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{{Todo|review|inline=1|text=Adopt scale tree template, review entries}}{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
Some notable temperaments that form a MOS with this pattern are [[Magic|magic]] and [[Würschmidt|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.


==Modes==
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.
{{MOS modes}}


==Scale tree==
== Scale properties ==
{| class="wikitable"
{{TAMNAMS use}}
|-
 
| | 1\3
=== Intervals ===
| |
{{MOS intervals}}
| |
 
| |
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| |
=== Modes ===
| |
{{MOS mode degrees}}
| |
 
| |
== Scale tree ==
| | 400
{{MOS tuning spectrum
| style="text-align:center;" |
| 3/2 = [[Sephiroth]]
|-
| 13/8 = Golden sephiroth
| |
| 13/5 = Unnamed golden tuning
| |
| 8/3 = [[Muggles]]
| |
| 10/3 = [[Magic]] / witchcraft
| |
| 7/2 = Magic
| |
| 11/3 = Magic / necromancy
| |
| 9/2 = [[Marveltri]]
| |
| 6/1 = [[Würschmidt]] ↓
| |
}}
| |
| | 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)
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 373.6775
| |
|-
| |
| |
| |
| | 14\45
| |
| |
| |
| |
| |
| |
| | 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:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
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