@@ Line 419: / Line 419: @@
 yaza: D is the obvious tonic for either scale
+==41-edo MOS scales==
+*[[List of edo-distinct 41et rank two temperaments]]
+Mathematically, 41edo has 20 edo-distinct temperaments, and each one has infinite MOS scales. This table only lists musically useful ones. MOS scales listed are those with:
+* 5-13 notes
+* s >= 2
+* L/s <= 4.5
+* L/s <= 2 if 1L
+{| class="wikitable right-1 right-2"
+|+Table of Temperaments by generator
+|-
+!edosteps
+!Cents
+!Temperament(s)
+![[Pergen]]
+!MOS Scales
+!L s
+!moves
+|-
+|1 = ^1
+|29.27
+|Sepla-sezo = {{monzo| -100 33  0 17 }}
+|(P8, P4/17)
+|lopsided, s=1
+|
+|
+|-
+|2 = vm2
+|58.54
+|[[Hemimiracle]]
+|(P8, P5/12)
+|L/s too big
+|
+|
+|-
+|3 = m2
+|87.80
+|88cET (approx), [[Octacot]]
+|(P8, P5/8)
+|13 = 1L 12s
+|5 3
+| -5, -4
+|-
+|4 = ^m2
+|117.07
+|[[Miracle]]
+|(P8, P5/6)
+|10 = 1L 9s
+|5 4
+| +2, -4
+|-
+|5 = ~2
+|146.34
+|[[Bohlen-Pierce]], [[Bohpier]]
+|(P8, P12/13)
+|8 = 1L 7s
+lopsided
+|6 5
+| +3, -4
+|-
+|6 = vM2
+|175.61
+|[[Tetracot]], [[Bunya]], [[Monkey]]
+|(P8, P5/4)
+|7 = 6L 1s
+lopsided
+|6 5
+| +3, -4
+|-
+|7 = M2
+|204.88
+|[[Baldy]]
+|(P8, c<sup>3</sup>P4/20)
+|6 = 5L 1s
+lopsided
+|7 6
+| +3, -3
+|-
+|8 = ^M2
+|234.15
+|[[Rodan]], [[Guiron]]
+|(P8, P5/3)
+|5 = 1L 4s
+, 11 lopsided
+|9 8
+| +4, -2
+|-
+|9 = vm3
+|263.41
+|[[Septimin]]
+|(P8, ccP4/11)
+|5 = 4L 1s
+= 5L 4s
+|9 5
+4
+| -2, -4
++2,-4
+|-
+|10 = m3
+|292.68
+|[[Quasitemp]]
+|(P8, c<sup>3</sup>P4/14)
+|lopsided, s=1
+|
+|
+|-
+|11 = ^m3
+|321.95
+|[[Superkleismic]]
+|(P8, ccP4/9)
+|7 = 4L 3s
+= 4L 7s
+|8 3
+3
+| +4, -5
+-5, -4
+|-
+|12 = ~3
+|351.22
+|[[Hemififths]], [[Karadeniz]]
+|(P8, P5/2)
+|7 = 3L 4s
+= 7L 3s
+|7 5
+2
+| -4, -3
++1, -3
+|-
+|13 = vM3
+|380.49
+|[[Magic|Magic (Latrizo)]], [[Witchcraft]]
+|(P8, P12/5)
+|'''10 = 3L 7s'''
+'''13 = 3L 10s'''
+|'''9 2'''
+'''7 2'''
+|'''+1, -2'''
+'''+1, -3'''
+|-
+|14 = M3
+|409.76
+|[[Hocus]]
+|(P8, c<sup>3</sup>P4/10)
+|lopsided, s=1
+|
+|
+|-
+|15 = ^M3
+|439.02
+|Sasa-tritribizo = {{monzo| 5 -35 0 18 }}
+|(P8, c<sup>6</sup>P5/18)
+|'''5 = 3L 2s'''
+'''8 = 3L 5s'''
+= 8L 3s
+|'''11 4'''
+'''7 4'''
+3
+|'''+2, -1'''
+'''+2, -3'''
++2, -5
+|-
+|16 = v4
+|468.29
+|[[Barbad]]
+|(P8, c<sup>7</sup>P4/19)
+|5 = 3L 2s
+= 5L 3s
+= 5L 8s
+|9 7
+2
+2
+| -2, -3
++1, -3
++1, -4
+|-
+|17 = P4
+|497.56
+|[[Schismatic]] ([[Helmholtz]],
+[[Garibaldi]], [[Cassandra]])
+|(P8, P5)
+|5 = 2L 3s
+= 5L 2s
+= 5L 7s
+|10 7
+3
+3
+| +5, -3
+-3, -5
++2, -5
+|-
+|18 = ^4
+|526.83
+|[[Trismegistus]]
+|(P8, c<sup>6</sup>P5/15)
+|5 = 2L 3s
+= 2L 5s
+= 7L 2s
+|13 5
+5
+3
+| -4, -0
++4, -4
+-4, -5
+|-
+|19 = ~4
+|556.10
+|Sasa-quadquadlu = {{monzo| 57 -1 0 0 -16 }}
+|(P8, c<sup>7</sup>P4/16)
+|7 = 2L 5s
+= 2L 7s
+= 2L 9s
+= 2L 11s
+|13 3
+3
+3
+3
+| -5, -0
++5, -5
+-5, -3
++2, -3
+|-
+|20 = d5
+|585.37
+|[[Pluto]]
+|(P8, c<sup>3</sup>P4/7)
+|lopsided, s=1
+|
+|
+|}
+Most MOS scales either lack a perfect 5th or are awkward to play on the Kite Guitar. Awkward scales require more than 3 string hops per octave, or moves by more than 4 frets. The In terms of playability, the standout scales are the one generated by the ^M3.

Kite Giedraitis's Categorizations of 41edo Scales: Difference between revisions