Quintaleap family: Difference between revisions

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== Quintaleap ==

The name ''quintaleap'' comes from "quintans" (Latin for "one fifth") and "leapday", because the generator is 1/5 of the [[Hemifamity temperaments #Leapday|leapday]] fourth (~4/3, about ~~495.8~~ cents).

The name ''quintaleap'' comes from "quintans" (Latin for "one fifth") and "leapday", because the generator is 1/5 of the [[Hemifamity temperaments #Leapday|leapday]] fourth (~4/3, about 496 cents).

Subgroup: 2.3.5

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== 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). [[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).''

The ''quintupole'' temperament tempers out the octagar comma (4000/3969) 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).''

Subgroup: 2.3.5.7

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== 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). [[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).''

The ''quintapole'' temperament (12&85) tempers out the marvel comma (225/224) and 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).''

Subgroup: 2.3.5.7

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

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

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Badness: 0.028440

== Decimaleap ==

The ''decimaleap'' temperament (24&121) has a quarter-tone generator and tempers out the porwell comma (6144/6125) and 393379840/387420489 (sasaquadzo-ayo) in the 7-limit; 896/891 and 14700/14641 in the 11-limit. The name ''decimaleap'' comes from "decima" (Latin for "one tenth") and "leapday", because the generator is 1/10 of the leapday fourth.

Subgroup: 2.3.5.7

[[Comma list]]: 6144/6125, 393379840/387420489

[[Mapping]]: [{{val|1 2 1 5}}, {{val|0 -10 32 -53}}]

[[POTE generator]]: ~36/35 = 49.621

[[Badness]]: 0.314227

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 896/891, 6144/6125, 14700/14641

Mapping: [{{val|1 2 1 5 4}}, {{val|0 -10 32 -53 -13}}]

POTE generator: ~36/35 = 49.622

Vals: {{Val list| 24, 97d, 121, 145, 266e }}

Badness: 0.084612

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363, 676/675, 6144/6125

Mapping: [{{val|1 2 1 5 4 3}}, {{val|0 -10 32 -53 -13 17}}]

POTE generator: ~36/35 = 49.620

Vals: {{Val list| 24, 97d, 121, 266ef }}

Badness: 0.041763

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 352/351, 364/363, 676/675, 1156/1155

Mapping: [{{val|1 2 1 5 4 3 5}}, {{val|0 -10 32 -53 -13 17 -22}}]

POTE generator: ~34/33 = 49.621

Vals: {{Val list| 24, 97dg, 121, 266efg }}

Badness: 0.025552

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 256/255, 352/351, 361/360, 364/363, 456/455, 665/663

Mapping: [{{val|1 2 1 5 4 3 5 4}}, {{val|0 -10 32 -53 -13 17 -22 6}}]

POTE generator: ~34/33 = 49.624

Vals: {{Val list| 24, 97dg, 121, 145, 266efg }}

Badness: 0.021208

[[Category:Regular temperament theory]]

@@ Line 2: / Line 2: @@
 == Quintaleap ==
-The name ''quintaleap'' comes from "quintans" (Latin for "one fifth") and "leapday", because the generator is 1/5 of the [[Hemifamity temperaments #Leapday|leapday]] fourth (~4/3, about 495.8 cents).
+The name ''quintaleap'' comes from "quintans" (Latin for "one fifth") and "leapday", because the generator is 1/5 of the [[Hemifamity temperaments #Leapday|leapday]] fourth (~4/3, about 496 cents).
 Subgroup: 2.3.5
@@ Line 36: / Line 36: @@
 == 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). [[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).''
+The ''quintupole'' temperament tempers out the octagar comma (4000/3969) 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).''
 Subgroup: 2.3.5.7
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 == 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). [[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).''
+The ''quintapole'' temperament (12&amp;85) tempers out the marvel comma (225/224) and 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).''
 Subgroup: 2.3.5.7
@@ Line 112: / Line 112: @@
 [[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]
+{{Multival|legend=1| 5 -16 -22 -37 -49 -6 }}
 [[POTE generator]]: ~21/20 = 98.994
@@ Line 200: / Line 202: @@
 Badness: 0.028440
+== Decimaleap ==
+The ''decimaleap'' temperament (24&amp;121) has a quarter-tone generator and tempers out the porwell comma (6144/6125) and 393379840/387420489 (sasaquadzo-ayo) in the 7-limit; 896/891 and 14700/14641 in the 11-limit. The name ''decimaleap'' comes from "decima" (Latin for "one tenth") and "leapday", because the generator is 1/10 of the leapday fourth.
+Subgroup: 2.3.5.7
+[[Comma list]]: 6144/6125, 393379840/387420489
+[[Mapping]]: [{{val|1 2 1 5}}, {{val|0 -10 32 -53}}]
+{{Multival|legend=1| 10 -32 53 -74 56 213 }}
+[[POTE generator]]: ~36/35 = 49.621
+{{Val list|legend=1| 24, 97d, 121, 145, 266 }}
+[[Badness]]: 0.314227
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 896/891, 6144/6125, 14700/14641
+Mapping: [{{val|1 2 1 5 4}}, {{val|0 -10 32 -53 -13}}]
+POTE generator: ~36/35 = 49.622
+Vals: {{Val list| 24, 97d, 121, 145, 266e }}
+Badness: 0.084612
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 352/351, 364/363, 676/675, 6144/6125
+Mapping: [{{val|1 2 1 5 4 3}}, {{val|0 -10 32 -53 -13 17}}]
+POTE generator: ~36/35 = 49.620
+Vals: {{Val list| 24, 97d, 121, 266ef }}
+Badness: 0.041763
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 256/255, 352/351, 364/363, 676/675, 1156/1155
+Mapping: [{{val|1 2 1 5 4 3 5}}, {{val|0 -10 32 -53 -13 17 -22}}]
+POTE generator: ~34/33 = 49.621
+Vals: {{Val list| 24, 97dg, 121, 266efg }}
+Badness: 0.025552
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 256/255, 352/351, 361/360, 364/363, 456/455, 665/663
+Mapping: [{{val|1 2 1 5 4 3 5 4}}, {{val|0 -10 32 -53 -13 17 -22 6}}]
+POTE generator: ~34/33 = 49.624
+Vals: {{Val list| 24, 97dg, 121, 145, 266efg }}
+Badness: 0.021208
 [[Category:Regular temperament theory]]