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 ==
Line 73: Line 72:
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]]

Latest revision as of 12:43, 8 September 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The olympic clan of rank-3 temperaments tempers out the olympia (ratio: 131072/130977, monzo: [17 -5 0 -2 -1⟩). This has the effect of equating the undecimal quartertone (33/32) with a stack of two septimal commas (64/63).

For the rank-4 olympic temperament, see Rank-4 temperament #Olympic (131072/130977).

Olympian

Subgroup: 2.3.7.11

Comma list: 131072/130977

Subgroup-val mapping: [⟨1 0 0 17], ⟨0 1 0 -5], ⟨0 0 1 -2]]

mapping generators: ~2, ~3, ~7

Optimal tunings:

  • WE: ~2 = 1199.9460 ¢, ~3/2 = 702.0489 ¢, ~7/4 = 968.9839 ¢
error map: ⟨-0.054 +0.040 +0.050 +0.038]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.0853 ¢, ~7/4 = 969.0242 ¢
error map: ⟨0.000 +0.130 +0.198 +0.207]

Optimal ET sequence: 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee

Badness (Sintel): 0.267

Overview to extensions

The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds 385/384, and finds the harmonic 5 by equating the syntonic comma (81/80) with the septimal comma. Orthoschismic adds 32805/32768, and finds the harmonic 5 on the chain of fifths. Cassaschismic adds 19712/19683 with an independent generator for harmonic 5. Pessoal adds 9801/9800, splitting the octave into two. Lif adds 2401/2400, splitting the perfect fifth into two. Baffin adds 5632/5625, splitting the perfect twelfth into two. Lux adds 3025/3024, splitting the ~21/16 into two. Hera adds 6144/6125 or 8019/8000, splitting the ~21/16 into three. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both 2080/2079 and 4096/4095.

Temperaments discussed elsewhere are:

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

Orthoschismic

Orthoschismic is related to schismic, but with an additional generator for prime 7, extended to the 11-limit in one of the most efficient ways possible.

Orthoschismic can be notated with chain-of-fifths notation with two additional set of accidentals, one for the generic comma step (one should choose whether this step represents the syntonic comma, which is more characteristic in schismic, or the septimal comma, which is more characteristic in olympic), and the other for the generic aberschisma step which stands in for the garischisma and the aberschisma.

It was named by Flora Canou in 2023, using the Greek prefix ortho- to signify the additional rank.

Subgroup: 2.3.5.7.11

Comma list: 540/539, 32805/32768

Mapping: [⟨1 0 15 0 17], ⟨0 1 -8 0 -5], ⟨0 0 0 1 -2]]

Optimal tunings:

  • WE: ~2 = 1199.9335 ¢, ~3/2 = 701.6817 ¢, ~7/4 = 969.6199 ¢
error map: ⟨-0.067 -0.340 -0.233 +0.661 +0.502]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7248 ¢, ~7/4 = 969.6728 ¢
error map: ⟨0.000 -0.230 -0.112 +0.847 +0.713]

Optimal ET sequence: 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de

Badness (Sintel): 1.41

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 4096/4095

Mapping: [⟨1 0 15 0 17 -3], ⟨0 1 -8 0 -5 6], ⟨0 0 0 1 -2 -1]]

Optimal tunings:

  • WE: ~2 = 1199.9399 ¢, ~3/2 = 701.6899 ¢, ~7/4 = 969.6107 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7264 ¢, ~7/4 = 969.6672 ¢

Optimal ET sequence: 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d

Badness (Sintel): 0.779

Pessoal

See also: Pessoalisma

Pessoal tempers out the kalisma. It was named by Aura in 2023, meaning "personal", for the fact that it is associated with abigail, which is in turn a person's name.

