C

C(4/4) Part or CP: 1 2 3 4

Consonance: 4 2 3 1

Dissonance: 1 3 2 4

Fig.2. Empirical estimation of a value for the Rhythmical Consonance and Dissonances of each stroke in a 4/4 measure.

3 / 4 Part and CP 1 2 3

Consonance: 3 2 1

Dissonance: 1 2 3

8 / 4 Part and CP: 1 2 3 4 5 6 7 8

Consonance: 8 2 4 2 6 2 2 1

Dissonance: 1 7 5 7 3 7 7 8

Fig.3. Empirical estimation of a value for the Rhythmical Consonance of each stroke in 3/8 and 8/4 measures.

0 5 10 15 20 25 30 35 40 45

per. +++++++++++++++++++++++++++++++++++++++++++++++++

2 x x x x x x x x x x x x x x x x x x x x x x x x x

3 o o o o o o o o o o o o o o o o o

6 v v v v v v v v v

4 o o o o o o o o o o o o o

5 x x x x x x x x x x

20 v v v

6 o o o o o o o o o

8 x x x x x x x

24 v v v

+++++++++++++++++++++++++++++++++++++++++++++++++

0 5 10 15 20 25 30 35 40 45

Fig. 4. Beating of two tempi in simple frequency ratio. Stroke coincidences at the minimum common multiple: two simultaneous periods of 2 y 3 seconds compound another of 6.

4 o...o...o...o...o...o...o...o...o...o...o...o...o

5 x....x....x....x....x....x....x....x....x....x...

20 v...................v...................v........

‒‒‒‒‒ ‒eeeee eeeee eeeee eeeee- eeeee eeeee eeeee eeeee- eeeee- eee

Fig. 5. A measure of 20/8, obtained with two simultaneous tempi with frequencies in the ratio 5 to 4.

4 / 4 Part and CP: 1 2 3 4

Euler Diss.: 1 7 4 9

RED₁: 0 6 3 8

Intuitive Diss. 1 3 2 4

8 / 4 Part and CP: 1 2 3 4 5 6 7 8

Euler Diss.: 1 8 7 14 4 16 9 10

RED₁: 0 7 6 13 3 15 8 9

Intuitive Diss. 1 8 3 8 2 8 4 8

Fig.6. Comparison between intuitive y calculated sonances.

R1.

XXXXX

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SItuation and order of strokes.

1 8

2 9

3 10

4 11

5 12

6 13

7 14

8 15

Fig.7. Two rhythms R1 and R2 with 8 parts and very different dissonance. Each stroke is numbered (third row) with it situation in the measure and with its Rhythmic Order, defined as its order when counting, beginning with 0, from the previous bar.

4-4 \‒E‒q‒‒e‒Q‒-q‒-\