Ragismic microtemperaments: Difference between revisions
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* ''[[Srutal]]'', {2048/2025, 4375/4374} → [[Diaschismic family #Srutal|Diaschismic family]] | * ''[[Srutal]]'', {2048/2025, 4375/4374} → [[Diaschismic family #Srutal|Diaschismic family]] | ||
* ''[[Maja]]'', {2430/2401, 3125/3087} → [[Maja family #Septimal maja|Maja family]] | * ''[[Maja]]'', {2430/2401, 3125/3087} → [[Maja family #Septimal maja|Maja family]] | ||
* [[Amity]], {4375/4374, 5120/5103} → [[Amity family #Septimal amity|Amity family]] | |||
* [[Pontiac]], {4375/4374, 32805/32768} → [[Schismatic family #Pontiac|Schismatic family]] | * [[Pontiac]], {4375/4374, 32805/32768} → [[Schismatic family #Pontiac|Schismatic family]] | ||
* ''[[Zarvo]]'', {4375/4374, 33075/32768} → [[Gravity family #Zarvo|Gravity family]] | * ''[[Zarvo]]'', {4375/4374, 33075/32768} → [[Gravity family #Zarvo|Gravity family]] | ||
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Microtemperaments considered below are ennealimmal, supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. | Microtemperaments considered below are ennealimmal, supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. | ||
Some near-microtemperaments are appended as octoid | Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. | ||
== Ennealimmal == | == Ennealimmal == | ||
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Badness: 0.023731 | Badness: 0.023731 | ||
== Parakleismic == | == Parakleismic == | ||
{{ | {{Main| Parakleismic }} | ||
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo|8 14 -13}}, with the [[118edo|118EDO]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 give 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being {{multival|13 14 35 -8 19 42}} and adding 3136/3125 and 4375/4374, and the 11-limit wedgie {{multival|13 14 35 -36 -8 19 -102 42 -132 -222}} adding 385/384. For the 7-limit [[99edo|99EDO]] may be preferred, but in the 11-limit it is best to stick with 118. | In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo|8 14 -13}}, with the [[118edo|118EDO]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 give 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being {{multival|13 14 35 -8 19 42}} and adding 3136/3125 and 4375/4374, and the 11-limit wedgie {{multival|13 14 35 -36 -8 19 -102 42 -132 -222}} adding 385/384. For the 7-limit [[99edo|99EDO]] may be preferred, but in the 11-limit it is best to stick with 118. | ||
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== Trideci == | == Trideci == | ||
{{ | {{See also| High badness temperaments #Tridecatonic }} | ||
The ''trideci'' temperament (26&65) has a period of 1/13 octave and tempers out 245/242 and 385/384 in the 11-limit. It tempers out the same 5-limit comma as the [[Octagar temperaments #Tridecatonic|tridecatonic temperament]], but with the ragisma (4375/4374) rather than the octagar (4000/3969) tempered out. The name ''trideci'' comes from "tridecim" (Latin for "[[wikipedia:13|thirteen]]"). | The ''trideci'' temperament (26&65) has a period of 1/13 octave and tempers out 245/242 and 385/384 in the 11-limit. It tempers out the same 5-limit comma as the [[Octagar temperaments #Tridecatonic|tridecatonic temperament]], but with the ragisma (4375/4374) rather than the octagar (4000/3969) tempered out. The name ''trideci'' comes from "tridecim" (Latin for "[[wikipedia:13|thirteen]]"). | ||
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[[Category:Microtemperaments]] | [[Category:Microtemperaments]] | ||
[[Category:Abigail]] | [[Category:Abigail]] | ||
[[Category:Deca]] | [[Category:Deca]] | ||
[[Category:Enneadecal]] | [[Category:Enneadecal]] | ||