[schismatic|schismatic aka helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to [[quarter-comma meantone]].
: 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>
=== Odd harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|2100}}
<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 2100 equal division divides the octave into 2100 parts of precisely 4/7 cents (0.5714 cents) each. The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka [[Schismatic family|helmholtz]] temperament, and the 7-limit [[Schismatic family#Sesquiquartififths|sesquiquartififths temperament]]. As with any equal division of this size, it supports a number of possible meantone tunings, but &lt;2100 3319 4876 5890| is notable for being nearly identical to [[quarter-comma meantone]].</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;2100edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 2100 equal division divides the octave into 2100 parts of precisely 4/7 cents (0.5714 cents) each. The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka &lt;a class="wiki_link" href="/Schismatic%20family"&gt;helmholtz&lt;/a&gt; temperament, and the 7-limit &lt;a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths"&gt;sesquiquartififths temperament&lt;/a&gt;. As with any equal division of this size, it supports a number of possible meantone tunings, but &amp;lt;2100 3319 4876 5890| is notable for being nearly identical to &lt;a class="wiki_link" href="/quarter-comma%20meantone"&gt;quarter-comma meantone&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 2100 factors into {{factorization|2100}}, 2100edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050 }}.
 
[[Category:Meantone]]

Latest revision as of 14:16, 20 February 2025

← 2099edo 2100edo 2101edo →
Prime factorization 22 × 3 × 52 × 7
Step size 0.571429 ¢ 
Fifth 1228\2100 (701.714 ¢) (→ 307\525)
Semitones (A1:m2) 196:160 (112 ¢ : 91.43 ¢)
Dual sharp fifth 1229\2100 (702.286 ¢)
Dual flat fifth 1228\2100 (701.714 ¢) (→ 307\525)
Dual major 2nd 357\2100 (204 ¢) (→ 17\100)
Consistency limit 7
Distinct consistency limit 7

2100 equal divisions of the octave (abbreviated 2100edo or 2100ed2), also called 2100-tone equal temperament (2100tet) or 2100 equal temperament (2100et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2100 equal parts of about 0.571 ¢ each. Each step represents a frequency ratio of 21/2100, or the 2100th root of 2.

The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka helmholtz temperament, and the 7-limit sesquiquartififths temperament. As with any equal division of this size, it supports a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to quarter-comma meantone.

Odd harmonics

Approximation of odd harmonics in 2100edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.241 -0.028 -0.254 +0.090 +0.111 +0.044 -0.269 +0.187 +0.201 +0.076 -0.274
Relative (%) -42.1 -4.9 -44.5 +15.7 +19.4 +7.7 -47.0 +32.8 +35.2 +13.3 -48.0
Steps
(reduced) 		3328
(1228) 		4876
(676) 		5895
(1695) 		6657
(357) 		7265
(965) 		7771
(1471) 		8204
(1904) 		8584
(184) 		8921
(521) 		9224
(824) 		9499
(1099)

Subsets and supersets

Since 2100 factors into 22 × 3 × 52 × 7, 2100edo has subset edos 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050.

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