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12L 5s: Difference between revisions

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{{Todo|review|inline=1|text=Adopt scale tree template, add note that mode names are tuning-specific (they only apply to specific tunings)}}{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro|Other Names=p-enharmonic}}
Temperaments supported by this scale include those under the [[Pythagorean tuning|Pythagorean]] and [[Schismatic family|schismic]] families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the [[chroma]].
Temperaments supported by this scale include those under the [[Pythagorean tuning|Pythagorean]] and [[Schismatic family|schismic]] families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the [[chroma]].


The [[leapday]]/[[leapweek]] version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).
The [[leapday]]/[[leapweek]] version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).


== Modes ==
== Scale properties ==
Mode names are borrowed from the [[Subaru scale]], proposed by [[Declan Paul Boushy]].
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Proposed tuning-specific names ===
[[Declan Paul Boushy]] has proposed names for these modes corresponding to step ratios [[Subaru scale|3:1]] and [[Tanegashima scale|4:1]].
{{todo|add etymology|add Template:MOS modes and annotate each row using Boushy’s names}}


{| class="wikitable"
! Mode
! UDP
! Mode name
|-
| LLLsLLsLLLsLLsLLs
| 16<nowiki>|</nowiki>0
| Harumi
|-
| LLLsLLsLLsLLLsLLs
| 15<nowiki>|</nowiki>1
| Yuzuha
|-
| LLsLLLsLLsLLLsLLs
| 14<nowiki>|</nowiki>2
| Maho
|-
| LLsLLLsLLsLLsLLLs
| 13<nowiki>|</nowiki>3
| Sakura
|-
| LLsLLsLLLsLLsLLLs
| 12<nowiki>|</nowiki>4
| Hanako
|-
| LLsLLsLLLsLLsLLsL
| 11<nowiki>|</nowiki>5
| Saori
|-
| LLsLLsLLsLLLsLLsL
| 10<nowiki>|</nowiki>6
| Machiko
|-
| LsLLLsLLsLLLsLLsL
| 9<nowiki>|</nowiki>7
| Sae
|-
| LsLLLsLLsLLsLLLsL
| 8<nowiki>|</nowiki>8
| Kaguya
|-
| LsLLsLLLsLLsLLLsL
| 7<nowiki>|</nowiki>9
| Nae
|-
| LsLLsLLLsLLsLLsLL
| 6<nowiki>|</nowiki>10
| Sachiko
|-
| LsLLsLLsLLLsLLsLL
| 5<nowiki>|</nowiki>11
| Kaori
|-
| sLLLsLLsLLLsLLsLL
| 4<nowiki>|</nowiki>12
| Kanako
|-
| sLLLsLLsLLsLLLsLL
| 3<nowiki>|</nowiki>13
| Sakurajima
|-
| sLLsLLLsLLsLLLsLL
| 2<nowiki>|</nowiki>14
| Kaho
|-
| sLLsLLLsLLsLLsLLL
| 1<nowiki>|</nowiki>15
| Suzuha
|-
| sLLsLLsLLLsLLsLLL
| 0<nowiki>|</nowiki>16
| Narumi
|}
== Scales ==
== Scales ==
* [[Edson17]] – 29edo tuning
* [[Edson17]] – 29edo tuning
Line 87: Line 27:
* [[Garibaldi17]] – 94edo tuning
* [[Garibaldi17]] – 94edo tuning
* [[Pythagorean17]] – Pythagorean tuning
* [[Pythagorean17]] – Pythagorean tuning
* [[Tanegashima scale]] – 53edo tuning
* [[Nestoria17]] – 171edo tuning
* [[Nestoria17]] – 171edo tuning


