Table 3 Statistics of mean rating improvement from the initial to the final rating iterations, for all raters and setups, in all the respective simulations

\(\hbox {R}_1\)

 \(\hbox {S}_1\)

  Rhythm

5.63 (2.69)

9.20 (0.67)

3.57 (1.53)

0.93 (1.47)

  Tone

5.88 (2.70)

9.11 (1.01)

3.29 (1.24)

0.63 (0.39)

 \(\hbox {S}_2\)

  Rhythm

5.87 (2.55)

9.17 (0.68)

3.30 (1.44)

0.66 (0.45)

  Tone

5.72 (2.97)

9.15 (1.14)

3.55 (1.28)

0.68 (0.37)

 \(\hbox {S}_3\)

  Rhythm

5.95 (2.55)

9.25 (0.78)

3.30 (1.43)

0.64 (0.45)

  Tone

5.84 (2.94)

9.23 (1.02)

3.39 (1.30)

0.63 (0.36)

 \(\hbox {S}_4\)

 Rhythm

5.51 (2.77)

9.00 (1.05)

3.51 (1.65)

0.82 (0.74)

 Tone

6.04 (2.81)

9.33 (0.69)

3.30 (1.11)

0.58 (0.27)

\(\hbox {R}_2\)

 \(\hbox {S}_1\)

  Rhythm

2.80 (1.79)

6.59 (1.59)

3.78 (1.37)

1.56 (0.92)

  Tone

3.31 (2.23)

7.25 (1.38)

4.00 (1.40)

1.34 (0.70)

\(\hbox {S}_2\)

  Rhythm

3.10 (1.78)

6.82 (1.51)

3.72 (1.36)

1.43 (0.85)

  Tone

3.32 (2.00)

6.76 (1.80)

3.55 (1.60)

1.16 (0.79)

 \(\hbox {S}_3\)

  Rhythm

3.02 (1.93)

6.86 (1.48)

3.84 (1.15)

1.63 (1.28)

  Tone

3.32 (2.14)

7.49 (1.49)

4.17 (1.51)

1.36 (0.81)

 \(\hbox {S}_4\)

  Rhythm

3.28 (1.89)

6.79 (1.65)

3.51 (1.41)

1.29 (0.95)

  Tone

3.21 (2.12)

6.91 (1.56)

3.81 (1.35)

1.31 (0.70)

\(\hbox {R}_3\)

 \(\hbox {S}_1\)

  Rhythm

1.86 (1.21)

5.11 (1.44)

3.25 (1.25)

1.93 (0.94)

  Tone

2.18 (1.52)

5.17 (1.45)

3.01 (1.47)

1.57 (1.06)

 \(\hbox {S}_2\)

  Rhythm

1.88 (1.22)

4.71 (1.37)

2.83 (1.06)

1.84 (1.36)

  Tone

2.07 (1.44)

4.95 (1.60)

2.93 (1.38)

1.56 (1.04)

 \(\hbox {S}_3\)

  Rhythm

1.78 (1.19)

4.76 (1.40)

2.98 (1.13)

1.86 (1.09)

  Tone

1.98 (1.47)

4.67 (1.52)

2.69 (1.21)

1.47 (0.88)

 \(\hbox {S}_4\)

  Rhythm

2.02 (1.18)

4.88 (1.32)

2.87 (1.19)

1.73 (1.48)

  Tone

2.16 (1.48)

5.24 (1.43)

3.12 (1.34)

1.58 (0.89)

\(\hbox {R}_4\)

 \(\hbox {S}_1\)

  Rhythm

0.78 (0.54)

2.36 (0.93)

1.59 (0.82)

2.40 (1.81)

  Tone

0.99 (0.65)

2.71 (0.93)

1.74 (0.84)

1.94 (1.18)

 \(\hbox {S}_2\)

  Rhythm

1.87 (1.20)

4.44 (1.41)

2.59 (1.13)

1.67 (1.23)

  Tone

2.18 (1.39)

4.69 (1.85)

2.64 (1.62)

1.31 (0.93)

 \(\hbox {S}_3\)

  Rhythm

1.87 (1.24)

4.69 (1.46)

2.83 (1.10)

1.70 (0.89)

  Tone

2.25 (1.53)

4.96 (1.46)

2.73 (1.27)

1.30 (0.73)

 \(\hbox {S}_4\)

  Rhythm

1.95 (1.20)

4.97 (1.42)

3.02 (1.24)

1.85 (1.40)

  Tone

2.24 (1.49)

5.28 (1.63)

3.11 (1.45)

1.52 (0.91)