12L 17s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS}}
| Other names =
{{MOS intro}}
| Periods = 1
Its [[chroma-positive]] generator is a near-perfect fourth of no more than 5\12 (500{{cent}}), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3. [[Pythagorean tuning]] generates this scale, with a hardness of 2.8459. It is known as '''pythagotonic''' in [[TAMNAMS Extension]].
| nLargeSteps = 12
 
| nSmallSteps = 17
== Intervals ==
| Equalized = 12
{{MOS intervals}}
| Collapsed = 5
| Pattern = LsLsLssLsLssLsLsLssLsLssLsLss
}}
The '''12L 17s''' [[MOS scale]] splits the small steps 1-1-2-1-2-1-1-2-1-2-1-2 between the large steps. Its [[chroma-positive]] generator is a near-perfect fourth of no more than 5\12 (500{{cent}}), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.


== Scale tree ==
== Scale tree ==
{| class="wikitable"
{{MOS tuning spectrum
|-
| 4/3 = [[Undecental]]
| 12/29
| 10/7 = Argent tuning (497.056{{c}})
|
| 13/8 = Unnamed golden tuning (497.254{{c}})
|
| 7/4 = [[Kwai]]
|
| 9/4 = [[Cotoneum]]
|
| 5/2 = [[Garibaldi]] / [[cassandra]]
| 496.552
| 11/4 = [[Pythagorean tuning]] (498.045{{c}})
|-
| 3/1 = Garibaldi / [[helenus]]
|
| 10/3 = [[Pontiac]]
|
| 6/1 = [[Grackle]], ↓ [[gracecordial]]
|
}}
|
| 53/128
| 496.875
|-
|
|
|
| 41/99
|
| 496.97
|-
|
|
|
|
| 70/169
| 497.041
|-
|
|
| 29/70
|
|
| 497.143
|-
|
|
|
|
|
| 497.211
|-
|
|
|
|
| 75/181
| 497.238
|-
|
|
|
|
|
| 497.254
|-
|
|
|
| 46/111
|
| 497.297
|-
|
|
|
|
|
| 497.353
|-
|
|
|
|
| 63/152
| 497.368
|-
|
| 17/41
|
|
|
| 497.561
|-
|
|
|
|
| 56/135
| 497.778
|-
|
|
|
| 39/94
|
| 497.842
|-
|
|
|
|
|
| 497.935
|-
|
|
|
|
| 61/147
| 497.959
|-
|
|
|
|
|
| 497.985
|-
|
|
| 22/53
|
|
| 498.113
|-
|
|
|
|
|
| 498.178
|-
|
|
|
|
| 49/118
| 498.305
|-
|
|
|
| 27/65
|
| 498.4615
|-
|
|
|
|
| 32/77
| 498.701
|-
| 5/12
|
|
|
|
| 500
|}