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Semaphore and godzilla: Difference between revisions

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{{interwiki
{{interwiki
| en = Semaphore and godzilla
| de = Semiphor, Semaphor, Godzilla
| de = Semiphor, Semaphor, Godzilla
| en = Semaphore and Godzilla
| es =  
| es =  
| ja =  
| ja =  
}}
}}
'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[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."
{{Infobox regtemp
| 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)
| Edo join 1 = 5 | Edo join 2 = 19
| Mapping = 1; 2 8 1 11
| Generators = 7/4
| Generators 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 = 9 | Mistuning 1 = 20.5 | Complexity 1 = 9
| 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".


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'''. 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]].
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.  


See [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]] for technical data.  
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]].
 
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 ==
== Interval chains ==
Line 77: Line 94:


=== 5-note (proper) ===
=== 5-note (proper) ===
{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! Small ("minor") interval
! Small ("minor") interval
| 198.46
| 202.8
| 448.85
| 452.1
| 699.23
| 701.4
| 949.62
| 950.7
|-
|-
! [[JI|JI]] intervals represented
! [[JI]] intervals represented
| 9/8
| 9/8
| 9/7~13/10
| 9/7~13/10
| 3/2
| 3/2
| 12/7~7/4~26/15
| 7/4~12/7
|-
|-
! Large ("major") interval
! Large ("major") interval
| 250.38
| 249.3
| 500.77
| 498.6
| 751.15
| 747.9
| 1001.54
| 997.2
|-
|-
! JI intervals represented
! JI intervals represented
| 8/7~7/6~15/13
| 7/6~8/7
| 4/3
| 4/3
| 14/9~20/13
| 14/9~20/13
Line 105: Line 122:


=== 9-note (improper) ===
=== 9-note (improper) ===
{{Main|5L 4s}}
{{Main| 5L 4s }}
{| class="wikitable"
 
{| class="wikitable center-all"
|-
|-
! Small ("minor") interval
! Small ("minor") interval
| 63.17
| 60.0
| 252.63
| 252.0
| 315.81
| 312.0
| 505.27
| 504.0
| 568.44
| 564.0
| 757.90
| 756.0
| 821.08
| 816.0
| 1010.54
| 1008.0
|-
|-
! JI intervals represented
! JI intervals represented
|  
|  
| 8/7~7/6~15/13
| 7/6~8/7
| 6/5
| 6/5
| 4/3
| 4/3
Line 126: Line 144:
| 14/9~20/13
| 14/9~20/13
| 8/5~13/8
| 8/5~13/8
| 16/9~9/5
| 9/5~16/9
|-
|-
! Large ("major") interval
! Large ("major") interval
| 189.46
| 192.0
| 378.92
| 384.0
| 442.10
| 444.0
| 631.56
| 636.0
| 694.73
| 696.0
| 884.19
| 888.0
| 947.37
| 948.0
| 1136.83
| 1140.0
|-
|-
! JI intervals represented
! JI intervals represented
| 10/9~9/8
| 9/8~10/9
| 5/4
| 5/4
| 9/7~13/10
| 9/7~13/10
Line 145: Line 163:
| 3/2
| 3/2
| 5/3
| 5/3
| 12/7~7/4~26/15
| 7/4~12/7
|  
|  
|}
|}
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== Tunings ==
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.7-subgroup prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.7-subgroup norm-based tunings
|-
|-
! rowspan="2" |  
! rowspan="2" |  
Line 180: Line 198:


{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
|-
! rowspan="2" |  
! rowspan="2" |  
Line 190: Line 208:
|-
|-
! Tenney
! Tenney
| CTE: ~3/2 = 948.7959{{c}}
| CTE: ~7/4 = 948.7959{{c}}
| CWE: ~3/2 = 947.8216{{c}}
| CWE: ~7/4 = 947.8216{{c}}
| POTE: ~3/2 = 947.3650{{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}}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo <br>generator
! [[Eigenmonzo|Unchanged interval <br>(eigenmonzo)]]*
! Generator (¢)
! Comments
|-
|
| 7/6
| 933.129
|
|-
| [[9edo|7\9]]
|
| 933.333
| 9cff val
|-
| [[14edo|11\14]]
|
| 942.857
| 14cf val, lower bound of 7- and 9-odd-limit diamond monotone
|-
|
| 9/7
| 945.028
|
|-
|
| 7/5
| 945.355
|
|-
|
| 13/7
| 947.170
|
|-
| [[19edo|15\19]]
|
| 947.368
| Lower bound of {{nowrap|no-11}} 13-odd-limit diamond monotone <br>{{nowrap|No-11}} 15-odd-limit diamond monotone (singleton)
|-
|
| 5/3
| 947.393
|
|-
|
| 13/9
| 948.088
|
|-
|
| 5/4
| 948.289
| 7-, 9-odd-limit, {{nowrap|no-11}} 13- and 15-odd-limit minimax
|-
|
| 13/12
| 948.730
|
|-
|
| 13/8
| 949.139
|
|-
| [[24edo|19\24]]
|
| 950.000
|
|-
|
| 3/2
| 950.978
|
|-
|
| 13/10
| 951.405
|
|-
| [[5edo|4\5]]
|
| 960.000
| Upper bound of 7-, 9-odd-limit, and {{nowrap|no-11}} 13-odd-limit diamond monotone
|-
|
| 7/4
| 968.826
|
|}
|}
<nowiki/>* Besides the octave


== Music ==
== Music ==
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; [[Starshine]]
; [[Starshine]]
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – Semaphore[9] in 19edo
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – in Semaphore[9], 19edo tuning


== See also ==
== See also ==
Retrieved from "https://en.xen.wiki/w/Semaphore_and_godzilla"