Semaphore and godzilla: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>hstraub
**Imported revision 610203435 - Original comment: **
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
No edit summary
Tags: Mobile edit Mobile web edit
 
(70 intermediate revisions by 15 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = Semaphore and godzilla
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-04-04 04:46:43 UTC</tt>.<br>
| de = Semiphor, Semaphor, Godzilla
: The original revision id was <tt>610203435</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
}}
<h4>Original Wikitext content:</h4>
{{Infobox regtemp
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Semiphor, Semaphor, Godzilla|Deutsch]]
| Title = {{nowrap|Semaphore; Godzilla}}
&lt;/span&gt;
| Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.13
Semaphore, of the [[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]] 2.3.7 [[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."
| 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 5 is mapped at all, it can be sensibly mapped to -8 [[generator]]s by [[tempering out]] [[81_80|81/80]], making it a [[Meantone family#Godzilla|meantone temperament]]. This temperament is called [[Meantone family#Godzilla|godzilla]].
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.  


==Interval chains==
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]].
===Semaphore===
|| 198.46 || 448.85 || 699.23 || 949.62 || 0 || 250.38 || 500.77 || 751.15 || 1001.54 ||
|| [[9_8|9/8]] || [[9_7|9/7]] || [[3_2|3/2]] || 12/7~7/4 || [[1_1|1/1]] || 8/7~7/6 || [[4_3|4/3]] || [[14_9|14/9]] || [[16_9|16/9]] ||
===Godzilla===
|| 378.92 || 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]] || [[10_7|10/7]] || [[5_3|5/3]] || 27/14 || 10/9~9/8 || 9/7 || 3/2 || 12/7~7/4 || 1/1 || 8/7~7/6 || 4/3 || 14/9 || 16/9~9/5 || 28/27~21/20 || [[6_5|6/5]] || [[7_5|7/5]] || [[8_5|8/5]] ||
==MOSes==
===5-note (proper)===
|| Small ("minor") interval || 198.46 || 448.85 || 699.23 || 949.62 ||
|| [[JI]] intervals represented || 9/8 || 9/7 || 3/2 || 12/7~7/4 ||
|| Large ("major") interval || 250.38 || 500.77 || 751.15 || 1001.54 ||
|| JI intervals represented || 8/7~7/6 || 4/3 || 14/9 || 16/9 ||
===9-note (improper)===
|| Small ("minor") interval || 63.17 || 252.63 || 315.81 || 505.27 || 568.44 || 757.90 || 821.08 || 1010.54 ||
|| JI intervals represented ||  || 8/7~7/6 || 6/5 || 4/3 || 7/5 || 14/9 || 8/5 || 16/9~9/5 ||
|| Large ("major") interval || 189.46 || 378.92 || 442.10 || 631.56 || 694.73 || 884.19 || 947.37 || 1136.83 ||
|| JI intervals represented || 10/9~9/8 || 5/4 || 9/7 || 10/7 || 3/2 || 5/3 || 12/7~7/4 ||  ||


In 19edo, godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
For technical information, see [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]]. For a discussion on 11- and 13-limit extensions, see [[Godzilla extensions]].


* Meantone pentatonic (5 3 5 3 3).
== Interval chains ==
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.
 
=== Semaphore ===
{| class="wikitable center-1 right-2"
|-
! # !! Cents* !! Approximate ratios
|-
| 0 || 0.0 || '''1/1'''
|-
| 1 || 950.7 || '''7/4''', 12/7
|-
| 2 || 701.4 || '''3/2'''
|-
| 3 || 452.1 || 9/7, 21/16
|-
| 4 || 202.8 || '''9/8'''
|-
| 5 || 1153.4 || 27/14, 63/32
|}
<nowiki/>* In 2.3.7-subgroup CWE tuning, octave reduced
 
=== 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]]
 
=== 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
|-
! Large ("major") interval
| 249.3
| 498.6
| 747.9
| 997.2
|-
! JI intervals represented
| 7/6~8/7
| 4/3
| 14/9~20/13
| 16/9
|}
 
=== 9-note (improper) ===
{{Main| 5L 4s }}
 
{| 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 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 39: 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.


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).


