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3L 10s: Difference between revisions

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"3L 10s" is a [[MOSScales|MOS]] scale pattern with 3 large steps and 10 small steps. Some notable temperaments that form a MOS with this pattern are [[Magic|magic]] and [[Würschmidt|würschmidt]].
{{Infobox MOS}}
{{MOS intro}}


Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.
Some notable temperaments that form a mos with this pattern are [[magic]] and [[würschmidt]]. Of course, Magic[13] is still slightly improper and Würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13-tone-per-octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13-tone circles favor multiple times over.


{| class="wikitable"
== Scale properties ==
|-
{{TAMNAMS use}}
| | 1\3
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 400
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 13\40
| | 390
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 12\37
| |
| | 389.189
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 11\34
| |
| |
| | 388.235
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 32\99
| | 387.879
| style="text-align:center;" | Whirrschmidt
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 21\65
| |
| | 387.692
| style="text-align:center;" | Worschmidt
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 31\96
| | 387.5
| style="text-align:center;" | Würschimdt
|-
| |
| |
| |
| |
| |
| |
| | 10\31
| |
| |
| |
| | 387.097
| style="text-align:center;" | Würschimdt
|-
| |
| |
| |
| |
| |
| |
| |
| | 19\59
| |
| |
| | 386.441
| style="text-align:center;" | Sulis
|-
| |
| |
| |
| |
| |
| | 9\28
| |
| |
| |
| |
| | 385.714
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 8\25
| |
| |
| |
| |
| |
| | 384
| style="text-align:center;" | Marveltri
|-
| |
| |
| |
| | 7\22
| |
| |
| |
| |
| |
| |
| | 381.818
| style="text-align:center;" | Sorcery
|-
| |
| |
| |
| |
| |
| | 20\63
| |
| |
| |
| |
| | 380.952
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 33\104
| |
| |
| |
| | 380.769
| style="text-align:center;" | Optimal patent val for 11-limit magic
|-
| |
| |
| |
| |
| | 13\41
| |
| |
| |
| |
| |
| | 380.488
| style="text-align:center;" | Optimal patent val for 13-limit magic
|-
| |
| |
| |
| |
| |
| | 19\60
| |
| |
| |
| |
| | 380
| style="text-align:center;" | Optimal patent val for 5-limit magic
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 379.408
| |
|-
| |
| |
| | 6\19
| |
| |
| |
| |
| |
| |
| |
| | 378.947
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 377.967
| |
|-
| |
| |
| |
| |
| | 17\54
| |
| |
| |
| |
| |
| | 377.778
| |
|-
| |
| |
| |
| |
| |
| |
| | 45\143
| |
| |
| |
| | 377.622
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 118\375
| |
| | 377.6
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 191\607
| | 377.595
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 73\232
| |
| |
| | 377.586
| |
|-
| |
| |
| |
| |
| |
| | 28\89
| |
| |
| |
| |
| | 377.528
| |
|-
| |
| |
| |
| | 11\35
| |
| |
| |
| |
| |
| |
| | 377.143
| style="text-align:center;" |
|-
| |
| | 5\16
| |
| |
| |
| |
| |
| |
| |
| |
| | 375
| style="text-align:center;" | Boundary of propriety


(Smaller generators are proper)
=== Intervals ===
|-
{{MOS intervals}}
| |
 
| |
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| |
=== Modes ===
| |
{{MOS mode degrees}}
| |
 
| |
== Scale tree ==
| |
{{MOS tuning spectrum
| |
| 3/2 = [[Sephiroth]]
| | 373.6775
| 13/8 = Golden sephiroth
| |
| 13/5 = Unnamed golden tuning
|-
| 8/3 = [[Muggles]]
| |
| 10/3 = [[Magic]] / witchcraft
| |
| 7/2 = Magic
| |
| 11/3 = Magic / necromancy
| | 14\45
| 9/2 = [[Marveltri]]
| |
| 6/1 = [[Würschmidt]] ↓
| |
}}
| |
 
| |
[[Category:Abstract MOS patterns]]
| |
| |
| | 373.333
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 37\119
| |
| |
| |
| |
| | 373.109
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 97\312
| |
| |
| | 373.077
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 254\817
| | 373.072
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 157\505
| |
| | 373.069
| |
|-
| |
| |
| |
| |
| |
| |
| | 60/193
| |
| |
| |
| | 373.057
| |
|-
| |
| |
| |
| |
| | 23\74
| |
| |
| |
| |
| |
| | 372.973
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 372.812
| |
|-
| |
| |
| | 9\29
| |
| |
| |
| |
| |
| |
| |
| | 372.414
| style="text-align:center;" |
|-
| |
| |
| |
| | 13\42
| |
| |
| |
| |
| |
| |
| | 371.429
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 17\55
| |
| |
| |
| |
| |
| | 370.909
| |
|-
| |
| |
| |
| |
| |
| | 21\68
| |
| |
| |
| |
| | 370.588
| |
|-
| |
| |
| |
| |
| |
| |
| | 25\81
| |
| |
| |
| | 370.37
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 29\94
| |
| |
| | 370.213
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 33\107
| |
| | 370.0935
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 37\120
| | 370
| |
|-
| | 4\13
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 369.231
| style="text-align:center;" |
|}
[[Category:MOS scales]]
[[Category:Table]]
Retrieved from "https://en.xen.wiki/w/3L_10s"