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190edo: 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>2011-07-10 04:18:40 UTC</tt>.<br>
 
: The original revision id was <tt>240682945</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
190edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]] with a flat tendency, as [[harmonic]]s 3 through 13 are all tuned flat.  
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>
190edo is interesting because of the utility of its approximations; it [[tempering out|tempers out]] [[1029/1024]], [[4375/4374]], [[385/384]], [[441/440]], [[3025/3024]], and [[9801/9800]]. It provides the [[optimal patent val]] for both the 7- and 11-limit versions of [[unidec]], the {{nowrap|72 &amp; 118}} temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament [[portent]], which tempers out 385/384 and 441/440, and [[gamelan]], the rank-3 7-limit temperament which tempers out 1029/1024, as well as [[slendric]], the 2.3.7 subgroup temperament featured in the [[#Music]] section. In the 13-limit, 190et tempers out [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.
<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">//190edo// divides the octave into 190 equal parts of size 6.316 cents each. It is interesting because of the utility of its approximations; it tempers out 1029/1024, 4375/4374, 385/384, 441/440, 3025/3024 and 9801/9800. It provides the [[optimal patent val]] for both the 7 and 11 limit versions of unidec, the 118&amp;190 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank three 11-limit temperament portent, which tempers out 385/384 and 441/440, and gamelismic, the rank three 7-limit temperament gamelismic, which tempers out 1029/1024.</pre></div>
 
<h4>Original HTML content:</h4>
The 190g [[val]] shows us a smooth path to the even higher limits. This extension tempers out [[289/288]], [[561/560]], [[595/594]] in the 17-limit; [[343/342]], [[476/475]], [[495/494]] in the 19-limit; and [[391/390]], [[529/528]] in the 23-limit.
<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;190edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;190edo&lt;/em&gt; divides the octave into 190 equal parts of size 6.316 cents each. It is interesting because of the utility of its approximations; it tempers out 1029/1024, 4375/4374, 385/384, 441/440, 3025/3024 and 9801/9800. It provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for both the 7 and 11 limit versions of unidec, the 118&amp;amp;190 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank three 11-limit temperament portent, which tempers out 385/384 and 441/440, and gamelismic, the rank three 7-limit temperament gamelismic, which tempers out 1029/1024.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== Prime harmonics ===
{{Harmonics in equal|190|intervals=prime}}
 
=== Subsets and supersets ===
Since 190 factors into {{factorization|190}}, 190edo has subset edos {{EDOs| 2, 5, 10, 19, 38, and 95 }}.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! 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| -301 190 }}
| {{Mapping| 190 301 }}
| +0.285
| 0.285
| 4.51
|-
| 2.3.5
| 2109375/2097152, {{monzo| -7 22 -12 }}
| {{Mapping| 190 301 441 }}
| +0.341
| 0.246
| 3.89
|-
| 2.3.5.7
| 1029/1024, 4375/4374, 235298/234375
| {{Mapping| 190 301 441 533 }}
| +0.479
| 0.321
| 5.07
|-
| 2.3.5.7.11
| 385/384, 441/440, 4375/4374, 234375/234256
| {{Mapping| 190 301 441 533 657 }}
| +0.490
| 0.288
| 4.55
|-
| 2.3.5.7.11.13
| 385/384, 441/440, 625/624, 729/728, 847/845
| {{Mapping| 190 301 441 533 657 703 }}
| +0.432
| 0.293
| 4.63
|-
| 2.3.5.7.11.13.17
| 289/288, 385/384, 441/440, 561/560, 625/624, 847/845
| {{Mapping| 190 301 441 533 657 703 776 }} (190g)
| +0.507
| 0.327
| 5.18
|-
| 2.3.5.7.11.13.17.19
| 289/288, 343/342, 385/384, 441/440, 476/475, 495/494, 847/845
| {{Mapping| 190 301 441 533 657 703 776 807 }} (190g)
| +0.463
| 0.327
| 5.17
|-
| 2.3.5.7.11.13.17.19.23
| 289/288, 343/342, 385/384, 391/390, 441/440, 476/475, 495/494, 529/528
| {{Mapping| 190 301 441 533 657 703 776 807 859 }} (190g)
| +0.486
| 0.315
| 4.98
|}
* 190et (190g val) has a lower relative error in the 23-limit than any previous equal temperaments, being the first to beat [[94edo|94]]. However, [[193edo|193]], only slightly larger, beats it.
* It is also prominent in the 13- and 19-limit, with lower absolute errors than any previous equal temperaments. It beats [[183edo|183]] in either subgroup and is bettered by [[198edo|198]] in the 13-limit, and by 193 in the 19-limit.
 
=== 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*
! Temperament
|-
| 1
| 37\190
| 233.68
| 8/7
| [[Slendric]]
|-
| 1
| 43\190
| 271.58
| 75/64
| [[Sabric]]
|-
| 1
| 49\190
| 309.47
| 448/375
| [[Triwell]]
|-
| 1
| 71\190
| 448.42
| 35/27
| [[Semidimfourth]]
|-
| 1
| 83\190
| 524.21
| 65/48
| [[Widefourth]]
|-
| 2
| 28\190
| 176.84
| 195/176
| [[Quatracot]]
|-
| 2
| 29\190
| 183.16
| 10/9
| [[Unidec]] / ekadash
|-
| 2
| 59\190<br>(36\190)
| 372.63<br>(227.37)
| 26/21<br>(297/260)
| [[Essence]]
|-
| 2
| 71\190<br>(24\190)
| 448.42<br>(151.58)
| 35/27<br>(12/11)
| [[Neusec]]
|-
| 5
| 79\190<br>(3\190)
| 498.95<br>(18.95)
| 4/3<br>(81/80)
| [[Quintile]]
|-
| 10
| 50\190<br>(7\190)
| 315.79<br>(45.79)
| 6/5<br>(40/39)
| [[Deca]]
|-
| 10
| 79\190<br>(3\190)
| 498.95<br>(18.95)
| 4/3<br>(81/80)
| [[Decile]]
|-
| 19
| 79\190<br>(1\190)
| 498.95<br>(6.32)
| 4/3<br>(225/224)
| [[Enneadecal]]
|-
| 38
| 79\190<br>(1\190)
| 265.26<br>(6.32)
| 4/3<br>(225/224)
| [[Hemienneadecal]]
|-
| 38
| 42\190<br>(2\190)
| 265.26<br>(12.63)
| 500/429<br>(144/143)
| [[Semihemienneadecal]]
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Scales ==
* [[Slendric5]]
* [[Slendric6]]
* [[Slendric11]]
* [[Slendric16]]
 
== Music ==
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3 ''The 11th Slendric Fanfare'']
* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 ''16 Slendric Virgins'']
 
[[Category:Ekadash]]
[[Category:Gamelismic]]
[[Category:Listen]]
[[Category:Portent]]
[[Category:Portentous]]
[[Category:Unidec]]
Retrieved from "https://en.xen.wiki/w/190edo"