"...might compose elaborate and scientific pieces of music of any degree of complexity or extent"

Ada Lovelace

Charles Babbage

$$H_P = - \sum_{i > j} J_{ij}s_i s_j - \sum _i h_is_i,$$

$$H(t) = \left(1-\frac{t}{T}\right)H_0+  \frac{t}{T}H_P$$

- Can be encoded in Binary Values

$s_i \in \{-1,+1\}$

$s_i \leftrightarrow x_i = \frac{1-s_i}{2}$

$x_i \in\{0,1\}$

4

1

rest

measure

Durations

2

Pitches

$$\sum_{j \in P} x_{i,j} = 1$$

$$\left ( 1- \sum_{j \in P} x_{i,j} \right )^2$$

$$x_{i,C} + x_{i+1,D} \leq 1$$

$$x_{i,C} + x_{i+1,C} + x_{i+2,C} \leq 2$$

$x_{i,j}$ for $i \in [n]$ and $j \in P$

$$P=\{\mathtt{C}, \mathtt{D}, \mathtt{E}, \mathtt{G}\}$$

weights

Exemple: Ode to Joy excerpt

$$W_{F\#4,E4} = 2,$$

$$W_{F\#4,F\#4} = 2,$$

$$W_{F\#4,G4} = 1$$

    $$\sum_{\substack{i \in [n] \\ j \in D}} d(j)y_{i,j} = L$$

$$\sum_{j \in D} y_{i,j} = 1$$

    $$D = \{1,2,3,4\}$$

    $$j \in D$$

$$\sum_{j \in P} x_{i,j} = 3$$

$$(1-x_{i,p_{i_j}})$$

G

E

D

G

B

B

G