Marvel temperaments: Difference between revisions

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* ''[[Houborizic]]'' {225/224, 1250000/1240029} → [[Amity family #Houborizic|Amity family]]

* ''[[Qintosec]]'', {225/224, 2560000/2470629} → [[Qintosec family #Qintosec|Qintosec family]]

* ''[[Quintapole]]'', {225/224, 7812500/7411887} → [[Quintaleap family #Quintapole|Quintaleap family]]

* ''[[Maquila]]'', {225/224, 30233088/28824005} → [[Maquila family #Septimal maquila|Maquila family]]

* ''[[Marvo]]'', {225/224, 78125000/78121827} → [[Gravity family #Marvo|Gravity family]]

Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, gracecordial~~, and quintapole~~.

Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.

Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

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Badness: 0.052235

~~== Quintapole ==~~

~~: ''See also: [[16ed5/2 #Regular temperaments]] or [[42ed11 #Regular temperaments]]''~~

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>'''u'''</u>pole]] temperament (12&121).''

~~Subgroup: 2.3.5.7~~

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

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

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

~~{{Val list|legend=1| 12, 73c, 85, 97d }}~~

~~[[Badness]]: 0.192498~~

~~=== 11-limit ===~~

~~Subgroup: 2.3.5.7.11~~

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

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

~~POTE generator: ~21/20 = 98.954~~

~~Vals: {{Val list| 12, 73ce, 85, 97d }}~~

~~Badness: 0.104353~~

[[Category:Regular temperament theory]]

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 * ''[[Houborizic]]'' {225/224, 1250000/1240029} → [[Amity family #Houborizic|Amity family]]
 * ''[[Qintosec]]'', {225/224, 2560000/2470629} → [[Qintosec family #Qintosec|Qintosec family]]
+* ''[[Quintapole]]'', {225/224, 7812500/7411887} → [[Quintaleap family #Quintapole|Quintaleap family]]
 * ''[[Maquila]]'', {225/224, 30233088/28824005} → [[Maquila family #Septimal maquila|Maquila family]]
 * ''[[Marvo]]'', {225/224, 78125000/78121827} → [[Gravity family #Marvo|Gravity family]]
-Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, gracecordial, and quintapole.
+Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.
 Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
@@ Line 1,046: / Line 1,047: @@
 Badness: 0.052235
-== Quintapole ==
-: ''See also: [[16ed5/2 #Regular temperaments]] or [[42ed11 #Regular temperaments]]''
-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).''
-Subgroup: 2.3.5.7
-[[Comma list]]: 225/224, 7812500/7411887
-[[Mapping]]: [{{val|1 2 1 1}}, {{val|0 -5 16 22}}]
-[[POTE generator]]: ~21/20 = 98.994
-{{Val list|legend=1| 12, 73c, 85, 97d }}
-[[Badness]]: 0.192498
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 100/99, 225/224, 85184/84035
-Mapping: [{{val|1 2 1 1 0}}, {{val|0 -5 16 22 42}}]
-POTE generator: ~21/20 = 98.954
-Vals: {{Val list| 12, 73ce, 85, 97d }}
-Badness: 0.104353
 [[Category:Regular temperament theory]]