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12L 5s: Difference between revisions

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This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19|24/19]] and [[32/25|32/25]], thus its generator is a perfect fourth between 7/17edo (494.412) and 5/12edo (500 cents).
{{Infobox MOS}}
{{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]].


{| class="wikitable"
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).
|-
 
| | 7/17
== Scale properties ==
| |
{{TAMNAMS use}}
| |
 
| |
=== Intervals ===
| |
{{MOS intervals}}
| | 494.412
 
|-
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| |
=== Modes ===
| |
{{MOS mode degrees}}
| | 33/80
 
| | 495
=== 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}}
| |
 
| |
== Scales ==
| | 26/63
* [[Edson17]] – 29edo tuning
| |
* [[Subaru scale]] – 41edo tuning
| | 495,238
* [[Cotoneum17]] – 217edo tuning
|-
* [[Garibaldi17]] – 94edo tuning
| |
* [[Pythagorean17]] – Pythagorean tuning
| |
* [[Tanegashima scale]] – 53edo tuning
| |
* [[Nestoria17]] – 171edo tuning
| |
 
| | 45/109
== Scale tree ==
| | 495.412
{{MOS tuning spectrum
|-
| 4/3 = [[Leapfrog]]
| |
| 7/5 = [[Leapweek]]
| |
| 3/2 = [[Leapday]]
| | 19/46
| 11/7 = [[Polypyth]]
| |
| 13/8 = Golden neogothic (495.904{{c}})
| |
| 7/3 = [[Undecental]]
| | 495.625
| 12/5 = Argent tuning (497.056{{c}})
|-
| 13/5 = Unnamed golden tuning (497.254{{c}})
| |
| 11/4 = [[Kwai]]
| |
| 3/1 = [[Garibaldi]] / [[andromeda]]
| |
| 7/2 = Garibaldi / [[cassandra]]
| |
| 4/1 = Garibaldi / [[helenus]], Pythagorean tuning (498.045{{c}})
| |
| 9/2 = [[Pontiac]]
| | 495.807
| 5/1 = [[Photia]]
|-
| 6/1 = ↓ [[Grackle]], ↓↓ [[gracecordial]]
| |
}}
| |
 
| |
[[Category:17-tone scales]]
| |
[[Category:Mega chromatic scales]]
| | 50/121
| | 495.868
|-
| |  
| |
| |
| |
| |
| | 495.904
|-
| |  
| |
| |
| | 31/75
| |
| | 496
|-
| |
| |
| |
| |
| |
| | 496.123
|-
| |
| |
| |
| |
| | 43/104
| | 496.154
|-
| |
| | 12/29
| |
| |
| |
| | 496.552
|-
| |
| |
| |
| |
| | 41/99
| | 496.97
|-
| |
| |
| |
| | 29/70
| |
| | 497.143
|-
| |
| |
| |
| |
| |
| | 497.254
|-
| |
| |
| |
| |
| | 46/111
| | 497.297
|-
| |
| |
| |
| |
| |
| | 497.342
|-
| |
| |
| | 17/41
| |
| |
| | 497.561
|-
| |
| |
| |
| |
| |
| | 497.658
|-
| |
| |
| |
| |
| | 39/94
| | 497.872
|-
| |
| |
| |
| | 22/53
| |
| | 498.113
|-
| |
| |
| |
| |
| | 27/65
| | 498,4615
|-
| | 5/12
| |
| |
| |
| |
| | 500
|}
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