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| * ''[[Triglav]]'' (+3136/3125) → [[Hemimean family #Triglav|Hemimean family]] | | * ''[[Triglav]]'' (+3136/3125) → [[Hemimean family #Triglav|Hemimean family]] |
| * ''[[Thor]]'' (+4375/4374) → [[Ragismic family #Thor|Ragismic family]] | | * ''[[Thor]]'' (+4375/4374) → [[Ragismic family #Thor|Ragismic family]] |
| * ''[[Kapo]]'' (+5120/5103) → [[Hemifamity family #Kapo|Hemifamity family]] | | * ''[[Kapo]]'' (+5120/5103) → [[Aberschismic family #Kapo|Aberschismic family]] |
| | * ''[[Ganesha]]'' (+5632/5625) → [[Vishdelismic clan #Ganesha|Vishdelismic clan]] |
| * ''[[Tyr]]'' (+102487/102400) → [[Landscape family #Tyr|Landscape family]] | | * ''[[Tyr]]'' (+102487/102400) → [[Landscape family #Tyr|Landscape family]] |
| | * ''[[Lux]]'' (+131072/130977) → [[Olympic clan #Lux|Olympic clan]] |
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| Considered below are skadi, ganesha, hanuman, lux, and galaxy, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]]. | | Considered below are skadi, hanuman, and galaxy, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]]. |
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| == Skadi == | | == Skadi == |
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| [[Badness]] (Sintel): 0.419 | | [[Badness]] (Sintel): 0.419 |
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| == Ganesha ==
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| : ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Quasiorwellismic]].''
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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 3025/3024, 5632/5625
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| {{Mapping|legend=1| 1 0 0 -22 -9 | 0 1 0 1 2 | 0 0 1 10 4 }}
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.9176{{c}}, ~3/2 = 702.1769{{c}}, ~5/4 = 386.6642{{c}}
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| : [[error map]]: {{val| -0.082 +0.139 +0.186 +0.075 -0.390 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1836{{c}}, ~5/4 = 386.6860{{c}}
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| : error map: {{val| 0.000 +0.229 +0.372 +0.218 -0.207 }}
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| {{Optimal ET sequence|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}
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| [[Badness]] (Sintel): 0.469
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| == Hanuman == | | == Hanuman == |
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| Badness (Sintel): 0.610 | | Badness (Sintel): 0.610 |
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| == Lux ==
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| 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]].
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| 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.
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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 3025/3024, 131072/130977
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| {{Mapping|legend=1| 1 0 -5 4 9 | 0 1 4 -1 -3 | 0 0 5 2 -4 }}
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| : mapping generators: ~2, ~3, ~55/48
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.9605{{c}}, ~3/2 = 702.0886{{c}}, ~55/48 = 235.5706{{c}}
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| : [[error map]]: {{val| -0.039 +0.094 -0.067 +0.108 -0.103 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1120{{c}}, ~55/48 = 235.5763{{c}}
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| : error map: {{val| 0.000 +0.157 +0.016 +0.215 +0.041 }}
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| {{Optimal ET sequence|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }}
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| [[Badness]] (Sintel): 0.611
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 2080/2079, 3025/3024, 4096/4095
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| Mapping: {{mapping| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9727{{c}}, ~3/2 = 702.0946{{c}}, ~55/48 = 235.5597{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1109{{c}}, ~55/48 = 235.5649{{c}}
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| {{Optimal ET sequence|legend=0| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}
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| Badness (Sintel): 0.337
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| == Galaxy == | | == Galaxy == |