Xenharmonic Wiki

Fifive family: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>TallKite
**Imported revision 624085645 - Original comment: **
Tags: Mobile edit Mobile web edit
 
(22 intermediate revisions by 10 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''fifive family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[fifive comma]] ({{monzo|legend=1| -1 -14 10 }}, [[ratio]]: 9765625/9565938).
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-12-19 21:08:25 UTC</tt>.<br>
: The original revision id was <tt>624085645</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">This tempers out the fifive comma, 9765625/9565938 = (-1, -14, 10).


=Fifive=
The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2|perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>
Comma: 9765625/9565938


POTE generator: ~27/25 = 140.624
Considered below are crepuscular, fifives, and fourfives.  


Map: [&lt;2 2 3|, &lt;0 5 7|]
== Fifive ==
EDOs: 8, 26, 34, 94, 128
[[Subgroup]]: 2.3.5
Badness: 0.2058


=Crepuscular=
[[Comma list]]: 9765625/9565938
Commas: 50/49 4375/4374


POTE generator: ~27/25 = 140.349
{{Mapping|legend=1| 2 2 3 | 0 5 7 }}


Map: [&lt;2 2 3 4|, &lt;0 5 7 7|]
: mapping generators: ~78125/50421, ~27/25
Wedgie: &lt;&lt;10 14 14 -1 -6 -7||
EDOs: 26, 34d, 60d, 94d
Badness: 0.0867


==11-limit==
[[Optimal tuning]]s:
Commas: 50/49, 99/98, 1944/1925
* [[CTE]]: ~78125/50421 = 1\2, ~27/25 = 140.6349
* [[POTE]]: ~78125/50421 = 1\2, ~27/25 = 140.624


POTE generator: ~12/11 = ~27/25 = 140.587
{{Optimal ET sequence|legend=1| 8, 18bc, 26, 34, 94, 128 }}


Map: [&lt;2 2 3 4 6|, &lt;0 5 7 7 4|]
[[Badness]]:
EDOs: 26, 34d, 60d, 94de
* Smith: 0.205812
Badness: 0.0408
* Dirichlet: 4.828


==13-limit==  
=== 2.3.5.13 subgroup ===
Commas: 50/49, 78/77, 99/98, 144/143
Subgroup: 2.3.5.13


POTE generator: ~12/11 = 140.554
Comma list: 325/324, 20000/19773


Map: [&lt;2 2 3 4 6 6|, &lt;0 5 7 7 4 6|]
Mapping: {{mapping| 2 2 3 6 | 0 5 7 6 }}
EDOs: 26, 34d, 60d, 94de
Badness: 0.0244


=Fifives=
: mapping generators: ~351/250, ~13/12
Commas: 875/864, 83349/81920


=Fourfives=
Optimal tunings:
Commas: 245/243, 235298/234375</pre></div>
* CTE: ~351/250 = 1\2, ~13/12 = 140.5685
<h4>Original HTML content:</h4>
* CWE: ~351/250 = 1\2, ~13/12 = 140.6232
<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;Fifive family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tempers out the fifive comma, 9765625/9565938 = (-1, -14, 10).&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 8, 18bcf, 26, 34, 94, 128 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Fifive"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Fifive&lt;/h1&gt;
 
Comma: 9765625/9565938&lt;br /&gt;
Badness:  
&lt;br /&gt;
* Smith: 0.0240
POTE generator: ~27/25 = 140.624&lt;br /&gt;
* Dirichlet: 0.800
&lt;br /&gt;
 
Map: [&amp;lt;2 2 3|, &amp;lt;0 5 7|]&lt;br /&gt;
=== 2.3.5.13.17 subgroup ===
EDOs: 8, 26, 34, 94, 128&lt;br /&gt;
Subgroup: 2.3.5.13.17
Badness: 0.2058&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 170/169, 289/288, 325/324
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Crepuscular"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Crepuscular&lt;/h1&gt;
 
Commas: 50/49 4375/4374&lt;br /&gt;
Mapping: {{mapping| 2 2 3 6 7 | 0 5 7 6 5 }}
&lt;br /&gt;
 
