Semaphore and godzilla: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = Semaphore and godzilla

| de = Semiphor, Semaphor, Godzilla

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| Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.13

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

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

| Mapping = 1; 2 8 1 11

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

| Generators = 7/4

~~| Generator~~ = 7/4

| Generators tuning = 948.0

| ~~Generator~~ tuning = ~~947~~.8

| Optimization method = CWE

| Pergen = (P8, P4/2)

| Color name = Zozoti

| MOS scales = [[4L 1s]], [[5L 4s]], [[5L 9s]], [[5L 14s]]

| Odd limit 1 = 7 | Mistuning 1 = 20.5 | Complexity 1 = 9

| Odd limit 1 = 9 | Mistuning 1 = 20.5 | Complexity 1 = 9

| Odd limit 2 = ~~(L7~~.13) 15 | Mistuning 2 = 20.5 | Complexity 2 = 19

| 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]].

~~See~~ [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]] ~~for technical data~~.

For technical information, see [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]]. For a discussion on 11- and 13-limit extensions, see [[Godzilla extensions]].

== Interval chains ==

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| CWE: ~7/4 = 947.8216{{c}}

| POTE: ~7/4 = 947.3650{{c}}

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings

|-

! rowspan="2" |

! colspan="3" | Euclidean

|-

! Constrained

! Constrained & skewed

! Destretched

|-

! Tenney

| CTE: ~7/4 = 948.9311{{c}}

| CWE: ~7/4 = 948.0037{{c}}

| POTE: ~7/4 = 947.5708{{c}}

|}

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{| class="wikitable center-all left-4"

|-

! Edo generator

! Edo generator

! [[Eigenmonzo|Unchanged interval (eigenmonzo)]]*

! [[Eigenmonzo|Unchanged interval (eigenmonzo)]]*

! Generator (¢)

! Comments

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|

| 947.368

| Lower bound of no-11 13-odd-limit diamond monotone No-11 15-odd-limit diamond monotone (singleton)

| Lower bound of {{nowrap|no-11}} 13-odd-limit diamond monotone {{nowrap|No-11}} 15-odd-limit diamond monotone (singleton)

|-

|

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| 5/4

| 948.289

|

| 7-, 9-odd-limit, {{nowrap|no-11}} 13- and 15-odd-limit minimax

|-

|

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|

| 960.000

| Upper bound of 7-, 9-odd-limit, ~~ ~~and no-11 13-odd-limit diamond monotone

| Upper bound of 7-, 9-odd-limit, and {{nowrap|no-11}} 13-odd-limit diamond monotone

|-

|

@@ Line 1: / Line 1: @@
-{{interwiki
+{{Interwiki
 | en = Semaphore and godzilla
 | de = Semiphor, Semaphor, Godzilla
@@ Line 9: / Line 9: @@
 | 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)
+| Edo join 1 = 5 | Edo join 2 = 19
 | Mapping = 1; 2 8 1 11
-| Edo join 1 = 5 | Edo join 2 = 19
+| Generators = 7/4
-| Generator = 7/4
+| Generators tuning = 948.0
-| Generator tuning = 947.8
 | Optimization method = CWE
 | Pergen = (P8, P4/2)
 | Color name = Zozoti
 | MOS scales = [[4L&nbsp;1s]], [[5L&nbsp;4s]], [[5L&nbsp;9s]], [[5L&nbsp;14s]]
-| Odd limit 1 = 7 | Mistuning 1 = 20.5 | Complexity 1 = 9
+| Odd limit 1 = 9 | Mistuning 1 = 20.5 | Complexity 1 = 9
-| Odd limit 2 = (L7.13) 15 | Mistuning 2 = 20.5 | Complexity 2 = 19
+| 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]].
-See [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]] for technical data.
+For technical information, see [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]]. For a discussion on 11- and 13-limit extensions, see [[Godzilla extensions]].
 == Interval chains ==
@@ Line 211: / Line 211: @@
 | CWE: ~7/4 = 947.8216{{c}}
 | POTE: ~7/4 = 947.3650{{c}}
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~7/4 = 948.9311{{c}}
+| CWE: ~7/4 = 948.0037{{c}}
+| POTE: ~7/4 = 947.5708{{c}}
 |}
@@ Line 216: / Line 232: @@
 {| class="wikitable center-all left-4"
 |-
-! Edo<br>generator
+! Edo <br>generator
-! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
+! [[Eigenmonzo|Unchanged interval <br>(eigenmonzo)]]*
 ! Generator (¢)
 ! Comments
@@ Line 254: / Line 270: @@
 |
 | 947.368
-| Lower bound of no-11 13-odd-limit diamond monotone<br>No-11 15-odd-limit diamond monotone (singleton)
+| Lower bound of {{nowrap|no-11}} 13-odd-limit diamond monotone <br>{{nowrap|No-11}} 15-odd-limit diamond monotone (singleton)
 |-
 |
@@ Line 269: / Line 285: @@
 | 5/4
 | 948.289
-|
+| 7-, 9-odd-limit, {{nowrap|no-11}} 13- and 15-odd-limit minimax
 |-
 |
@@ Line 299: / Line 315: @@
 |
 | 960.000
-| Upper bound of 7-, 9-odd-limit, <br>and no-11 13-odd-limit diamond monotone
+| Upper bound of 7-, 9-odd-limit, and {{nowrap|no-11}} 13-odd-limit diamond monotone
 |-
 |