Semicomma family: Difference between revisions

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Badness (Sintel): 0.815

==== 2.3.5.7.11.13.19 ====

Subgroup: 2.3.5.7.11.13.19

Comma list: 99/98, 121/120, 176/175, 275/273, [[400/399]]

Mapping: {{mapping| 1 0 3 1 3 8 9| 0 7 -3 8 2 -19 -21}}

Optimal tunings:

* WE: ~2 = 1200.320{{c}}, ~7/6 = 271.640{{c}}

* CWE: ~2 = 1200.000{{c}}, ~7/6 = 271.566{{c}}

Badness (Sintel): 0.881

==== Blair ====

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=== Newspeak ===

In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with ~~basic 11-limit~~ orwell at [[31edo]].

In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with undecimal orwell at [[31edo]].

Subgroup: 2.3.5.7.11

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== Triwell ==

Triwell may be described as the {{nowrap| 31 & 159 }} temperament. It slices orwell ~~major sixth ~128/75~~ into three generators, ~~nine of~~ which ~~give~~ the ~~5th harmonic~~. Its ploidacot is 15-sheared-21-cot.

Triwell tempers out the gamelisma, [[1029/1024]], and the triwellisma, [[235298/234375]]. It may be described as the {{nowrap| 31 & 159 }} temperament. It slices orwell's generator plus two octaves into three generators, and seven generators octave reduced make a ~8/7, which is the generator of [[slendric]]. Its ploidacot is 15-sheared-21-cot.

[[Subgroup]]: 2.3.5.7

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== Quadrawell ==

Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. Its ploidacot is 22-sheared-28-cot.

Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. It can also be viewed as [[2.5.7|2.5.7-subgroup]] [[mothra]] with a different mapping of prime [[3/1|3]]. Its ploidacot is 22-sheared-28-cot.

[[Subgroup]]: 2.3.5.7

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[[Category:Temperament families]]

~~[[Category:Pages with mostly numerical content]]~~

[[Category:Semicomma family| ]]

[[Category:Rank 2]]

[[Category:Orson]]

[[Category:Orwell]]

@@ Line 115: / Line 115: @@
 Badness (Sintel): 0.815
+==== 2.3.5.7.11.13.19 ====
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 99/98, 121/120, 176/175, 275/273, [[400/399]]
+Mapping: {{mapping| 1 0 3 1 3 8 9| 0 7 -3 8 2 -19 -21}}
+Optimal tunings:
+* WE: ~2 = 1200.320{{c}}, ~7/6 = 271.640{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~7/6 = 271.566{{c}}
+Badness (Sintel): 0.881
 ==== Blair ====
@@ Line 172: / Line 186: @@
 === Newspeak ===
-In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with basic 11-limit orwell at [[31edo]].
+In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with undecimal orwell at [[31edo]].
 Subgroup: 2.3.5.7.11
@@ Line 228: / Line 242: @@
 == Triwell ==
-Triwell may be described as the {{nowrap| 31 & 159 }} temperament. It slices orwell major sixth ~128/75 into three generators, nine of which give the 5th harmonic. Its ploidacot is 15-sheared-21-cot.
+Triwell tempers out the gamelisma, [[1029/1024]], and the triwellisma, [[235298/234375]]. It may be described as the {{nowrap| 31 & 159 }} temperament. It slices orwell's generator plus two octaves into three generators, and seven generators octave reduced make a ~8/7, which is the generator of [[slendric]]. Its ploidacot is 15-sheared-21-cot.
 [[Subgroup]]: 2.3.5.7
@@ Line 263: / Line 277: @@
 == Quadrawell ==
-Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. Its ploidacot is 22-sheared-28-cot.
+Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. It can also be viewed as [[2.5.7|2.5.7-subgroup]] [[mothra]] with a different mapping of prime [[3/1|3]]. Its ploidacot is 22-sheared-28-cot.
 [[Subgroup]]: 2.3.5.7
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 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Semicomma family| ]] <!-- main article -->
 [[Category:Rank 2]]
 [[Category:Orson]]
 [[Category:Orwell]]