Quintaleap family: Difference between revisions

Line 27:

Vals: {{Val list| 12, 109, 121, 133 }}

[[Badness]]: 0.014623

Badness: 0.014623

== Quintupole ==

The ''quintupole'' temperament tempers out the octagar comma and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents). ~~Proper~~ pronunciation of the word "quintupole" is /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[~~Marvel temperaments~~ #Quintapole|quint'''a'''pole]] temperament (12&85).''

The ''quintupole'' temperament tempers out the octagar comma and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[#Quintapole|quint'''a'''pole]] temperament (12&85).''

Line 37:

[[Comma list]]: 4000/3969, 458752/455625

[[Mapping]]: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]

[[Mapping]]: [{{val| 1 2 1 0 }}, {{val| 0 -5 16 34 }}]

Line 52:

Comma list: 896/891, 1375/1372, 4375/4356

Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]

Mapping: [{{val| 1 2 1 0 -1 }}, {{val| 0 -5 16 34 54 }}]

POTE generator: ~35/33 = 99.156

Line 65:

Comma list: 352/351, 364/363, 625/624, 2704/2695

Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]

Mapping: [{{val| 1 2 1 0 -1 -2 }}, {{val| 0 -5 16 34 54 69 }}]

POTE generator: ~35/33 = 99.165

Line 78:

Comma list: 256/255, 352/351, 364/363, 375/374, 442/441

Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]

Mapping: [{{val| 1 2 1 0 -1 -2 5 }}, {{val| 0 -5 16 34 54 69 -11 }}]

POTE generator: ~18/17 = 99.172

Line 91:

Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374

Mapping: [{{val|1 2 1 0 -1 -2 5 4}}, {{val|0 -5 16 34 54 69 -11 3}}]

Mapping: [{{val| 1 2 1 0 -1 -2 5 4 }}, {{val| 0 -5 16 34 54 69 -11 3 }}]

POTE generator: ~18/17 = 99.164

Line 100:

== Quintapole ==

Aside from the marvel comma, the ''quintapole'' temperament (12&85) tempers out 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the [[Marvel family #Appolo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). ~~Proper~~ pronunciation of the word "quintapole" is /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[~~Octagar temperaments~~ #Quintupole|quint'''u'''pole]] temperament (12&121).''

Aside from the marvel comma, the ''quintapole'' temperament (12&85) tempers out 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the [[Marvel family #Appolo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintapole" as /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[#Quintupole|quint'''u'''pole]] temperament (12&121).''

Line 107:

[[Comma list]]: 225/224, 7812500/7411887

[[Mapping]]: [{{val|1 2 1 1}}, {{val|0 -5 16 22}}]

[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]

[[POTE generator]]: ~21/20 = 98.994

Line 120:

Comma list: 100/99, 225/224, 85184/84035

Mapping: [{{val|1 2 1 1 0}}, {{val|0 -5 16 22 42}}]

Mapping: [{{val| 1 2 1 1 0 }}, {{val| 0 -5 16 22 42 }}]

POTE generator: ~21/20 = 98.954

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== Quinticosiennic ==

The ''quinticosiennic'' temperament (12&145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo~~|29EDO~~]] fourth, i.e. 12\145, is a possible generator.

The ''quinticosiennic'' temperament (12&145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo]] fourth, i.e. 12\145, is a possible generator.

Line 136:

[[Comma list]]: 5120/5103, 395136/390625

[[Mapping]]: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}]

[[Mapping]]: [{{val| 1 2 1 -1 }}, {{val| 0 -5 16 46 }}]

[[POTE generator]]: ~135/128 = 99.345

Line 151:

Comma list: 441/440, 896/891, 78408/78125

Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}]

Mapping: [{{val| 1 2 1 -1 -2 }}, {{val| 0 -5 16 46 66 }}]

POTE generator: ~35/33 = 99.318

Line 164:

Comma list: 196/195, 352/351, 364/363, 78408/78125

Mapping: [{{val|1 2 1 -1 -2 -3}}, {{val|0 -5 16 46 66 81}}]

Mapping: [{{val| 1 2 1 -1 -2 -3 }}, {{val| 0 -5 16 46 66 81 }}]

POTE generator: ~35/33 = 99.307

Line 177:

Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750

Mapping: [{{val|1 2 1 -1 -2 -3 5}}, {{val|0 -5 16 46 66 81 -11}}]

Mapping: [{{val| 1 2 1 -1 -2 -3 5 }}, {{val| 0 -5 16 46 66 81 -11 }}]

POTE generator: ~18/17 = 99.308

Line 190:

Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475

Mapping: [{{val|1 2 1 -1 -2 -3 5 4}}, {{val|0 -5 16 46 66 81 -11 3}}]

Mapping: [{{val| 1 2 1 -1 -2 -3 5 4 }}, {{val| 0 -5 16 46 66 81 -11 3 }}]

