Xenharmonic Wiki

Semaphore and godzilla: Difference between revisions

← Older edit
VisualWikitext
Cleanup
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
No edit summary
Tags: Mobile edit Mobile web edit
 
(29 intermediate revisions by 7 users not shown)
Line 1: Line 1:
{{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 [[slendro 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'''. 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 &minus;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]].
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 [[Slendro clan #Semaphore]] and [[Slendro 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 ==
== Interval chains ==
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.
=== Semaphore ===
=== Semaphore ===
{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
| 198.46
! # !! Cents* !! Approximate ratios
| 448.85
| 699.23
| 949.62
| 0
| 250.38
| 500.77
| 751.15
| 1001.54
|-
|-
| [[9/8|9/8]]
| 0 || 0.0 || '''1/1'''
| [[9/7|9/7]]
|-
| [[3/2|3/2]]
| 1 || 950.7 || '''7/4''', 12/7
| 12/7~7/4
|-
| [[1/1|1/1]]
| 2 || 701.4 || '''3/2'''
| 8/7~7/6
|-
| [[4/3|4/3]]
| 3 || 452.1 || 9/7, 21/16
| [[14/9|14/9]]
|-
| [[16/9|16/9]]
| 4 || 202.8 || '''9/8'''
|-
| 5 || 1153.4 || 27/14, 63/32
|}
|}
<nowiki/>* In 2.3.7-subgroup CWE tuning, octave reduced


=== Godzilla ===
=== Godzilla ===
 
{| class="wikitable center-1 right-2"
{| class="wikitable"
|-
! # !! Cents* !! Approximate ratios
|-
| 0 || 0.0 || '''1/1'''
|-
| 1 || 948.0 || '''7/4''', 12/7, 26/15
|-
| 2 || 696.0 || '''3/2'''
|-
| 3 || 444.0 || 9/7, 13/10, 21/16
|-
| 4 || 192.0 || '''9/8''', 10/9
|-
| 5 || 1140.0 || 27/14, 39/20, 40/21, 52/27, 63/32
|-
| 6 || 888.0 || 5/3
|-
| 7 || 636.0 || 10/7, 13/9
|-
| 8 || 384.0 || '''5/4'''
|-
| 9 || 132.0 || 13/12, 15/14
|-
| 10 || 1080.0 || 13/7, 15/8
|-
| 11 || 828.0 || '''13/8'''
|-
| 12 || 576.0 || 25/18, 39/28, 45/32
|-
|-
| 378.92
| 13 || 324.0 || 39/32
| 631.56
| 884.19
| 1136.83
| 189.46
| 442.10
| 694.73
| 947.37
| 0
| 252.63
| 505.27
| 757.90
| 1010.54
| 63.17
| 315.81
| 568.44
| 821.08
|-
|-
| [[5/4|5/4]]~16/13
| 14 || 72.1 || 25/24, 50/49
| [[10/7|10/7]]~13/9
| [[5/3|5/3]]
| 27/14
| 10/9~9/8
| 9/7~13/10
| 3/2
| 12/7~7/4~26/15
| 1/1
| 8/7~7/6~15/13
| 4/3
| 14/9~20/13
| 16/9~9/5
| 28/27~21/20
| [[6/5|6/5]]
| [[7/5|7/5]]~18/13
| [[8/5|8/5]]~13/8
|}
|}
<nowiki/>* In 2.3.5.7.13-subgroup CWE tuning, octave reduced


== Scales ==
== Scales ==
Scala files:  
Scala files:  
* [[semaphore5]]
* [[Semaphore5]]
* [[semaphore9]]
* [[Semaphore9]]
* [[semaphore14]]
* [[Semaphore14]]


=== 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 112: 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 133: 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 152: Line 163:
| 3/2
| 3/2
| 5/3
| 5/3
| 12/7~7/4~26/15
| 7/4~12/7
|  
|  
|}
|}


In 19edo, godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
In 19edo, Godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
* Meantone pentatonic (5 3 5 3 3)
* Meantone pentic (5 3 5 3 3)
* Altered diatonic I (3 4 3 1 3 4 1)
* Altered diatonic I (3 4 3 1 3 4 1)
* Altered diatonic II (3 4 3 1 4 3 1)
* Altered diatonic II (3 4 3 1 4 3 1)
Line 163: Line 174:
* Altered diatonic IV (3 3 4 1 3 4 1)
* Altered diatonic IV (3 3 4 1 3 4 1)


It does not, however, contain the ordinary diatonic scale. Godzilla[9] thus expands on the pentatonic scale, but in a different way than diatonic scales do.
It does not, however, contain the ordinary diatonic scale. Godzilla[9] thus expands on the pentic scale, but in a different way than diatonic scales do.
 
