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200edo: 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-06-30 02:51:11 UTC</tt>.<br>
: The original revision id was <tt>239460511</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">&lt;span style="color: #007027; display: block; font-size: 118%;"&gt;200 tone equal temperament&lt;/span&gt;
200 [[EDO]] contains a [[perfect fourth]] and [[perfect fifth]] in exactly **498 and 702 cents.**


**200 tone equal modes:**
== Theory ==
34 34 15 34 34 34 15 = MOS 5L2s (Pytagorean tuning)
200edo contains a [[perfect fifth]] of exactly 702 cents and a [[perfect fourth]] of exactly 498 cents, which is accurate due to 200 being the denominator of a continued fraction convergent to log<sub>2</sub>(3/2). Only about 0.045 cents sharp, it is the next best fifth in absolute error after [[53edo]]'s. In light of having its perfect fifth precise and the step divisible by 9, it is essentially a perfect edo for [[Carlos Alpha]], even up many octaves (the difference between 13 steps of 200edo and 1 step of Carlos Alpha is only 0.03501 cents).
32 32 20 32 32 32 20 = Meantone tuning (like a 50edo)
 
27 27 27 27 27 27 27 11 = MOS 7L1s (Porcupine-8 tuning (aka Octamonatonic Scale))
It [[tempering out|tempers out]] the [[schisma]] (32805/32768) and the quartemka, {{monzo| 2 -32 21 }} in the 5-limit, and the [[gamelisma]], 1029/1024, in the [[7-limit]], so that it [[support]]s the [[guiron]] temperament.
26 26 26 9 26 26 26 26 9 = MOS 7L2s (The most important Armodue-Hornbostel (aka Nonnadiatonic Scale), (Bright mode))
 
24 24 24 16 24 24 24 24 16 = Armodue-Mesotonic tuning (like a 25edo), (Mellow mode)
One step of 200edo is close to [[289/288]]. Unfortunately, it is not compatible with any obvious 2.3.17 subgroup mappings of 200edo.
22 22 8 22 22 22 8 22 22 22 8 = Sensi-11 (or Undecimal Triatonic)
 
16 16 16 8 16 16 16 16 8 16 16 16 16 8 = Tetradecimal Triatonic Scale (Witnots)</pre></div>
=== Prime harmonics ===
<h4>Original HTML content:</h4>
{{Harmonics in equal|200}}
<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;200edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #007027; display: block; font-size: 118%;"&gt;200 tone equal temperament&lt;/span&gt;&lt;br /&gt;
 
200 &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; contains a &lt;a class="wiki_link" href="/perfect%20fourth"&gt;perfect fourth&lt;/a&gt; and &lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt; in exactly &lt;strong&gt;498 and 702 cents.&lt;/strong&gt;&lt;br /&gt;
=== Subsets and supersets ===
&lt;br /&gt;
200 factorizes as 2<sup>3</sup> × 5<sup>2</sup>, and has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}.
&lt;strong&gt;200 tone equal modes:&lt;/strong&gt;&lt;br /&gt;
 
34 34 15 34 34 34 15 = MOS 5L2s (Pytagorean tuning)&lt;br /&gt;
[[400edo]], which doubles it, provides good correction for the harmonics 5 and 7, and makes for a strong 19-limit system.
32 32 20 32 32 32 20 = Meantone tuning (like a 50edo)&lt;br /&gt;
 
27 27 27 27 27 27 27 11 = MOS 7L1s (Porcupine-8 tuning (aka Octamonatonic Scale))&lt;br /&gt;
== Regular temperament properties ==
26 26 26 9 26 26 26 26 9 = MOS 7L2s (The most important Armodue-Hornbostel (aka Nonnadiatonic Scale), (Bright mode))&lt;br /&gt;
{| class="wikitable center-4 center-5 center-6"
24 24 24 16 24 24 24 24 16 = Armodue-Mesotonic tuning (like a 25edo), (Mellow mode)&lt;br /&gt;
|-
22 22 8 22 22 22 8 22 22 22 8 = Sensi-11 (or Undecimal Triatonic)&lt;br /&gt;
! rowspan="2" | [[Subgroup]]
16 16 16 8 16 16 16 16 8 16 16 16 16 8 = Tetradecimal Triatonic Scale (Witnots)&lt;/body&gt;&lt;/html&gt;</pre></div>
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 317 -200 }}
| {{mapping| 200 317 }}
| −0.0142
| 0.0142
| 0.24
|-
| 2.3.5
| 32805/32768, {{monzo| 2 -32 21 }}
| {{mapping| 200 317 464 }}
| +0.3226
| 0.4767
| 7.95
|-
| 2.3.5.7
| 1029/1024, 10976/10935, 390625/387072
| {{mapping| 200 317 464 561 }}
| +0.4937
| 0.5082
| 8.47
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 23\200
| 138.00
| 27/25
| [[Quartemka]]
|-
| 1
| 39\200
| 234.00
| 8/7
| [[Guiron]]
|-
| 1
| 83\200
| 498.00
| 4/3
| [[Helmholtz (temperament)|Helmholtz]]
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 
== Scales ==
* 34 34 15 34 34 34 15 = [[5L 2s|Pythagorean tuning]]
* 32 32 20 32 32 32 20 = [[5L 2s|Meantone tuning]] in the same way of [[50edo]]
* 27 27 27 27 27 27 27 11 = [[7L 1s|Porcupine tuning]]
* 26 26 26 9 26 26 26 26 9 = [[7L 2s|Superdiatonic tuning]]
* 24 24 24 16 24 24 24 24 16 = [[7L 2s|Superdiatonic tuning]] in the same way of [[25edo]]
* 22 22 8 22 22 22 8 22 22 22 8 = [[8L 3s|Sensi]]
* 16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L 3s|Ketradektriatoh tuning]]
 
== Music ==
; [[Francium]]
* "On Fire" from ''Mysteries'' (2023) – [https://open.spotify.com/track/6janPwh3S8FLgIzWf9S0oQ Spotify] | [https://francium223.bandcamp.com/track/on-fire Bandcamp] | [https://www.youtube.com/watch?v=S1NKb_EoYrw YouTube]
 
; [[Claudi Meneghin]]
* ''Fugue on Elgar’s Enigma Theme'' – [https://www.youtube.com/watch?v=h4rjMFAzjow YouTube] | [http://soonlabel.com/xenharmonic/archives/1324 soonlabel archive]{{dead link}} | [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Claudi_Meneghin_Enigma_Fugue.mp3 play]{{dead link}}
 
[[Category:3-limit record edos|###]] <!-- 3-digit number -->
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/200edo"