No-fives subgroup temperaments: Difference between revisions
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==== Flutterpyth ==== | ==== Flutterpyth ==== | ||
Restricted to 2.3.7.11, this temperament is a no-5 restriction of 11-limit [[ultrapyth]]. This temperament was created to yield [[blackdye]] tunings where [[aberrisma|aberrisma-altered]] 3-limit thirds become tempered [[13/11]][[~]][[19/16]] and [[14/11]]. | Restricted to 2.3.7.11, this temperament is a no-5 restriction of 11-limit [[achytas clan #Ultrapyth|ultrapyth]]. This temperament was created to yield [[blackdye]] tunings where [[aberrisma|aberrisma-altered]] 3-limit thirds become tempered [[13/11]][[~]][[19/16]] and [[14/11]]. | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
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=== Navy === | === Navy === | ||
This temperament is the common [[restriction]] of [[tsaharuk]] and [[quanic]]. | This temperament is the common [[restriction]] of [[schismatic family #Tsaharuk|tsaharuk]] and [[aberschismic temperaments #Quanic|quanic]]. It can be seen as [[5edf]] with octaves, taking advantage of 5edf's extremely accurate 7th harmonic. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out. | Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out. | ||
Hemif is the common [[restriction]] of [[hemififths]] (41 & 58) and [[salsa]] (24 & 41), | Hemif is the common [[restriction]] of [[breedsmic temperaments #Hemififths|hemififths]] (41 & 58) and [[schismatic family #Salsa|salsa]] (24 & 41), as well as the low-accuracy [[meantone family #Mohamaq|mohamaq]] (7d & 24). It is the add-7 [[extension]] of [[rastmic clan #Namo|namo]]. [[Weak extension]]s of hemif include [[diaschismic family #Sruti|sruti]] (24 & 58) and [[tetracot family #Bunya|bunya]] (41 & 75). | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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{{See also| Heartland }} | {{See also| Heartland }} | ||
This temperament is the common [[restriction]] of [[monkey]] and [[sesquiquartififths]]. | This temperament is the common [[restriction]] of [[tetracot family #Monkey|monkey]] and [[schismatic family #Sesquiquartififths|sesquiquartififths]]. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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=== Magi === | === Magi === | ||
This temperament is the no-5 [[restriction]] of [[magic]], tempering out the [[septimagic comma]]. It is considerably more accurate than normal magic. | This temperament is the no-5 [[restriction]] of [[magic family #Septimal magic|magic]], tempering out the [[septimagic comma]]. It is considerably more accurate than normal magic. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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{{Main| Squares }} | {{Main| Squares }} | ||
Skwares is the | Skwares splits the [[6/1|6th harmonic]] into four [[~]][[14/9]] minor sixths. It is the common [[restriction]] of [[meantone family #Squares|squares]], [[orwellismic temperaments #Sentinel|sentinel]], [[dicot family #Sidi|sidi]], and [[smate family #Septimal smate|smate]]. [[Weak extension]]s of skwares include [[würschmidt family #Septimal würschmidt|septimal würschmidt]] and [[tetracot family #Weasel|weasel]]. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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===== Byhearted ===== | ===== Byhearted ===== | ||
This temperament is the restriction of | This temperament is the restriction of weasel to the 2.3.7.11.19 subgroup. | ||
Subgroup: 2.3.7.11.19 | Subgroup: 2.3.7.11.19 | ||
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=== Harrison === | === Harrison === | ||
Harrison is the no-5 [[restriction]] of [[meantone]]. | Harrison is the no-5 [[restriction]] of [[meantone family #Septimal meantone|meantone]]. There is little reason to consider this temperament in practice – since intervals of 5 in meantone are as accurate as intervals of 7, only simpler, they are always available by the time intervals of 7 are generated. As such, this temperament is only provided here for bookkeeping reasons. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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=== Bleu === | === Bleu === | ||
Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit, and is the common [[restriction]] of [[progression]], [[secund]] and [[jerome]]. | Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit, and is the common [[restriction]] of [[mint temperaments #Progression|progression]], [[greenwoodmic temperaments #Secund|secund]] and [[meantone family #Jerome|jerome]]. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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{{See also| Heartland }} | {{See also| Heartland }} | ||
This temperament is the no-5 [[restriction]] of [[octacot]]. | This temperament is the no-5 [[restriction]] of [[tetracot family #Octacot|octacot]]. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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A notable [[patent val|patent-val]] edo tuning not appearing in the [[optimal ET sequence]] is [[80edo]], which is approximately the just-13's tuning (as [[10edo]] is used as a [[consistent circle]] of [[~]][[16/13]]'s therein), with 13/8 still tuned slightly flat so qualifying a reasonable tuning for the 2.3.13 subgroup (as evidenced by appearing in the sequence for [[tetris]]). | A notable [[patent val|patent-val]] edo tuning not appearing in the [[optimal ET sequence]] is [[80edo]], which is approximately the just-13's tuning (as [[10edo]] is used as a [[consistent circle]] of [[~]][[16/13]]'s therein), with 13/8 still tuned slightly flat so qualifying a reasonable tuning for the 2.3.13 subgroup (as evidenced by appearing in the sequence for [[tetris]]). | ||
Strong extensions for prime 5 include [[leapday]] (29 & 46), [[leapweek]] (46 & 63), and [[leapmonth]] (63 & 80), all of which are more complex than vanilla leapfrog. A low-complexity low-accuracy extension is given by [[supermean]] (5de & 17c), where it is merged with [[meantone]]. [[Srutal]] (46 & 80), usually considered as a strong extension of [[diaschismic]], is a weak extension of leapfrog, and yet another weak extension is [[immune]] (29 & 63), which is in turn a strong extension of 5-limit [[immunity]]. | Strong extensions for prime 5 include [[sengic temperaments #Leapday|leapday]] (29 & 46), [[sensamagic clan #Leapweek|leapweek]] (46 & 63), and [[hemimage temperaments #Leapmonth|leapmonth]] (63 & 80), all of which are more complex than vanilla leapfrog. A low-complexity low-accuracy extension is given by [[meantone family #Supermean|supermean]] (5de & 17c), where it is merged with [[meantone family #Meantone|meantone]]. [[diaschismic family #Srutal|Srutal]] (46 & 80), usually considered as a strong extension of [[diaschismic family #Diaschismic|diaschismic]], is a weak extension of leapfrog, and yet another weak extension is [[immunity family #Immune|immune]] (29 & 63), which is in turn a strong extension of 5-limit [[immunity family #Immunity|immunity]]. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||