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Olympic clan: Difference between revisions

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- baffin (to vishdelismic clan), + pessoal (from kalismic temps), + lux (from lehmerismic temps)
 
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Temperaments discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea|Hemifamity family]]
* ''[[Akea]]'' (+385/384) → [[Aberschismic family #Akea|Aberschismic family]]
* [[Cassaschismic]] (+19712/19683) → [[Garischismic family #Cassaschismic|Garischismic family]]
* [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Cassaschismic|Septischismic family]]
* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]
* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif|Breed family]]
* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif|Breed family]]
* ''[[Lux]]'' (+3025/3024) → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]
* ''[[Baffin]]'' (+5632/5625) → [[Vishdelismic clan #Baffin|Vishdelismic clan]]
* ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]
* ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]


Considered below are orthoschismic, baffin and sophia.
Considered below are orthoschismic, pessoal, lux, and sophia.


== Orthoschismic ==
== Orthoschismic ==
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Badness (Sintel): 0.779
Badness (Sintel): 0.779


== Baffin ==
== Pessoal ==
: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Decovulture]].''
{{See also| Pessoalisma }}


Baffin tempers out [[5632/5625]] and [[160083/160000]] in addition to the olympia, so that the [[3/1|3rd]] [[harmonic]] is split in halves. This leads naturally to a [[13-limit]] temperament where [[676/675]], [[1001/1000]], [[2080/2079]] and [[4096/4095]] are all tempered out.  
Pessoal tempers out the [[kalisma]]. It was named by [[Aura]] in 2023, meaning [[Wiktionary: pessoal #Portuguese|"personal"]], for the fact that it is associated with [[abigail]], which is in turn a person's name.  


It was named by [[Gene Ward Smith]] some time before 2011 for {{w|Baffin Island}}, as part of a series of island-themed names<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group | ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>.  
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 9801/9800, 131072/130977
 
{{Mapping|legend=1| 2 0 1 10 14 | 0 1 0 -1 -3 | 0 0 3 -1 2 }}
: mapping generators: ~99/70, ~3, ~32/21
 
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 599.9711{{c}}, ~3/2 = 702.0265{{c}}, ~32/21 = 728.7942{{c}}
: [[error map]]: {{val| -0.058 +0.014 +0.040 +0.122 -0.040 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0635{{c}}, ~32/21 = 728.8214{{c}}
: error map: {{val| 0.000 +0.109 +0.150 +0.289 +0.134 }}
 
{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
 
[[Badness]] (Sintel): 0.599
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 4096/4095
 
Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}
 
Optimal tunings:
* WE: ~99/70 = 599.9835{{c}}, ~3/2 = 702.0253{{c}}, ~32/21 = 728.7700{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0477{{c}}, ~32/21 = 728.7882{{c}}
 
{{Optimal ET sequence|legend=0| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
 
Badness (Sintel): 0.366
 
== Lux ==
The last generator of lux, represented by [[55/48]], exceeds [[8/7]] by [[385/384]], which is equated with a number of important [[superparticular ratio]]s in the [[13-limit]]: [[325/324]], [[352/351]], [[364/363]], and [[441/440]].
 
This ultra-efficient full 13-limit temperament was first considered by [[Flora Canou]] in 2021. After a few attempts to come up with a memorable name, ''lux'', suggested by [[Godtone]], who associated certain intervals of 13 with light, was adopted.  


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 5632/5625, 131072/130977
[[Comma list]]: 3025/3024, 131072/130977


{{Mapping|legend=1| 1 0 0 13 -9 | 0 2 0 -7 4 | 0 0 1 -2 4 }}
{{Mapping|legend=1| 1 0 -5 4 9 | 0 1 4 -1 -3 | 0 0 5 2 -4 }}
: mapping generators: ~2, ~400/231, ~5
: mapping generators: ~2, ~3, ~55/48


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.9208{{c}}, ~400/231 = 950.9957{{c}}, ~5/4 = 386.7656{{c}}
* [[WE]]: ~2 = 1199.9605{{c}}, ~3/2 = 702.0886{{c}}, ~55/48 = 235.5706{{c}}
: [[error map]]: {{val| -0.079 +0.036 +0.293 -0.040 -0.193 }}
: [[error map]]: {{val| -0.039 +0.094 -0.067 +0.108 -0.103 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.0635{{c}}, ~5/4 = 386.7769{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1120{{c}}, ~55/48 = 235.5763{{c}}
: error map: {{val| 0.000 +0.172 +0.463 +0.176 +0.044 }}
: error map: {{val| 0.000 +0.157 +0.016 +0.215 +0.041 }}


{{Optimal ET sequence|legend=1| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}
{{Optimal ET sequence|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }}


[[Badness]] (Sintel): 1.17
[[Badness]] (Sintel): 0.611


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 676/675, 1001/1000, 4096/4095
Comma list: 2080/2079, 3025/3024, 4096/4095


Mapping: {{mapping| 1 0 0 13 -9 1 | 0 2 0 -7 4 3 | 0 0 1 -2 4 1 }}
Mapping: {{mapping| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9633{{c}}, ~400/231 = 951.0591{{c}}, ~5/4 = 386.7388{{c}}
* WE: ~2 = 1199.9727{{c}}, ~3/2 = 702.0946{{c}}, ~55/48 = 235.5597{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.0896{{c}}, ~5/4 = 386.7451{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1109{{c}}, ~55/48 = 235.5649{{c}}


{{Optimal ET sequence|legend=0| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }}
{{Optimal ET sequence|legend=0| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}


Badness (Sintel): 0.565
Badness (Sintel): 0.337
 
Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11


== Sophia ==
== Sophia ==
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Badness (Sintel): 0.940
Badness (Sintel): 0.940
== References ==


[[Category:Olympic clan| ]] <!-- main article -->
[[Category:Olympic clan| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Catalogs of rank-3 temperaments]]
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