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]] 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}}
|}


=Music=
{| class="wikitable mw-collapsible mw-collapsed"
[[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)]]
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
[[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]]</pre></div>
|-
<h4>Original HTML content:</h4>
! rowspan="2" |
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Semaphore and Godzilla&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Semiphor%2C%20Semaphor%2C%20Godzilla"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
! colspan="3" | Euclidean
&lt;/span&gt;&lt;br /&gt;
|-
Semaphore, of the &lt;a class="wiki_link" href="/Semiphore%20family"&gt;Semiphore family&lt;/a&gt;, is characterized by the vanishing of &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, so the generator represents &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt; and &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; equally. This results in a very low &lt;a class="wiki_link" href="/complexity"&gt;complexity&lt;/a&gt; 2.3.7 &lt;a class="wiki_link" href="/temperament"&gt;temperament&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. Semaphore is a play on the words &amp;quot;semi-&amp;quot; and &amp;quot;fourth.&amp;quot;&lt;br /&gt;
! Constrained
&lt;br /&gt;
! Constrained & skewed
If 5 is mapped at all, it can be sensibly mapped to -8 &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt;s by &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, making it a &lt;a class="wiki_link" href="/Meantone%20family#Godzilla"&gt;meantone temperament&lt;/a&gt;. This temperament is called &lt;a class="wiki_link" href="/Meantone%20family#Godzilla"&gt;godzilla&lt;/a&gt;.&lt;br /&gt;
! Destretched
&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Interval chains"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Interval chains&lt;/h2&gt;
! Tenney
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Interval chains-Semaphore"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Semaphore&lt;/h3&gt;
| CTE: ~7/4 = 948.7959{{c}}
| CWE: ~7/4 = 947.8216{{c}}
| POTE: ~7/4 = 947.3650{{c}}
|}


&lt;table class="wiki_table"&gt;
{| class="wikitable mw-collapsible mw-collapsed"
    &lt;tr&gt;
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings
        &lt;td&gt;198.46&lt;br /&gt;
|-
&lt;/td&gt;
! rowspan="2" |
        &lt;td&gt;448.85&lt;br /&gt;
! colspan="3" | Euclidean
&lt;/td&gt;
|-
        &lt;td&gt;699.23&lt;br /&gt;
! Constrained
&lt;/td&gt;
! Constrained & skewed
        &lt;td&gt;949.62&lt;br /&gt;
! Destretched
&lt;/td&gt;
|-
        &lt;td&gt;0&lt;br /&gt;
! Tenney
&lt;/td&gt;
| CTE: ~7/4 = 948.9311{{c}}
        &lt;td&gt;250.38&lt;br /&gt;
| CWE: ~7/4 = 948.0037{{c}}
&lt;/td&gt;
| POTE: ~7/4 = 947.5708{{c}}
        &lt;td&gt;500.77&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;751.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1001.54&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7~7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7~7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/16_9"&gt;16/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Interval chains-Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Godzilla&lt;/h3&gt;
=== 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


&lt;table class="wiki_table"&gt;
== Music ==
    &lt;tr&gt;
; [[Cameron Bobro]]
        &lt;td&gt;378.92&lt;br /&gt;
* [https://web.archive.org/web/20201127014130/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3 ''Godzilla Example'']
&lt;/td&gt;
        &lt;td&gt;631.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1136.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189.46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;442.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;694.73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;947.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;252.63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;505.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;757.90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1010.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;63.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315.81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;568.44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;821.08&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9~9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7~7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7~7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9~9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28/27~21/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-MOSes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;MOSes&lt;/h2&gt;
; [[Igliashon Jones]]
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-MOSes-5-note (proper)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;5-note (proper)&lt;/h3&gt;
* [http://tinyurl.com/4uyumk9 "Change is on the Wind"]{{dead link}} in Godzilla[9]


&lt;table class="wiki_table"&gt;
; [[Roncevaux]]
    &lt;tr&gt;
* [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'']
        &lt;td&gt;Small (&amp;quot;minor&amp;quot;) interval&lt;br /&gt;
* [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'']
&lt;/td&gt;
        &lt;td&gt;198.46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;448.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;699.23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;949.62&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/JI"&gt;JI&lt;/a&gt; intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7~7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Large (&amp;quot;major&amp;quot;) interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;250.38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;500.77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;751.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1001.54&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7~7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-MOSes-9-note (improper)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;9-note (improper)&lt;/h3&gt;
; [[Starshine]]
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – in Semaphore[9], 19edo tuning


