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149edo: Difference between revisions

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**Imported revision 214221602 - Original comment: **
+ note about 894edo
 
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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>2011-03-26 14:18:19 UTC</tt>.<br>
: The original revision id was <tt>214221602</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">The //149 equal division// divides the octave into 149 equal parts of 8.054 cents each. It provides the [[optimal patent val]] for 11- 13- and 17-limit [[Sensipent family|heinz temperament]] and the rank three temperament [[Gamelismic family|ominous]] in the 13- and 17- limits. It has a generally flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.


149 is a prime number.</pre></div>
== Theory ==
<h4>Original HTML content:</h4>
149edo is the smallest division which is [[consistency|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent 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;149edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;149 equal division&lt;/em&gt; divides the octave into 149 equal parts of 8.054 cents each. It provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 11- 13- and 17-limit &lt;a class="wiki_link" href="/Sensipent%20family"&gt;heinz temperament&lt;/a&gt; and the rank three temperament &lt;a class="wiki_link" href="/Gamelismic%20family"&gt;ominous&lt;/a&gt; in the 13- and 17- limits. It has a generally flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.&lt;br /&gt;
 
&lt;br /&gt;
In the 5-limit it [[tempering out|tempers out]] the [[sensipent comma]], 78732/78125; in the [[7-limit]], [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the [[11-limit]] [[385/384]] and [[441/440]]; in the [[13-limit]] [[351/350]], [[676/675]] and [[729/728]]; in the [[17-limit]] [[273/272]] and [[561/560]]; in the [[19-limit]] [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[gamelismic family #Ominous|ominous]] in the 13- and 17-limit.
149 is a prime number.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.
 
=== Prime harmonics ===
{{Harmonics in equal|149}}
 
=== Subsets and supersets ===
149edo is the 35th [[prime edo]]. As such, it does not contain any nontrivial subset edos.  
 
[[894edo]], which slices its step in six, is a notable system for the higher-limit, also consistent to the 17-odd-limit.
 
== 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| -236 149 }}
| {{Mapping| 149 236 }}
| +0.405
| 0.405
| 5.03
|-
| 2.3.5
| 78732/78125, {{monzo| -34 20 1 }}
| {{Mapping| 149 236 346 }}
| +0.232
| 0.411
| 5.11
|-
| 2.3.5.7
| 1029/1024, 3136/3125, 19683/19600
| {{Mapping| 149 236 346 418 }}
| +0.386
| 0.445
| 5.53
|-
| 2.3.5.7.11
| 385/384, 441/440, 3136/3125, 19683/19600
| {{Mapping| 149 236 346 418 515 }}
| +0.521
| 0.481
| 5.97
|-
| 2.3.5.7.11.13
| 351/350, 385/384, 441/440, 676/675, 847/845
| {{Mapping| 149 236 346 418 515 551 }}
| +0.567
| 0.451
| 5.60
|-
| 2.3.5.7.11.13.17
| 273/272, 351/350, 385/384, 441/440, 676/675, 847/845
| {{Mapping| 149 236 346 418 515 551 609 }}
| +0.495
| 0.453
| 5.62
|}
 
=== 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
| 3\149
| 24.16
| 686/675
| [[Sengagen]]
|-
| 1
| 16\149
| 128.86
| 14/13
| [[Tertiathirds]]
|-
| 1
| 18\149
| 144.97
| 49/45
| [[Swetneus]]
|-
| 1
| 24\149
| 193.29
| 28/25
| [[Hemithirds]]
|-
| 1
| 29\149
| 233.56
| 8/7
| [[Slendric]]
|-
| 1
| 47\149
| 378.52
| 56/45
| [[Subpental]]
|-
| 1
| 55\149
| 442.95
| 162/125
| [[Sensipent]]
|-
| 1
| 57\149
| 459.06
| 125/96
| [[Majvam]]
|-
| 1
| 60\149
| 483.22
| 45/34
| [[Hemiseven]]
|-
| 1
| 61\149
| 491.28
| 3645/2744
| [[Fifthplus]]
|-
| 1
| 68\149
| 547.65
| 11/8
| [[Heinz]]
|}
<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
 
[[Category:Heinz]]
Retrieved from "https://en.xen.wiki/w/149edo"