Semaphore and godzilla: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = Semaphore and godzilla

| de = Semiphor, Semaphor, Godzilla

Line 12:

| 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:

| 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]].

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| 9/7

| 945.028

| ~~2/3-comma~~

|

|-

|

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| 3/2

| 950.978

| ~~1/2-comma~~

|

|-

|

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| 951.405

|

|-

~~| [[29edo|23\29]]~~

|

~~| 951.724~~

|

|-

~~| [[34edo|27\34]]~~

|

~~| 952.941~~

|

|-

| [[5edo|4\5]]

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| 968.826

|

|-

~~| [[6edo|5\6]]~~

|

~~| 1000.000~~

|

|}

<nowiki/>* Besides the octave

@@ Line 1: / Line 1: @@
-{{interwiki
+{{Interwiki
 | en = Semaphore and godzilla
 | de = Semiphor, Semaphor, Godzilla
@@ Line 12: / Line 12: @@
 | 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]].
@@ Line 255: / Line 255: @@
 | 9/7
 | 945.028
-| 2/3-comma
+|
 |-
 |
@@ Line 305: / Line 305: @@
 | 3/2
 | 950.978
-| 1/2-comma
+|
 |-
 |
@@ Line 311: / Line 311: @@
 | 951.405
 |
-|-
-| [[29edo|23\29]]
-|
-| 951.724
-|
-|-
-| [[34edo|27\34]]
-|
-| 952.941
-|
 |-
 | [[5edo|4\5]]
@@ Line 331: / Line 321: @@
 | 968.826
 |
-|-
-| [[6edo|5\6]]
-|
-| 1000.000
-|
 |}
 <nowiki/>* Besides the octave