Lehmerismic temperaments: Difference between revisions

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* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]]

* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent|Gamelismic family]]

* ''[[Indra]]'' (+540/539) → [[~~Mirkwai family~~ #Indra|~~Mirkwai family~~]]

* ''[[Indra]]'' (+540/539) → [[Swetismic temperaments #Indra|Swetismic temperaments]]

* ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant|Pentacircle clan]]

* ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya|Breed family]]

* ''[[Triglav]]'' (+3136/3125) → [[Hemimean family #Triglav|Hemimean 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]]

* ''[[Lux]]'' (+131072/130977) → [[Olympic clan #Lux|Olympic clan]]

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)]].

== Skadi ==

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[[Badness]] (Sintel): 0.419

~~== Ganesha ==~~

~~: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Quasiorwellismic]].''~~

~~[[Subgroup]]: 2.3.5.7.11~~

~~[[Comma list]]: 3025/3024, 5632/5625~~

~~{{Mapping|legend=1| 1 0 0 -22 -9 | 0 1 0 1 2 | 0 0 1 10 4 }}~~

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1199.9176{{c}}, ~3/2 = 702.1769{{c}}, ~5/4 = 386.6642{{c}}

~~: [[error map]]: {{val| -0.082 +0.139 +0.186 +0.075 -0.390 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1836{{c}}, ~5/4 = 386.6860{{c}}

~~: error map: {{val| 0.000 +0.229 +0.372 +0.218 -0.207 }}~~

~~{{Optimal ET sequence|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}~~

~~[[Badness]] (Sintel): 0.469~~

== Hanuman ==

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Badness (Sintel): 0.610

~~== 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]].

~~[[Subgroup]]: 2.3.5.7.11~~

~~[[Comma list]]: 3025/3024, 131072/130977~~

~~{{Mapping|legend=1| 1 0 -5 4 9 | 0 1 4 -1 -3 | 0 0 5 2 -4 }}~~

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

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1199.9605{{c}}, ~3/2 = 702.0886{{c}}, ~55/48 = 235.5706{{c}}

~~: [[error map]]: {{val| -0.039 +0.094 -0.067 +0.108 -0.103 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1120{{c}}, ~55/48 = 235.5763{{c}}

~~: error map: {{val| 0.000 +0.157 +0.016 +0.215 +0.041 }}~~

~~{{Optimal ET sequence|legend=1| 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: {{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{{c}}, ~3/2 = 702.0946{{c}}, ~55/48 = 235.5597{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1109{{c}}, ~55/48 = 235.5649{{c}}

~~{{Optimal ET sequence|legend=0| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}~~

~~Badness (Sintel): 0.337~~

== Galaxy ==

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Badness (Sintel): 0.888

[[Category:Lehmerismic temperaments| ]]

[[Category:Temperament collections]]

[[Category:~~Lehmerismic temperaments| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-3 temperaments]]

~~[[Category:Rank~~ 3]]

@@ Line 7: / Line 7: @@
 * ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]]
 * ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent|Gamelismic family]]
-* ''[[Indra]]'' (+540/539) → [[Mirkwai family #Indra|Mirkwai family]]
+* ''[[Indra]]'' (+540/539) → [[Swetismic temperaments #Indra|Swetismic temperaments]]
 * ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant|Pentacircle clan]]
 * ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya|Breed family]]
 * ''[[Triglav]]'' (+3136/3125) → [[Hemimean family #Triglav|Hemimean 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]]
+* ''[[Lux]]'' (+131072/130977) → [[Olympic clan #Lux|Olympic clan]]
-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)]].
 == Skadi ==
@@ Line 34: / Line 36: @@
 [[Badness]] (Sintel): 0.419
-== Ganesha ==
-: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Quasiorwellismic]].''
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 3025/3024, 5632/5625
-{{Mapping|legend=1| 1 0 0 -22 -9 | 0 1 0 1 2 | 0 0 1 10 4 }}
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9176{{c}}, ~3/2 = 702.1769{{c}}, ~5/4 = 386.6642{{c}}
-: [[error map]]: {{val| -0.082 +0.139 +0.186 +0.075 -0.390 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1836{{c}}, ~5/4 = 386.6860{{c}}
-: error map: {{val| 0.000 +0.229 +0.372 +0.218 -0.207 }}
-{{Optimal ET sequence|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}
-[[Badness]] (Sintel): 0.469
 == Hanuman ==
@@ Line 86: / Line 69: @@
 Badness (Sintel): 0.610
-== 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]].
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 3025/3024, 131072/130977
-{{Mapping|legend=1| 1 0 -5 4 9 | 0 1 4 -1 -3 | 0 0 5 2 -4 }}
-: mapping generators: ~2, ~3, ~55/48
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9605{{c}}, ~3/2 = 702.0886{{c}}, ~55/48 = 235.5706{{c}}
-: [[error map]]: {{val| -0.039 +0.094 -0.067 +0.108 -0.103 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1120{{c}}, ~55/48 = 235.5763{{c}}
-: error map: {{val| 0.000 +0.157 +0.016 +0.215 +0.041 }}
-{{Optimal ET sequence|legend=1| 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: {{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{{c}}, ~3/2 = 702.0946{{c}}, ~55/48 = 235.5597{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1109{{c}}, ~55/48 = 235.5649{{c}}
-{{Optimal ET sequence|legend=0| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}
-Badness (Sintel): 0.337
 == Galaxy ==
@@ Line 170: / Line 118: @@
 Badness (Sintel): 0.888
+[[Category:Lehmerismic temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Lehmerismic temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]