Xenharmonic Wiki

Semaphore and godzilla: Difference between revisions

← Older edit
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,636 edits
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
No edit summary
Tags: Mobile edit Mobile web edit
 
(63 intermediate revisions by 12 users not shown)
Line 1: Line 1:
<span style="display: block; text-align: right;">[[de:Semiphor,_Semaphor,_Godzilla]]</span>
{{interwiki
| en = Semaphore and godzilla
| de = Semiphor, Semaphor, Godzilla
| es =
| ja =
}}
{{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".


Semaphore, of the [[Semiphore_family|Semiphore family]], is characterized by the vanishing of [[49/48|49/48]], so the generator represents [[8/7|8/7]] and [[7/6|7/6]] equally. This results in a very low [[complexity|complexity]] 2.3.7 [[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|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 5 is mapped at all, it can be sensibly mapped to -8 [[generator|generator]]s by [[tempering_out|tempering out]] [[81/80|81/80]], making it a [[Meantone_family#Godzilla|meantone temperament]]. This temperament is called [[Meantone_family#Godzilla|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]].


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


===Semaphore===
== Interval chains ==
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.


{| class="wikitable"
=== Semaphore ===
{| 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"
|-
! # !! 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
|-
| 13 || 324.0 || 39/32
|-
| 14 || 72.1 || 25/24, 50/49
|}
<nowiki/>* In 2.3.5.7.13-subgroup CWE tuning, octave reduced
 
== Scales ==
Scala files:
* [[Semaphore5]]
* [[Semaphore9]]
* [[Semaphore14]]


{| class="wikitable"
=== 5-note (proper) ===
{| class="wikitable center-all"
|-
! Small ("minor") interval
| 202.8
| 452.1
| 701.4
| 950.7
|-
! [[JI]] intervals represented
| 9/8
| 9/7~13/10
| 3/2
| 7/4~12/7
|-
|-
| | 378.92
! Large ("major") interval
| | 631.56
| 249.3
| | 884.19
| 498.6
| | 1136.83
| 747.9
| | 189.46
| 997.2
| | 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
! JI intervals represented
| | [[10/7|10/7]]~13/9
| 7/6~8/7
| | [[5/3|5/3]]
| 4/3
| | 27/14
| 14/9~20/13
| | 10/9~9/8
| 16/9
| | 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
|}
|}


==MOSes==
=== 9-note (improper) ===
{{Main| 5L 4s }}


===5-note (proper)===
{| class="wikitable center-all"
|-
! Small ("minor") interval
| 60.0
| 252.0
| 312.0
| 504.0
| 564.0
| 756.0
| 816.0
| 1008.0
|-
! JI intervals represented
|
| 7/6~8/7
| 6/5
| 4/3
| 7/5~18/13
| 14/9~20/13
| 8/5~13/8
| 9/5~16/9
|-
! Large ("major") interval
| 192.0
| 384.0
| 444.0
| 636.0
| 696.0
| 888.0
| 948.0
| 1140.0
|-
! JI intervals represented
| 9/8~10/9
| 5/4
| 9/7~13/10
| 10/7~13/9
| 3/2
| 5/3
| 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:
* Meantone pentic (5 3 5 3 3)
* Altered diatonic I (3 4 3 1 3 4 1)
* Altered diatonic II (3 4 3 1 4 3 1)
* Altered diatonic III (4 3 3 1 4 3 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 pentic scale, but in a different way than diatonic scales do.


{| class="wikitable"
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
|-
|-
| | Small ("minor") interval
! Tenney
| | 198.46
| CTE: ~7/4 = 952.2948{{c}}
| | 448.85
| CWE: ~7/4 = 950.6890{{c}}
| | 699.23
| POTE: ~7/4 = 949.6154{{c}}
| | 949.62
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
|-
| | [[JI|JI]] intervals represented
! rowspan="2" |  
| | 9/8
! colspan="3" | Euclidean
| | 9/7~13/10
| | 3/2
| | 12/7~7/4~26/15
|-
|-
| | Large ("major") interval
! Constrained
| | 250.38
! Constrained & skewed
| | 500.77
! Destretched
| | 751.15
| | 1001.54
|-
|-
| | JI intervals represented
! Tenney
| | 8/7~7/6~15/13
| CTE: ~7/4 = 948.7959{{c}}
| | 4/3
| CWE: ~7/4 = 947.8216{{c}}
| | 14/9~20/13
| POTE: ~7/4 = 947.3650{{c}}
| | 16/9
|}
|}


===9-note (improper)===
{| 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}}
|}


{| class="wikitable"
=== 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
|-
|-
| | Small ("minor") interval
|  
| | 63.17
| 13/12
| | 252.63
| 948.730
| | 315.81
|  
| | 505.27
| | 568.44
| | 757.90
| | 821.08
| | 1010.54
|-
|-
| | JI intervals represented
|  
| |
| 13/8
| | 8/7~7/6~15/13
| 949.139
| | 6/5
|  
| | 4/3
| | 7/5~18/13
| | 14/9~20/13
| | 8/5~13/8
| | 16/9~9/5
|-
|-
| | Large ("major") interval
| [[24edo|19\24]]
| | 189.46
|  
| | 378.92
| 950.000
| | 442.10
|  
| | 631.56
| | 694.73
| | 884.19
| | 947.37
| | 1136.83
|-
|-
| | JI intervals represented
|  
| | 10/9~9/8
| 3/2
| | 5/4
| 950.978
| | 9/7~13/10
|  
| | 10/7~13/9
|-
| | 3/2
|  
| | 5/3
| 13/10
| | 12/7~7/4~26/15
| 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


In 19edo, godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
== Music ==
 
; [[Cameron Bobro]]
<ul><li>Meantone pentatonic (5 3 5 3 3).</li><li>Altered diatonic I (3 4 3 1 3 4 1)</li><li>Altered diatonic II (3 4 3 1 4 3 1)</li><li>Altered diatonic III (4 3 3 1 4 3 1)</li><li>Altered diatonic IV (3 3 4 1 3 4 1)</li></ul>
* [https://web.archive.org/web/20201127014130/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3 ''Godzilla Example'']


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.
; [[Igliashon Jones]]
* [http://tinyurl.com/4uyumk9 "Change is on the Wind"]{{dead link}} in Godzilla[9]


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.
; [[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'']


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 [[biome|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).
; [[Starshine]]
====Modal harmony of Godzilla[9]====
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – in Semaphore[9], 19edo tuning
*221212121
*212212121
*212122121
*212121221
*212121212
*122121212
*121221212
*121212212
*121212122


=Music=
== See also ==
[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] by [https://soundcloud.com/lois-lancaster/s-no-contratempo Roncevaux (Löis Lancaster)]
* [[Diasem]], a [[maximum variety|max-variety-3]] JI [[detempering]] of semaphore
* [[Semaphore–chromatic equivalence continuum]]


[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] by[https://soundcloud.com/lois-lancaster/o-que-a-gente-quer-em-19-tet Roncevaux]      [[Category:5-tone]]
[[Category:Semaphore| ]] <!-- main article -->
[[Category:9-tone]]
[[Category:Godzilla]] <!-- main article -->
[[Category:godzilla]]
[[Category:Rank-2 temperaments]]
[[Category:mos]]
[[Category:Semaphoresmic clan]]
[[Category:temperament]]
[[Category:Meantone family]]
[[Category:Sensamagic clan]]
Retrieved from "https://en.xen.wiki/w/Semaphore_and_godzilla"