Octagar temperaments: Difference between revisions

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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&85).''

Subgroup: 2.3.5.7

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

POTE generator: ~~~132~~/~~125~~ = 99.156

POTE generator: ~35/33 = 99.156

Vals: {{Val list| 12, 109, 121, 351bde, 472bdee }}

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

POTE generator: ~55/52 = 99.165

POTE generator: ~35/33 = 99.165

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

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 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).''
 Subgroup: 2.3.5.7
@@ Line 111: / Line 112: @@
 Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]
-POTE generator: ~132/125 = 99.156
+POTE generator: ~35/33 = 99.156
 Vals: {{Val list| 12, 109, 121, 351bde, 472bdee }}
@@ Line 124: / Line 125: @@
 Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]
-POTE generator: ~55/52 = 99.165
+POTE generator: ~35/33 = 99.165
 Vals: {{Val list| 12f, 109, 121 }}