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 131072/130977

Mapping: [⟨2 0 1 10 14], ⟨0 1 0 -1 -3], ⟨0 0 3 -1 2]]

mapping generators: ~99/70, ~3, ~32/21

Optimal tunings:

  • WE: ~99/70 = 599.9711 ¢, ~3/2 = 702.0265 ¢, ~32/21 = 728.7942 ¢
error map: ⟨-0.058 +0.014 +0.040 +0.122 -0.040]
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.0635 ¢, ~32/21 = 728.8214 ¢
error map: ⟨0.000 +0.109 +0.150 +0.289 +0.134]

Optimal ET sequence: 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: [⟨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 ¢, ~3/2 = 702.0253 ¢, ~32/21 = 728.7700 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.0477 ¢, ~32/21 = 728.7882 ¢

Optimal ET sequence: 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 ratios 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

Comma list: 3025/3024, 131072/130977

Mapping: [⟨1 0 -5 4 9], ⟨0 1 4 -1 -3], ⟨0 0 5 2 -4]]

mapping generators: ~2, ~3, ~55/48

Optimal tunings:

  • WE: ~2 = 1199.9605 ¢, ~3/2 = 702.0886 ¢, ~55/48 = 235.5706 ¢
error map: ⟨-0.039 +0.094 -0.067 +0.108 -0.103]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1120 ¢, ~55/48 = 235.5763 ¢
error map: ⟨0.000 +0.157 +0.016 +0.215 +0.041]

Optimal ET sequence: 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d

Badness (Sintel): 0.611

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 4096/4095

Mapping: [⟨1 0 -5 4 9 13], ⟨0 1 4 -1 -3 -5], ⟨0 0 5 2 -4 -7]]

Optimal tunings:

  • WE: ~2 = 1199.9727 ¢, ~3/2 = 702.0946 ¢, ~55/48 = 235.5597 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1109 ¢, ~55/48 = 235.5649 ¢

Optimal ET sequence: 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d

Badness (Sintel): 0.337

Sophia

Named by Scott Dakota in 2022, sophia tempers out 42875/42768, and by virtue of the identity 42875/42768 = (595/594)⋅(1225/1224), it is naturally a 17-limit temperament.

Subgroup: 2.3.5.7.11

Comma list: 42875/42768, 131072/130977

Mapping: [⟨1 0 2 3 11], ⟨0 1 0 0 -5], ⟨0 0 5 -3 6]]

mapping generators: ~2, ~3, ~256/245

Optimal tunings:

  • WE: ~2 = 1199.9947 ¢, ~3/2 = 702.2994 ¢, ~256/245 = 77.1949 ¢
error map: ⟨-0.005 +0.339 -0.350 -0.426 +0.323]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.3025 ¢, ~256/245 = 77.1949 ¢
error map: ⟨0.000 +0.347 -0.339 -0.411 +0.339]

Optimal ET sequence: 46, 94, 140, 171, 217, 311, 979, 1290

Badness (Sintel): 4.54

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095, 13720/13689

Mapping: [⟨1 0 2 3 11 7], ⟨0 1 0 0 -5 -2], ⟨0 0 5 -3 6 -2]]

Optimal tunings:

  • WE: ~2 = 1199.9732 ¢, ~3/2 = 702.3162 ¢, ~117/112 = 77.2135 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.3335 ¢, ~117/112 = 77.2145 ¢

Optimal ET sequence: 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290

Badness (Sintel): 1.56

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 595/594, 833/832, 1156/1155, 4096/4095

Mapping: [⟨1 0 2 3 11 7 7], ⟨0 1 0 0 -5 -2 -2], ⟨0 0 5 -3 6 -2 4]]

Optimal tunings:

  • WE: ~2 = 1199.9956 ¢, ~3/2 = 702.3179 ¢, ~68/65 = 77.2252 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.3207 ¢, ~68/65 = 77.2254 ¢

Optimal ET sequence: 46, 77e, 94, 140, 171, 217, 311, 668, 839e, 979g

Badness (Sintel): 0.940

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