&lt;table class="wiki_table"&gt;
== See also ==
    &lt;tr&gt;
* [[Diasem]], a [[maximum variety|max-variety-3]] JI [[detempering]] of semaphore
        &lt;td&gt;Small (&amp;quot;minor&amp;quot;) interval&lt;br /&gt;
* [[Semaphore–chromatic equivalence continuum]]
&lt;/td&gt;
        &lt;td&gt;63.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;252.63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315.81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;505.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;568.44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;757.90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;821.08&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1010.54&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7~7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9~9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Large (&amp;quot;major&amp;quot;) interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189.46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;442.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;631.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;694.73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;947.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1136.83&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9~9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7~7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[[Category:Semaphore| ]] <!-- main article -->
In 19edo, godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:&lt;br /&gt;
[[Category:Godzilla]] <!-- main article -->
&lt;br /&gt;
[[Category:Rank-2 temperaments]]
&lt;ul&gt;&lt;li&gt;Meantone pentatonic (5 3 5 3 3).&lt;/li&gt;&lt;li&gt;Altered diatonic I (3 4 3 1 3 4 1)&lt;/li&gt;&lt;li&gt;Altered diatonic II (3 4 3 1 4 3 1)&lt;/li&gt;&lt;li&gt;Altered diatonic III (4 3 3 1 4 3 1)&lt;/li&gt;&lt;li&gt;Altered diatonic IV (3 3 4 1 3 4 1)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
[[Category:Semaphoresmic clan]]
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.&lt;br /&gt;
[[Category:Meantone family]]
&lt;br /&gt;
[[Category:Sensamagic clan]]
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 &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, as both are improper and made up of whole-tones and third-tones.&lt;br /&gt;
&lt;br /&gt;
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 &lt;a class="wiki_link" href="/biome"&gt;biome&lt;/a&gt; temperament. Godzilla[9] has only &lt;em&gt;one&lt;/em&gt; 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).&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Music&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/S__no_Contratempo_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3" rel="nofollow"&gt;Só no Contratempo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="https://soundcloud.com/lois-lancaster/s-no-contratempo" rel="nofollow"&gt;Roncevaux (Löis Lancaster)&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/__O_que_a_gente_quer__em_19_TET__temperamento_Godzilla__9___by_Roncevaux.mp3" rel="nofollow"&gt;O que a gente quer&lt;/a&gt; by&lt;a class="wiki_link_ext" href="https://soundcloud.com/lois-lancaster/o-que-a-gente-quer-em-19-tet" rel="nofollow"&gt;Roncevaux&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 00:10, 23 May 2026

Semaphore; Godzilla
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)
Reduced mapping ⟨1; 2 8 1 11]
ET join 5 & 19
Generators (CWE) ~7/4 = 947.8 ¢
MOS scales 4L 1s, 5L 4s, 5L 9s, 5L 14s
Ploidacot alpha-dicot
Pergen (P8, P4/2)
Color name Zozoti
Minimax error 9-odd-limit: 20.5 ¢;
2.3.5.7.13 15-odd-limit: 20.5 ¢
Target scale size 9-odd-limit: 9 notes;
2.3.5.7.13 15-odd-limit: 14 notes

Semaphore, of the semaphoresmic clan, is characterized by 49/48 being 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 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 cents. Semaphore is a play on the words "semi-" and "fourth".

If the 5th harmonic's intervals are desired, 5/4 can be sensibly mapped to +8 generators by tempering out 81/80, making it a 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.

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

Interval chains

In the following tables, odd harmonics 1–13 and their inverses are in bold.

Semaphore

# Cents* Approximate ratios
0 0.0 1/1
1 950.7 7/4, 12/7
2 701.4 3/2
3 452.1 9/7, 21/16
4 202.8 9/8
5 1153.4 27/14, 63/32

* In 2.3.7-subgroup CWE tuning, octave reduced

Godzilla

# 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

* In 2.3.5.7.13-subgroup CWE tuning, octave reduced

Scales

Scala files:

5-note (proper)

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
Large ("major") interval 249.3 498.6 747.9 997.2
JI intervals represented 7/6~8/7 4/3 14/9~20/13 16/9

9-note (improper)

Main article: 5L 4s
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.

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 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

2.3.7-subgroup norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~7/4 = 952.2948 ¢ CWE: ~7/4 = 950.6890 ¢ POTE: ~7/4 = 949.6154 ¢
7-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~7/4 = 948.7959 ¢ CWE: ~7/4 = 947.8216 ¢ POTE: ~7/4 = 947.3650 ¢
2.3.5.7.13-subgroup norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~7/4 = 948.9311 ¢ CWE: ~7/4 = 948.0037 ¢ POTE: ~7/4 = 947.5708 ¢

Tuning spectrum

Edo
generator 		Unchanged interval
(eigenmonzo)* 		Generator (¢) Comments
7/6 933.129
7\9 933.333 9cff val
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
15\19 947.368 Lower bound of no-11 13-odd-limit diamond monotone
No-11 15-odd-limit diamond monotone (singleton)
5/3 947.393
13/9 948.088
5/4 948.289 7-, 9-odd-limit, no-11 13- and 15-odd-limit minimax
13/12 948.730
13/8 949.139
19\24 950.000
3/2 950.978
13/10 951.405
4\5 960.000 Upper bound of 7-, 9-odd-limit, and no-11 13-odd-limit diamond monotone
7/4 968.826

* Besides the octave

Music

Cameron Bobro
Igliashon Jones
Roncevaux
Starshine

See also

Retrieved from "https://en.xen.wiki/index.php?title=Semaphore_and_godzilla&oldid=230775"