POTE generator: ~27/25 = 140.349&lt;br /&gt;
: mapping generators: ~17/12, ~13/12
&lt;br /&gt;
 
Map: [&amp;lt;2 2 3 4|, &amp;lt;0 5 7 7|]&lt;br /&gt;
Optimal tunings:
Wedgie: &amp;lt;&amp;lt;10 14 14 -1 -6 -7||&lt;br /&gt;
* CTE: ~17/12 = 1\2, ~13/12 = 140.5958
EDOs: 26, 34d, 60d, 94d&lt;br /&gt;
* CWE: ~17/12 = 1\2, ~13/12 = 140.6057
Badness: 0.0867&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 8, 18bcfg, 26, 34, 94, 128 }}
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Crepuscular-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 
Commas: 50/49, 99/98, 1944/1925&lt;br /&gt;
Badness:
&lt;br /&gt;
* Smith: 0.0110
POTE generator: ~12/11 = ~27/25 = 140.587&lt;br /&gt;
* Dirichlet: 0.488
&lt;br /&gt;
 
Map: [&amp;lt;2 2 3 4 6|, &amp;lt;0 5 7 7 4|]&lt;br /&gt;
== Crepuscular ==
EDOs: 26, 34d, 60d, 94de&lt;br /&gt;
{{See also| Jubilismic clan #Crepuscular }}
Badness: 0.0408&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Crepuscular-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
 
Commas: 50/49, 78/77, 99/98, 144/143&lt;br /&gt;
[[Comma list]]: 50/49, 4375/4374
&lt;br /&gt;
 
POTE generator: ~12/11 = 140.554&lt;br /&gt;
{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 2 3 4 6 6|, &amp;lt;0 5 7 7 4 6|]&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
EDOs: 26, 34d, 60d, 94de&lt;br /&gt;
 
Badness: 0.0244&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Fifives"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Fifives&lt;/h1&gt;
[[Badness]]: 0.086669
Commas: 875/864, 83349/81920&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Fourfives"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Fourfives&lt;/h1&gt;
Subgroup: 2.3.5.7.11
Commas: 245/243, 235298/234375&lt;/body&gt;&lt;/html&gt;</pre></div>
 
Comma list: 50/49, 99/98, 864/847
 
Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}
 
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587
 
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
 
Badness: 0.040758
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 50/49, 78/77, 99/98, 144/143
 
Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}
 
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554
 
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
 
Badness: 0.024368
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 50/49, 78/77, 85/84, 99/98, 144/143
 
Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }}
 
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405
 
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
 
Badness: 0.018567
 
== Fifives ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 875/864, 83349/81920
 
{{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}
 
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/25 = 139.909
 
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
 
[[Badness]]: 0.130589
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 385/384, 3969/3872
 
Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}
 
Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884
 
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
 
Badness: 0.080306
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 105/104, 144/143, 1352/1331
 
Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }}
 
Optimal tuning (POTE): ~55/39 = 1\2, ~12/11 = 139.867
 
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
 
Badness: 0.044253
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 100/99, 105/104, 144/143, 170/169, 221/220
 
Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }}
 
Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868
 
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
 
Badness: 0.029429
 
== Fourfives ==
{{See also| Sensamagic clan }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 245/243, 235298/234375
 
{{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}
 
: mapping generators: ~25/21, ~27/25
 
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~27/25 = 140.754
 
{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}
 
[[Badness]]: 0.114143
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 245/243, 385/384, 235298/234375
 
Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771
 
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }}
 
Badness: 0.120165
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 245/243, 385/384, 20000/19773
 
Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.760
 
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }}
 
Badness: 0.067365
 
=== Quadrafives ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 245/243, 1375/1372
 
Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630
 
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
 
Badness: 0.057268
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 196/195, 245/243, 275/273
 
Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.728
 
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
 
Badness: 0.036128
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243
 
Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.718
 
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
 
Badness: 0.024796
 
== Notes ==
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Fifive family| ]] <!-- main article -->
[[Category:Fifive| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Fifive_family"