Marvel temperaments: Difference between revisions
List of temps |
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Temperaments considered in families and clans are: | Temperaments considered in families and clans are: | ||
* ''[[Pelogic]]'' → [[Mavila family #Pelogic|Mavila family]] | * ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]] | ||
* [[Meantone]] → [[Meantone family #Septimal meantone|Meantone family]] | * [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]] | ||
* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] | * [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]] | ||
* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] | * [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]] | ||
* ''[[Sharpie]]'' → [[Dicot family #Sharpie|Dicot family]] | * ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]] | ||
* ''[[Immune]]'' → [[Immunity family #Immune|Immunity family]] | * ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]] | ||
* ''[[August]]'' → [[Augmented family #August|Augmented family]] | * ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]] | ||
* ''[[Fog]]'' → [[Misty family #Fog|Misty family]] (+ | * ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]] | ||
* [[Negri]] → [[ | * [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]] | ||
* [[Magic]] → [[Magic family #Magic|Magic family]] | * [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]] | ||
* ''[[Passive]]'' → [[Passion family #Passive|Passion family]] | * [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]] | ||
* ''[[Quintapole]]'' → [[Quintaleap family #Quintapole|Quintaleap family]] | * ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]] | ||
* ''[[Houborizic]]'' → [[Amity family #Houborizic|Amity family]] | * ''[[Quintapole]]'' (+7812500/7411887) → [[Quintaleap family #Quintapole|Quintaleap family]] | ||
* ''[[Qintosec]]'' → [[Quintosec family #Qintosec|Quintosec family]] | * ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]] | ||
* [[Miracle]] → [[Gamelismic clan #Miracle|Gamelismic clan]] | * ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]] | ||
* [[Catakleismic]] → [[Kleismic family #Catakleismic|Kleismic family]] | * [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]] | ||
* ''[[Marvo]]'' → [[Gravity family #Marvo|Gravity family]] | * [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]] | ||
* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] | * ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]] | ||
* ''[[Snipes]]'' → [[Wesley family #Snipes|Wesley family]] | * [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]] | ||
* ''[[ | * ''[[Snipes]]'' (+6125/5832) → [[Wesley family #Snipes|Wesley family]] | ||
* ''[[Escapist]]'' → [[Escapade family #Escapist|Escapade family]] | * ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]] | ||
* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] | * ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]] | ||
* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] | * ''[[Decic]]'' (+16807/16384) → [[Cloudy clan #Decic|Cloudy clan]] | ||
* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] | * ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]] | ||
* ''[[Hendeca]]'' → [[11th-octave temperaments #Hendeca|11th-octave temperaments]] | * ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]] | ||
* | * ''[[Hendeca]]'' (+122880/117649) → [[11th-octave temperaments #Hendeca|11th-octave temperaments]] | ||
* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] | * [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]] | ||
* ''[[Maquila]]'' → [[Maquila family #Septimal maquila|Maquila family]] | * ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]] | ||
* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] | * ''[[Maquila]]'' (+30233088/28824005) → [[Maquila family #Septimal maquila|Maquila family]] | ||
* ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]] | |||
Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, gwazy, and tertiosec, in the order of increasing [[badness]]. | Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, gwazy, and tertiosec, in the order of increasing [[badness]]. | ||
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Badness (Sintel): 1.20 | Badness (Sintel): 1.20 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness (Sintel): 1.14 | Badness (Sintel): 1.14 | ||
=== Mermaid === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 225/224, 385/384, 532400/531441 | |||
Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}} | |||
{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }} | |||
Badness (Sintel): 1.46 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 225/224, 325/324, 385/384, 10648/10647 | |||
Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}} | |||
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }} | |||
Badness (Sintel): 1.47 | |||
== Slender == | == Slender == | ||
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== Triton == | == Triton == | ||
: ''For the 5-limit version, see [[ | : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].'' | ||
Triton may be described as the {{nowrap| 19 & 21 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, three generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is alpha-tricot. | Triton may be described as the {{nowrap| 19 & 21 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, three generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is alpha-tricot. | ||
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: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].'' | ||
Tertiosec may be described as the {{nowrap| 21 & 75 }} temperament. It was initially named ''tertiomar'' by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, but was changed to ''tertiosec''. | Tertiosec may be described as the {{nowrap| 21 & 75 }} temperament. It was initially named ''tertiomar'' by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, but was changed to ''tertiosec'' in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo! Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||