== Scale tree ==
== Scale tree ==
Generator ranges:
{{MOS tuning spectrum
* Bright generator: 494.1176 cents (7\17) to 500 cents (5\12)
| 4/3 = [[Leapfrog]]  
* Dark generator: 700 cents (7\12) to 705.8824 cents (10\17)
| 7/5 = [[Leapweek]]  
 
| 3/2 = [[Leapday]]  
{| class="wikitable center-all"
| 11/7 = [[Polypyth]]  
! colspan="6" | Bright generator
| 13/8 = Golden neogothic (495.904{{c}})  
! Cents
| 7/3 = [[Undecental]]  
! L
| 12/5 = Argent tuning (497.056{{c}})  
! s
| 13/5 = Unnamed golden tuning (497.254{{c}})  
! L/s
| 11/4 = [[Kwai]]  
! Comments
| 3/1 = [[Garibaldi]] / [[andromeda]]  
|-
| 7/2 = Garibaldi / [[cassandra]]  
| 7\17 || || || || || || 494.118 || 1 || 1 || 1.000 ||
| 4/1 = Garibaldi / [[helenus]], Pythagorean tuning (498.045{{c}})  
|-
| 9/2 = [[Pontiac]]  
| || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||
| 5/1 = [[Photia]]  
|-
| 6/1 = ↓&nbsp;[[Grackle]], ↓↓&nbsp;[[gracecordial]]
| || || || || 33\80 || || 495.000 || 5 || 4 || 1.250 ||
}}
|-
| || || || || || 59\143 || 495.105 || 9 || 7 || 1.286 ||
|-
| || || || 26\63 || || || 495.238 || 4 || 3 || 1.333 || [[Leapfrog]]
|-
| || || || || || 71\172 || 495.349 || 11 || 8 || 1.375 ||
|-
| || || || || 45\109 || || 495.413 || 7 || 5 || 1.400 || [[Leapweek]]
|-
| || || || || || 64\155 || 495.484 || 10 || 7 || 1.428 ||
|-
| || || 19\46 || || || || 495.652 || 3 || 2 || 1.500 ||
|-
| || || || || || 69\167 || 495.808 || 11 || 7 || 1.571 || [[Leapday]] / [[polypyth]]
|-
| || || || || 50\121 || || 495.868 || 8 || 5 || 1.600 ||
|-
| || || || || || 81\196 || 495.918 || 13 || 8 || 1.625 || Golden neogothic (495.9044¢)
|-
| || || || 31\75 || || || 496.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 74\179 || 496.089 || 12 || 7 || 1.714 ||
|-
| || || || || 43\104 || || 496.154 || 7 || 4 || 1.750 ||
|-
| || || || || || 55\133 || 496.241 || 9 || 5 || 1.800 ||
|-
| || 12\29 || || || || || 496.552 || 2 || 1 || 2.000 || Basic 12L 5s <br>(Generators smaller than this are proper)
|-
| || || || || || 53\128 || 496.875 || 9 || 4 || 2.250 ||
|-
| || || || || 41\99 || || 496.970 || 7 || 3 || 2.333 || [[Undecental]]
|-
| || || || || || 70\169 || 497.041 || 12 || 5 || 2.400 || Argent tuning (497.0563¢)
|-
| || || || 29\70 || || || 497.143 || 5 || 2 || 2.500 ||
|-
| || || || || || 75\181 || 497.238 || 13 || 5 || 2.600 || Unnamed golden tuning (497.2540¢)
|-
| || || || || 46\111 || || 497.297 || 8 || 3 || 2.667 ||
|-
| || || || || || 63\152 || 497.368 || 11 || 4 || 2.750 || [[Kwai]]
|-
| || || 17\41 || || || || 497.561 || 3 || 1 || 3.000 || [[Garibaldi]] / [[andromeda]]
|-
| || || || || || 56\135 || 497.778 || 10 || 3 || 3.333 ||
|-
| || || || || 39\94 || || 497.872 || 7 || 2 || 3.500 || Garibaldi / [[cassandra]]
|-
| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
|-
| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[helenus]], [[Pythagorean tuning]] (498.0450¢)
|-
| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]
|-
| || || || || 27\65 || || 498.462 || 5 || 1 || 5.000 || [[Photia]]
|-
| || || || || || 32\77 || 498.701 || 6 || 1 || 6.000 || [[Grackle]]↓
|-
| 5\12 || || || || || || 500.000 || 1 || 0 || → inf ||
|}


[[Category:17-tone scales]]
[[Category:17-tone scales]]
[[Category:Mega chromatic scales]]
[[Category:Mega chromatic scales]]
Retrieved from "https://en.xen.wiki/w/12L_5s"