POTE generator: ~18/17 = 99.303

@@ Line 27: / Line 27: @@
 Vals: {{Val list| 12, 109, 121, 133 }}
-[[Badness]]: 0.014623
+Badness: 0.014623
 == Quintupole ==
-The ''quintupole'' temperament tempers out the octagar comma and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents). Proper pronunciation of the word "quintupole" is /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[Marvel temperaments #Quintapole|quint<u>'''a'''</u>pole]] temperament (12&amp;85).''
+The ''quintupole'' temperament tempers out the octagar comma and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[#Quintapole|quint<u>'''a'''</u>pole]] temperament (12&amp;85).''
@@ Line 37: / Line 37: @@
 [[Comma list]]: 4000/3969, 458752/455625
-[[Mapping]]: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]
+[[Mapping]]: [{{val| 1 2 1 0 }}, {{val| 0 -5 16 34 }}]
 {{Multival|legend=1| 5 -16 -34 -37 -68 -34 }}
@@ Line 52: / Line 52: @@
 Comma list: 896/891, 1375/1372, 4375/4356
-Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]
+Mapping: [{{val| 1 2 1 0 -1 }}, {{val| 0 -5 16 34 54 }}]
 POTE generator: ~35/33 = 99.156
@@ Line 65: / Line 65: @@
 Comma list: 352/351, 364/363, 625/624, 2704/2695
-Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]
+Mapping: [{{val| 1 2 1 0 -1 -2 }}, {{val| 0 -5 16 34 54 69 }}]
 POTE generator: ~35/33 = 99.165
@@ Line 78: / Line 78: @@
 Comma list: 256/255, 352/351, 364/363, 375/374, 442/441
-Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]
+Mapping: [{{val| 1 2 1 0 -1 -2 5 }}, {{val| 0 -5 16 34 54 69 -11 }}]
 POTE generator: ~18/17 = 99.172
@@ Line 91: / Line 91: @@
 Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374
-Mapping: [{{val|1 2 1 0 -1 -2 5 4}}, {{val|0 -5 16 34 54 69 -11 3}}]
+Mapping: [{{val| 1 2 1 0 -1 -2 5 4 }}, {{val| 0 -5 16 34 54 69 -11 3 }}]
 POTE generator: ~18/17 = 99.164
@@ Line 100: / Line 100: @@
 == Quintapole ==
-Aside from the marvel comma, the ''quintapole'' temperament (12&amp;85) tempers out 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the [[Marvel family #Appolo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). Proper pronunciation of the word "quintapole" is /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[Octagar temperaments #Quintupole|quint<u>'''u'''</u>pole]] temperament (12&amp;121).''
+Aside from the marvel comma, the ''quintapole'' temperament (12&amp;85) tempers out 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the [[Marvel family #Appolo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintapole" as /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[#Quintupole|quint<u>'''u'''</u>pole]] temperament (12&amp;121).''
@@ Line 107: / Line 107: @@
 [[Comma list]]: 225/224, 7812500/7411887
-[[Mapping]]: [{{val|1 2 1 1}}, {{val|0 -5 16 22}}]
+[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]
 [[POTE generator]]: ~21/20 = 98.994
@@ Line 120: / Line 120: @@
 Comma list: 100/99, 225/224, 85184/84035
-Mapping: [{{val|1 2 1 1 0}}, {{val|0 -5 16 22 42}}]
+Mapping: [{{val| 1 2 1 1 0 }}, {{val| 0 -5 16 22 42 }}]
 POTE generator: ~21/20 = 98.954
@@ Line 129: / Line 129: @@
 == Quinticosiennic ==
-The ''quinticosiennic'' temperament (12&amp;145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo|29EDO]] fourth, i.e. 12\145, is a possible generator.
+The ''quinticosiennic'' temperament (12&amp;145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo]] fourth, i.e. 12\145, is a possible generator.
@@ Line 136: / Line 136: @@
 [[Comma list]]: 5120/5103, 395136/390625
-[[Mapping]]: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}]
+[[Mapping]]: [{{val| 1 2 1 -1 }}, {{val| 0 -5 16 46 }}]
-{{Multival|legend=1|5 -16 -46 -37 -87 -62}}
+{{Multival|legend=1| 5 -16 -46 -37 -87 -62 }}
 [[POTE generator]]: ~135/128 = 99.345
@@ Line 151: / Line 151: @@
 Comma list: 441/440, 896/891, 78408/78125
-Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}]
+Mapping: [{{val| 1 2 1 -1 -2 }}, {{val| 0 -5 16 46 66 }}]
 POTE generator: ~35/33 = 99.318
@@ Line 164: / Line 164: @@
 Comma list: 196/195, 352/351, 364/363, 78408/78125
-Mapping: [{{val|1 2 1 -1 -2 -3}}, {{val|0 -5 16 46 66 81}}]
+Mapping: [{{val| 1 2 1 -1 -2 -3 }}, {{val| 0 -5 16 46 66 81 }}]
 POTE generator: ~35/33 = 99.307
@@ Line 177: / Line 177: @@
 Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750
-Mapping: [{{val|1 2 1 -1 -2 -3 5}}, {{val|0 -5 16 46 66 81 -11}}]
+Mapping: [{{val| 1 2 1 -1 -2 -3 5 }}, {{val| 0 -5 16 46 66 81 -11 }}]
 POTE generator: ~18/17 = 99.308
@@ Line 190: / Line 190: @@
 Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475
-Mapping: [{{val|1 2 1 -1 -2 -3 5 4}}, {{val|0 -5 16 46 66 81 -11 3}}]
+Mapping: [{{val| 1 2 1 -1 -2 -3 5 4 }}, {{val| 0 -5 16 46 66 81 -11 3 }}]
 POTE generator: ~18/17 = 99.303