Lehmerismic temperaments: Difference between revisions

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__FORCETOC__
These are rank-3 temperaments tempering out [[3025/3024]], but we can begin by looking at the rank-4 temperament.  
These are rank-3 temperaments tempering out [[3025/3024]], but we can begin by looking at the rank-4 temperament.  


Temperaments discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* [[Starling family #Oxpecker|Oxpecker]]
* ''[[oxpecker]]'', {121/120, 126/125} → [[Starling family #Oxpecker]]
* [[Valinorsmic temperaments #Manwe|Manwe]]
* ''[[manwe]]'', {176/175, 1331/1323} → [[Valinorsmic temperaments #Manwe]]
* [[Marvel family #Spectacle|Spectacle]]
* ''[[spectacle]]'', {225/224, 243/242} → [[Marvel family #Spectacle]]
* [[Gamelismic family #Portent|Portent]]
* ''[[portent]]'', {385/384, 441/440} → [[Gamelismic family #Portent]]
* [[Mirkwai family #Indra|Indra]]
* ''[[indra]]'', {540/539, 1375/1372} → [[Mirkwai family #Indra]]
* [[Tolermic family #Tolerant|Tolerant]]
* ''[[tolerant]]'', {896/891, 2200/2187} → [[Tolermic family #Tolerant]]
* [[Breed family #Freya|Freya]]
* ''[[freya]]'', {2401/2400, 3025/3024} → [[Breed family #Freya]]
* [[Hemimean family #Triglav|Triglav]]
* ''[[triglav]]'', {3025/3024, 3136/3125} → [[Hemimean family #Triglav]]
* [[Ragismic family #Thor|Thor]]
* ''[[thor]]'', {3025/3024, 4375/4374} → [[Ragismic family #Thor]]
* [[Hemifamity family #Kapo|Kapo]]
* ''[[kapo]]'', {3025/3024, 5120/5103} → [[Hemifamity family #Kapo]]


= Lehmerismic =
== Lehmerismic ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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{{Val list|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
{{Val list|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}


= Tyr =
== Tyr ==
{{see also| Landscape family }}
{{see also| Landscape family }}


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[[Badness]]: 0.259 × 10<sup>-3</sup>
[[Badness]]: 0.259 × 10<sup>-3</sup>


= Skadi =
== Skadi ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
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[[Badness]]: 0.349 × 10<sup>-3</sup>
[[Badness]]: 0.349 × 10<sup>-3</sup>


= Ganesha =
== Ganesha ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
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[[Badness]]: 0.390 × 10<sup>-3</sup>
[[Badness]]: 0.390 × 10<sup>-3</sup>


= Hanuman =
== Hanuman ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
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[[Badness]]: 0.500 × 10<sup>-3</sup>
[[Badness]]: 0.500 × 10<sup>-3</sup>


== 13-limit ==
=== 13-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Badness: 0.653 × 10<sup>-3</sup>
Badness: 0.653 × 10<sup>-3</sup>


= Lux =
== Lux ==
== 7-limit ==
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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[[Badness]]: 1.709 × 10<sup>-3</sup>
[[Badness]]: 1.709 × 10<sup>-3</sup>


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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[[Badness]]: 0.5083 × 10<sup>-3</sup>
[[Badness]]: 0.5083 × 10<sup>-3</sup>


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


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[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Temperament collection]]
[[Category:Lehmerismic]]
[[Category:Lehmerismic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 10:18, 8 June 2021

These are rank-3 temperaments tempering out 3025/3024, but we can begin by looking at the rank-4 temperament.

Temperaments discussed elsewhere are:

Lehmerismic

Subgroup: 2.3.5.7.11

Comma list: 3025/3024

Mapping: [⟨1 0 0 0 2], ⟨0 1 0 1 2], ⟨0 0 1 0 -1], ⟨0 0 0 2 1]]

Mapping generators: ~2, ~3, ~5, ~55/36

Template:Val list

Tyr

See also: Landscape family

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 102487/102400

Mapping: [⟨3 0 0 4 8], ⟨0 2 0 -4 1], ⟨0 0 1 2 0]]

Mapping generators: ~63/50, ~400/231, ~5

Template:Val list

Badness: 0.259 × 10-3

Skadi

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 703125/702464

Mapping: [⟨1 0 5 8 1], ⟨0 1 1 3 2], ⟨0 0 -6 -14 -1]]

Mapping generators: ~2, ~3, ~18/11

Template:Val list

Badness: 0.349 × 10-3

Ganesha

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625

Mapping: [⟨1 0 0 -22 -9], ⟨0 1 0 1 2], ⟨0 0 1 10 4]]

Mapping generators: ~2, ~3, ~5

Template:Val list

Badness: 0.390 × 10-3

Hanuman

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993

Mapping: [⟨1 2 0 -8 1], ⟨0 -3 0 11 1], ⟨0 0 1 4 1]]

Mapping generators: ~2, ~11/10, ~5

Template:Val list

Badness: 0.500 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1575/1573, 2080/2079

Mapping: [⟨1 2 0 -8 1 -6], ⟨0 -3 0 11 1 3], ⟨0 0 1 4 1 4]]

Mapping generators: ~2, ~11/10, ~5

Vals: Template:Val list

Badness: 0.653 × 10-3

Lux

7-limit

Subgroup: 2.3.5.7

Comma list: 26843545600/26795786661

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

Wedgie: ⟨⟨⟨ 5 2 13 30 ]]]

POTE generators: ~3/2 = 702.1152, ~40960/35721 = 235.5941

Template:Val list

Badness: 1.709 × 10-3

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 131072/130977

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

Wedgie: ⟨⟨⟨ 5 2 -4 13 -1 10 30 25 34 71 ]]]

POTE generators: ~3/2 = 702.1117, ~55/48 = 235.5784

Template:Val list

Badness: 0.5083 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generators: ~3/2 = 702.0674, ~55/48 = 235.5870

Vals: Template:Val list

Badness: 0.3602 × 10-3

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