Xenharmonic Wiki

197edo: Difference between revisions

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**Imported revision 197086340 - Original comment: **
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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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>2011-01-29 17:57:04 UTC</tt>.<br>
: The original revision id was <tt>197086340</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 197 equal division gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic family|catakleismic]], the temperament tempering out both 225/224 and 4375/4374, which has wedgie &lt;&lt;6 5 22 -6 18 37||. Among [[Patent val|patent vals]], in fact, it gives the best results for both. In fact, the 11-limit patent val &lt;197 312 457 553 682| has a comma basis [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together (prodigy temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.


If we use &lt;197 312 457 553 681| for the val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.</pre></div>
== Theory ==
<h4>Original HTML content:</h4>
197edo gives excellent results for tuning both [[marvel]], the planar temperament [[tempering out]] [[225/224]], and [[catakleismic]], the temperament tempering out both 225/224 and [[4375/4374]]. Among [[patent val]]s, it gives the best results for both. In fact, the [[11-limit]] patent val {{val| 197 312 457 553 682 }} has a [[comma basis]] {225/224, 441/440, 4375/4374, 65536/65219}, so taking 225/224 and [[441/440]] together ([[prodigy]] temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.
<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;197edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 197 equal division gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic&lt;/a&gt;, the temperament tempering out both 225/224 and 4375/4374, which has wedgie &amp;lt;&amp;lt;6 5 22 -6 18 37||. Among &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt;, in fact, it gives the best results for both. In fact, the 11-limit patent val &amp;lt;197 312 457 553 682| has a comma basis [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together (prodigy temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.&lt;br /&gt;
 
&lt;br /&gt;
If we use 197e, the {{val| 197 312 457 553 681 }} val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out [[385/384]] as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that. The 197ef val, {{val| 197 312 457 553 681 728}}, is an excellent tuning for the 13-limit version of catakleismic.
If we use &amp;lt;197 312 457 553 681| for the val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== Odd harmonics ===
{{Harmonics in equal|197}}
 
=== Subsets and supersets ===
197edo is the 45th [[prime edo]].
 
== 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| -312 197 }}
| {{mapping| 197 312 }}
| +0.4566
| 0.4568
| 7.50
|-
| 2.3.5
| 15625/15552, {{monzo| -53 32 1 }}
| {{mapping| 197 312 457 }}
| +0.6717
| 0.4813
| 7.90
|-
| 2.3.5.7
| 225/224, 4375/4374, {{monzo| -25 6 -3 8 }}
| {{mapping| 197 312 457 553 }}
| +0.5302
| 0.4834
| 7.94
|}
 
=== 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
| 52\197
| 316.75
| 6/5
| [[Catakleismic]]
|-
| 1
| 53\197
| 322.84
| 3087/2560
| [[Seniority]]
|}
<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 ==
* [[Prismarv]]
* [[Marveldene]]
* [[Pump12 1]]
* [[Pump12 2]]
* [[Pump13]]
* [[Pump14]]
* [[Pump15]]
* [[Pump16]]
* [[Pump17]]
* [[Pump18]]
 
== Music ==
; [[Francium]]
* "Have You Ever Eaten A Square Cutlet?" from ''Questions'' (2024) – [https://open.spotify.com/track/7cA0T79hEkzEoMGvufGZ5R Spotify] | [https://francium223.bandcamp.com/track/have-you-ever-eaten-a-square-cutlet Bandcamp] | [https://www.youtube.com/watch?v=_LkriwwqbIY YouTube]
 
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 ''Pump1''] – in pump12 1
 
[[Category:Catakleismic]]
[[Category:Marvel]]
Retrieved from "https://en.xen.wiki/w/197edo"