Semaphore and godzilla: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = Semaphore and godzilla

| de = Semiphor, Semaphor, Godzilla

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| Title = {{nowrap|Semaphore; Godzilla}}

| Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.13

| Comma basis = [[49/48]] (2.3.7); <br> [[49/48]], [[81/80]] (2.3.5.7); <br> [[49/48]], [[81/80]], [[91/90]] (L7.13)

| Comma basis = [[49/48]] (2.3.7); <br> [[49/48]], [[81/80]] (2.3.5.7); <br> [[49/48]], [[81/80]], [[91/90]] (2.3.5.7.13)

| Edo join 1 = 5 | Edo join 2 = 19

| Mapping = 1; 2 8 1 11

| Generators = 7/4

| Generators tuning = ~~947~~.8

| Generators tuning = 948.0

| Optimization method = CWE

| Pergen = (P8, P4/2)

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| Odd limit 2 = 2.3.5.7.13 15 | Mistuning 2 = 20.5 | Complexity 2 = 14

}}

'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] 2.3.7-[[subgroup]] [[regular temperament|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".

'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] [[2.3.7 subgroup|2.3.7-subgroup]] [[regular temperament|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".

If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[~~Meantone~~ family #Extensions|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.

If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[meantone family #Extensions|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.

A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].

@@ Line 1: / Line 1: @@
-{{interwiki
+{{Interwiki
 | en = Semaphore and godzilla
 | de = Semiphor, Semaphor, Godzilla
@@ Line 8: / Line 8: @@
 | Title = {{nowrap|Semaphore; Godzilla}}
 | Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.13
-| Comma basis = [[49/48]] (2.3.7); <br> [[49/48]], [[81/80]] (2.3.5.7); <br> [[49/48]], [[81/80]], [[91/90]] (L7.13)
+| Comma basis = [[49/48]] (2.3.7); <br> [[49/48]], [[81/80]] (2.3.5.7); <br> [[49/48]], [[81/80]], [[91/90]] (2.3.5.7.13)
 | Edo join 1 = 5 | Edo join 2 = 19
 | Mapping = 1; 2 8 1 11
 | Generators = 7/4
-| Generators tuning = 947.8
+| Generators tuning = 948.0
 | Optimization method = CWE
 | Pergen = (P8, P4/2)
@@ Line 20: / Line 20: @@
 | Odd limit 2 = 2.3.5.7.13 15 | Mistuning 2 = 20.5 | Complexity 2 = 14
 }}
-'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] 2.3.7-[[subgroup]] [[regular temperament|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".
+'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] [[2.3.7 subgroup|2.3.7-subgroup]] [[regular temperament|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".
-If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[Meantone family #Extensions|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.
+If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[meantone family #Extensions|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.
 A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].