Semicomma family: Difference between revisions
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The 5-limit parent comma for the '''semicomma family''' is the [[semicomma]], 2109375/2097152 = {{monzo| -21 3 7 }}. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths. | The 5-limit parent comma for the '''semicomma family''' is the [[semicomma]], 2109375/2097152 = {{monzo| -21 3 7 }}. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths. | ||
= Orson = | == Orson == | ||
'''Orson''', first discovered by [[Erv Wilson]], is the [[5-limit]] temperament tempering out the semicomma. It has a [[generator]] of [[75/64]], which is sharper than [[7/6]] by [[225/224]] when untempered, and less sharp than that in any good orson tempering, for example [[53edo]] or [[84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell. | '''Orson''', first discovered by [[Erv Wilson]], is the [[5-limit]] temperament tempering out the semicomma. It has a [[generator]] of [[75/64]], which is sharper than [[7/6]] by [[225/224]] when untempered, and less sharp than that in any good orson tempering, for example [[53edo]] or [[84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell. | ||
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[[Badness]]: 0.040807 | [[Badness]]: 0.040807 | ||
== Seven limit children == | === Seven limit children === | ||
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65625/65536 (or 225/224) leads to orwell, but we could also add | The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65625/65536 (or 225/224) leads to orwell, but we could also add | ||
* 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or | * 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or | ||
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* 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}. | * 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}. | ||
= Orwell = | == Orwell == | ||
{{main| Orwell }} | {{main| Orwell }} | ||
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[[Badness]]: 0.020735 | [[Badness]]: 0.020735 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.015231 | Badness: 0.015231 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.019718 | Badness: 0.019718 | ||
=== Blair === | ==== Blair ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.023086 | Badness: 0.023086 | ||
=== Winston === | ==== Winston ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.019931 | Badness: 0.019931 | ||
=== Doublethink === | ==== Doublethink ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.027120 | Badness: 0.027120 | ||
== Newspeak == | === Newspeak === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.031438 | Badness: 0.031438 | ||
== Borwell == | === Borwell === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.038377 | Badness: 0.038377 | ||
= Triwell = | == Triwell == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.080575 | [[Badness]]: 0.080575 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.029807 | Badness: 0.029807 | ||
= Quadrawell = | == Quadrawell == | ||
The ''quadrawell'' temperament (31&212, named by [[User:Xenllium|Xenllium]]) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic. | The ''quadrawell'' temperament (31&212, named by [[User:Xenllium|Xenllium]]) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic. | ||
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[[Badness]]: 0.075754 | [[Badness]]: 0.075754 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.036493 | Badness: 0.036493 | ||
= Sabric = | == Sabric == | ||
The ''sabric'' temperament (53&190, named by [[User:Xenllium]]) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents). | The ''sabric'' temperament (53&190, named by [[User:Xenllium]]) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents). | ||
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[[Badness]]: 0.088355 | [[Badness]]: 0.088355 | ||
= Rainwell = | == Rainwell == | ||
The ''rainwell'' temperament (31&265, named by [[User:Xenllium]]) tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152. | The ''rainwell'' temperament (31&265, named by [[User:Xenllium]]) tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152. | ||
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Badness: 0.143488 | Badness: 0.143488 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||