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Below is a list of MOS with number of elements from 5 to 15, plus the names of some of the more significant MOS 11 and larger .
Pentatonic MOS

1L 4s

2L 3s

3L 2s

4L 1s

Hexatonic MOS

1L 5s

2L 4s

3L 3s

4L 2s

5L 1s

Heptatonic MOS

1L 6s

2L 5s

3L 4s

4L 3s

5L 2s

6L 1s

Octatonic MOS

1L 7s

2L 6s

3L 5s

4L 4s

5L 3s

6L 2s

7L 1s

Nonatonic MOS

1L 8s

2L 7s

3L 6s

4L 5s

5L 4s

6L 3s

7L 2s

8L 1s

Decatonic MOS

1L 9s

2L 8s

3L 7s

4L 6s

5L 5s

6L 4s

7L 3s

8L 2s

9L 1s

Hendecatonic MOS

1L 10s

2L 9s

3L 8s

4L 7s

5L 6s

6L 5s

7L 4s

8L 3s

9L 2s

10L 1s

Dodecatonic MOS

1L 11s

2L 10s

3L 9s

4L 8s

5L 7s

6L 6s

7L 5s

8L 4s

9L 3s

10L 2s

11L 1s

Tridecatonic MOS

1L 12s

2L 11s

3L 10s

4L 9s

5L 8s

6L 7s

7L 6s

8L 5s

9L 4s

10L 3s

11L 2s

12L 1s

Tetradecatonic MOS

1L 13s

2L 12s

3L 11s

4L 10s

5L 9s

6L 8s

7L 7s

8L 6s

9L 5s

10L 4s

11L 3s

12L 2s

13L 1s

Pentadecatonic MOS
1L 14s

2L 13s

3L 12s

4L 11s

5L 10s

6L 9s

7L 8s

8L 7s

9L 6s

10L 5s

11L 4s

12L 3s

13L 2s

14L 1s

Sensi[11] [8L 3s]
Machine[11], Baldy[11] [6L 5s]
Slendric[11] [5L 6s]
Keemun[11] [4L 7s]

Passion[12], Ripple[12] [11L 1s]
Pajara[12] [10L 2s]
August[12] [9L 3s]
Meantone[12] [7L 5s]
Hexe[12] [6L 6s]
Superpyth[12] [5L 7s]
Diminished[12] [4L 8s]
Augene[12] [3L 9s]
Injera[12] [2L 10s]

Heinz[13] [11L 2s]
Sephiroth[13] [10L 3s]
Orwell[13] [9L 4s]
Tridec[13] [8L 5s]
Tetracot[13] [7L 6s]
Leantone[13] [6L 7s]
Semisept[13] [5L 8s]
Huxley[13] [4L 9s]
Magic[13] [3L 10s]

See: Tridecatonic MOS

Octacot[14] [13L 1s]
Injera[14] [12L 2s]
Ketradektriatoh[14] [11L 3s]
Superpelog[14] [9L 5s]
Whitewood[14] [7L 7s]
Godzilla[14] [5L 9s]
Doublewide[14] [4L 10s]
Squares[14] [3L 11s]
Nautilus[14] [1L 13s]

Nautilus[15] [14L 1s]
Kangaroo[15] [13L 2s]
Superkleismic[15] [11L 4s]
Augene[15]: [12L 3s]
Blacksmith[15]: [10L 5s]
Triforce[15] [9L 6s]
Opossum[15] [8L 7s]
Porcupine[15] [7L 8s]
Terrain[15] [6L 9s]
Myna/Keemun[15] [4L 11s]
Progress[15] [2L 13s]
Valentine[15] [1L 14s]

Valentine[16] [15L 1s]
Kumonga[16] [11L 5s]
Lemba[16] [10L 6s]
Mavila[16] [9L 7s]
Mavila[16], Marvo[16], Gravity[16] [7L 9s]
Wizard[16] [6L 10s]
Mothra[16], Shoe[16] [5L 11s]
Magic[16] [3L 13s]

Progress[17] [15L 2s]
Squares[17] [14L 3s]
Garibaldi[17] [12L 5s]
Machine[17] [11L 6s]
Beatles[17] [10L 7s]
Bleu/Blue/Progression[17], Doublethink[17] [9L 8s]
Bleu/Blue/Progression[17], Indium/bohpier[17] [8L 9s]
Mohajira[17] [7L 10s]
Baldy[17] [6L 11s]
Superpyth[17] [5L 12s]
Roman[17] [3L 14s]
Tritonic[17] [2L 15s]

A-team[18] [13L 5s]

Liese[19] [17L 2s]
Muggles[19] [16L 3s]
Keemun[19] [15L 4s]
2-Flattone[19] [13L 6s]
Meantone[19] [12L 7s]
Clyde[19] [11L 8s]
Negri[19] [10L 9s]
Twothirdtonic[19] [9L 10s]
Sensi[19] [8L 11s]
Flattone[19] [7L 12s]
Hemiwuerschmidt[19] [6L 13s]
Semaphore[19], Godzilla[19] [5L 14s]
Myna[19] [4L 15s]
Magic[19] [3L 16s]
Tritonic[19] [2L 17s]

Bossier[20] [17L 3s]
Mitonic[20] [13L 7s]
Casablanca[20] [11L 9s]
Avila[20] [9L 11s]
Tetracot[20] [7L 13s]
Roman[20] [3L 17s]

Shoe[21] [16L 5s]
Miracle[21] [10L 11s]
Tridec[21] [8L 13s]
Rodan[21] [5L 16s]
Tritonic[21] [2L 19s]

Magic[22] [19L 3s]
Supra[22] [17L 5s]
Porcupine[22] [15L 7s]
Diaschismic[22] [12L 10s]
Orwell[22] [9L 13s]
Coendou[22] [7L 15s]
Wizard[22] [6L 16s]
Superpyth[22] [5L 17s]
Wuerschmidt[22] [3L 19s]
Shrutar[22] [2L 20s]

Barbad[23] [18L 5s]
Hemikleismic[23] [15L 8s]
Unidec[23] [13L 10s]
Ripple[23] [12L 11s]
Passion[23] [11L 12s]
Sephiroth[23] [10L 13s]
Greeley[23] [8L 15s]
Baldy[23] [6L 17s]
Roman[23] [3L 20s]

Godzilla[24] [19L 5s]
Hemififths[24] [17L 7s]
Mohajira[24] [7L 17s]
Semaphore[19] [5L 19s]

Hemimagic[25] [19L 6s]
Luna[25] [6L 19s]

Superpyth[27] [22L 5s]
Sensi[27] [19L 8s]
Ennealimmal[27] [18L 9s]
Octacot[27] narrow [14L 13s], wide [13L 14s]
Niner[27] [9L 18s],
Ultrapyth[27] [5L 22s]

Leapday[29], Grackle[29] [17L 12s]
Garibaldi[29] [12L 17s]
Tridec[29] [8L 21s]

Clyde[30] [19L 11s]

Luna[31] [25L 6s]
Meanpop[31] [19L 12s]
Squares[31] [17L 14s]
Grosstone[31] [12L 19s]
Miracle[31] [10L 21s]
Roulette[31] [6L 25s]

Tree of MOS derived from 1L 1s&1L
Tree of MOS derived from 1L 1s&1s