No-fives subgroup temperaments: Difference between revisions
m →Skwares |
→Temperaments with a 2.3.7 gene: complete converting links to data pages |
||
| (One intermediate revision by the same user not shown) | |||
| Line 10: | Line 10: | ||
==== 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 | ||
| Line 51: | Line 51: | ||
=== 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 | ||
| Line 204: | Line 204: | ||
{{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 | ||
| Line 254: | Line 254: | ||
=== 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 | ||
| Line 440: | Line 440: | ||
===== 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 | ||
| Line 458: | Line 458: | ||
=== 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 | ||
| Line 480: | Line 480: | ||
=== 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 | ||
| Line 541: | Line 541: | ||
{{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 | ||
| Line 652: | Line 652: | ||
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 | ||