Luna family: Difference between revisions

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Line 2: Line 2:


= Luna =
= Luna =
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 13: Line 12:
{{Val list|legend=1| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }}
{{Val list|legend=1| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }}


[[Badness]]: 0.0206
[[Badness]]: 0.020576


= Hemithirds =
= Hemithirds =
Line 39: Line 38:
{{Val list|legend=1| 31, 87, 118 }}
{{Val list|legend=1| 31, 87, 118 }}


[[Badness]]: 0.0443
[[Badness]]: 0.044284


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


Line 56: Line 54:
: Eigenmonzos: 2, 11/7
: Eigenmonzos: 2, 11/7


{{Val list|legend=1| 31, 87, 118 }}
Vals: {{Val list| 31, 87, 118 }}


Badness: 0.0190
Badness: 0.019003


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


Line 70: Line 67:
POTE generator: ~28/25 = 193.166
POTE generator: ~28/25 = 193.166


{{Val list|legend=1| 31, 56, 87, 118, 205d }}
Vals: {{Val list| 31, 56, 87, 118, 205d }}


Badness: 0.0217
Badness: 0.021738


= Lunatic =
= Lunatic =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 274877906944/274658203125
[[Comma list]]: 4375/4374, 274877906944/274658203125


[[Mapping]]: [{{val| 1 4 2 2 }}, {{val| 0 -15 2 -113 }}]
[[Mapping]]: [{{val| 1 4 2 21 }}, {{val| 0 -15 2 -113 }}]


{{Multival|legend=1| 15 -2 113 -38 137 268 }}
{{Multival|legend=1| 15 -2 113 -38 137 268 }}
Line 88: Line 84:
{{Val list|legend=1| 87d, 118, 323, 441, 1205, 1646 }}
{{Val list|legend=1| 87d, 118, 323, 441, 1205, 1646 }}


[[Badness]]: 0.0380
[[Badness]]: 0.037966
 
== 11-limit ==
Subgroup: 2.3.5.7.11
 
Comma list: 4375/4374, 12005/11979, 172032/171875
 
Mapping: [{{val| 1 4 2 21 14 }}, {{val| 0 -15 2 -113 -140 }}]
 
POTE generator: ~352/315 = 193.200
 
Vals: {{Val list| 118, 323e, 441, 559, 1000e }}
 
Badness: 0.058588


= Semiluna =
= Semiluna =
{{see also| Canousmic temperaments #Semiluna }}
{{see also| Canousmic temperaments #Semiluna }}


Line 99: Line 107:


[[Mapping]]: [{{val| 2 8 4 23 }}, {{val| 0 -15 2 -54 }}]
[[Mapping]]: [{{val| 2 8 4 23 }}, {{val| 0 -15 2 -54 }}]
{{Multival|legend=1| 30 -4 108 -76 87 262 }}


[[POTE generator]]: ~2187/1960 = 193.1725
[[POTE generator]]: ~2187/1960 = 193.1725
Line 104: Line 114:
{{Val list|legend=1| 56d, 118, 292, 410 }}
{{Val list|legend=1| 56d, 118, 292, 410 }}


[[Badness]]: 0.1922
[[Badness]]: 0.192167


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


Comma list: 5632/5625, 9801/9800, 14641/14580
Comma list: 5632/5625, 9801/9800, 14641/14580
Mapping: [{{val| 2 8 4 23 14 }}, {{val| 0 -15 2 -54 -22 }}]


POTE generator: ~121/108 = 193.1732
POTE generator: ~121/108 = 193.1732


Mapping: [{{val| 2 8 4 23 14 }}, {{val| 0 -15 2 -54 -22 }}]
Vals: {{Val list| 56d, 118, 292, 410 }}
 
{{Val list|legend=1| 56d, 118, 292, 410 }}


Badness: 0.0678
Badness: 0.067783


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 23:48, 9 April 2021

The luna family tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of [38 -2 -15⟩;

Luna

Subgroup: 2.3.5

Comma list: 274877906944/274658203125

Mapping: [⟨1 4 2], ⟨0 -15 2]]

POTE generator: ~262144/234375 = 193.201

Template:Val list

Badness: 0.020576

Hemithirds

Main article: Hemithirds
See also: Hemimean clan § Hemithirds

Subgroup: 2.3.5.7

Comma list: 1029/1024, 3136/3125

Mapping: [⟨1 4 2 2], ⟨0 -15 2 5]]

Wedgie: ⟨⟨ 15 -2 -5 -38 -50 -6 ]]

POTE generator: ~28/25 = 193.244

Minimax tuning:

[[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [11/5 -1/10 0 1/10⟩, [5/2 -1/4 0 1/4⟩]
Eigenmonzos: 2, 7/6
[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [82/35 -4/35 0 2/35⟩, [20/7 -2/7 0 1/7⟩]
Eigenmonzos: 2, 7/6

Template:Val list

Badness: 0.044284

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 3136/3125

Mapping: [⟨1 4 2 2 7], ⟨0 -15 2 5 -22]]

POTE generator: ~28/25 = 193.227

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [11/9 0 0 -5/9 5/9⟩, [64/27 0 0 2/27 -2/27⟩, [79/27 0 0 5/27 -5/27⟩, [79/27 0 0 -22/27 22/27⟩]
Eigenmonzos: 2, 11/7

Vals: Template:Val list

Badness: 0.019003

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 625/624

Mapping: [⟨1 4 2 2 7 0], ⟨0 -15 2 5 -22 23]]

POTE generator: ~28/25 = 193.166

Vals: Template:Val list

Badness: 0.021738

Lunatic

Subgroup: 2.3.5.7

Comma list: 4375/4374, 274877906944/274658203125

Mapping: [⟨1 4 2 21], ⟨0 -15 2 -113]]

Wedgie: ⟨⟨ 15 -2 113 -38 137 268 ]]

POTE generator: ~262144/234375 = 193.196

Template:Val list

Badness: 0.037966

11-limit

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 12005/11979, 172032/171875

Mapping: [⟨1 4 2 21 14], ⟨0 -15 2 -113 -140]]

POTE generator: ~352/315 = 193.200

Vals: Template:Val list

Badness: 0.058588

Semiluna

See also: Canousmic temperaments § Semiluna

Subgroup: 2.3.5.7

Comma list: 4802000/4782969, 95703125/95551488

Mapping: [⟨2 8 4 23], ⟨0 -15 2 -54]]

Wedgie: ⟨⟨ 30 -4 108 -76 87 262 ]]

POTE generator: ~2187/1960 = 193.1725

Template:Val list

Badness: 0.192167

11-limit

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 9801/9800, 14641/14580

Mapping: [⟨2 8 4 23 14], ⟨0 -15 2 -54 -22]]

POTE generator: ~121/108 = 193.1732

Vals: Template:Val list

Badness: 0.067783

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