The four heptatonic subsets can be regarded as chromatic alterations of the diatonic scale, or alternatively as variants of Archytas' septimal diatonic scale, but with a greatly exaggerated difference between the two different whole tone sizes. All five of these subsets are very expressive melodically. Godzilla[9] combines all of these and is expressive in its own right; it could even be thought of as 19edo's answer to the well-loved Supra[7] diatonic scale of [[17edo]], as both are improper and made up of whole-tones and third-tones.
 
Like Supra[7], Godzilla[9] is well stocked with subminor and supermajor triads; in this case they can be viewed as 6:7:9 and 10:13:15 since 19edo is a [[The Biosphere|biome]] temperament. Godzilla[9] has only ''one'' each of the more stable 5-limit major and minor triads, which might be considered a drawback, but could also be considered a strength for helping to establish a clearer tonal center (since all triads other than the tonic have tension in them).
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.7-subgroup norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~7/4 = 952.2948{{c}}
| CWE: ~7/4 = 950.6890{{c}}
| POTE: ~7/4 = 949.6154{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~7/4 = 948.7959{{c}}
| CWE: ~7/4 = 947.8216{{c}}
| POTE: ~7/4 = 947.3650{{c}}
|}


The four heptatonic subsets can be regarded as chromatic alterations of the diatonic scale, or alternatively as variants of Archytas' septimal diatonic scale, but with a greatly exaggerated difference between the two different whole tone sizes. All five of these subsets are very expressive melodically. Godzilla[9] combines all of these and is expressive in its own right; it could even be thought of as 19edo's answer to the well-loved supra[7] diatonic scale of [[17edo|17edo]], as both are improper and made up of whole-tones and third-tones.
{| 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}}
|}


Like supra[7], godzilla[9] is well stocked with subminor and supermajor triads; in this case they can be viewed as 6:7:9 and 10:13:15 since 19edo is a [[The_Biosphere|biome]] temperament. Godzilla[9] has only ''one'' each of the more stable 5-limit major and minor triads, which might be considered a drawback, but could also be considered a strength for helping to establish a clearer tonal center (since all triads other than the tonic have tension in them).
=== 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 ==
'''[[Cameron Bobro]]'''
; [[Cameron Bobro]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3 Godzilla Example]
* [https://web.archive.org/web/20201127014130/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3 ''Godzilla Example'']
'''[[Igliashon Jones]]'''
 
* [http://tinyurl.com/4uyumk9 "Change is on the Wind"] in Godzilla[9]
; [[Igliashon Jones]]
'''[[Roncevaux]]'''
* [http://tinyurl.com/4uyumk9 "Change is on the Wind"]{{dead link}} in Godzilla[9]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/S__no_Contratempo_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 Só no Contratempo]
 
* [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/__O_que_a_gente_quer__em_19_TET__temperamento_Godzilla__9___by_Roncevaux.mp3 O que a gente quer]
; [[Roncevaux]]
* [https://web.archive.org/web/20201127013241/http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/S__no_Contratempo_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 ''Só no Contratempo'']
* [https://web.archive.org/web/20201127013653/http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/__O_que_a_gente_quer__em_19_TET__temperamento_Godzilla__9___by_Roncevaux.mp3 ''O que a gente quer'']
 
; [[Starshine]]
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – in Semaphore[9], 19edo tuning


== See also ==
== See also ==
* [[Diasem]], a [[maximum variety|max-variety-3]] JI [[detempering]] of semaphore
* [[Diasem]], a [[maximum variety|max-variety-3]] JI [[detempering]] of semaphore
* [[Semaphore–chromatic equivalence continuum]]


[[Category:Temperaments]]
[[Category:Semaphore| ]] <!-- main article -->
[[Category:Semaphore]]
[[Category:Godzilla]] <!-- main article -->
[[Category:Godzilla]]
[[Category:Rank-2 temperaments]]
[[Category:Slendro]]
[[Category:Semaphoresmic clan]]
[[Category:5-tone scales]]
[[Category:Meantone family]]
[[Category:9-tone scales]]
[[Category:Sensamagic clan]]
[[Category:MOS scales]]
Retrieved from "https://en.xen.wiki/w/Semaphore_and_godzilla"