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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:xenwolf|xenwolf]] and made on <tt>2011-06-30 17:03:15 UTC</tt>.<br>
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| : The original revision id was <tt>239556997</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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 <<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 <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.
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| If we use <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. | | == Theory == |
| | 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. |
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| | 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. |
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| | === Odd harmonics === |
| | {{Harmonics in equal|197}} |
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| | === 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 |
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| == Scales == | | == Scales == |
| * [[prismarv]] | | * [[Prismarv]] |
| * [[marveldene]] | | * [[Marveldene]] |
| * [[pump12_1]] | | * [[Pump12 1]] |
| * [[pump12_1]] | | * [[Pump12 2]] |
| * [[pump13]] | | * [[Pump13]] |
| * [[pump14]] | | * [[Pump14]] |
| * [[pump15]] | | * [[Pump15]] |
| * [[pump16]] | | * [[Pump16]] |
| * [[pump17]] | | * [[Pump17]] |
| * [[pump18]]</pre></div> | | * [[Pump18]] |
| <h4>Original HTML content:</h4>
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| <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"><html><head><title>197edo</title></head><body>The 197 equal division gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and <a class="wiki_link" href="/Kleismic%20family">catakleismic</a>, the temperament <a class="wiki_link" href="/tempering%20out">tempering out</a> both 225/224 and 4375/4374, which has wedgie &lt;&lt;6 5 22 -6 18 37||. Among <a class="wiki_link" href="/Patent%20val">patent vals</a>, in fact, it gives the best results for both. In fact, the <a class="wiki_link" href="/11-limit">11-limit</a> 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 (<a class="wiki_link" href="/prodigy%20temperament">prodigy temperament</a>) 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.<br />
| | == Music == |
| <br />
| | ; [[Francium]] |
| 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 <a class="wiki_link" href="/marvel">marvel</a>, we get 11-limit <a class="wiki_link" href="/catakleismic">catakleismic</a>, and 197edo with the above <a class="wiki_link" href="/val">val</a> is also an excellent tuning for that.<br />
| | * "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] |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Scales"></a><!-- ws:end:WikiTextHeadingRule:0 --> Scales </h2>
| | ; [[Chris Vaisvil]] |
| <ul><li><a class="wiki_link" href="/prismarv">prismarv</a></li><li><a class="wiki_link" href="/marveldene">marveldene</a></li><li><a class="wiki_link" href="/pump12_1">pump12_1</a></li><li><a class="wiki_link" href="/pump12_1">pump12_1</a></li><li><a class="wiki_link" href="/pump13">pump13</a></li><li><a class="wiki_link" href="/pump14">pump14</a></li><li><a class="wiki_link" href="/pump15">pump15</a></li><li><a class="wiki_link" href="/pump16">pump16</a></li><li><a class="wiki_link" href="/pump17">pump17</a></li><li><a class="wiki_link" href="/pump18">pump18</a></li></ul></body></html></pre></div>
| | * [http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 ''Pump1''] – in pump12 1 |
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| | [[Category:Catakleismic]] |
| | [[Category:Marvel]] |