Handle: Engineering Artificial Musical Creativity at the “Trickery” Level - Computational Creativity Research: Towards Creative Machines - page 292

which state and no knowledge about which are required to learn by reasoning about
new inputs over time.
Handle jazz uses axioms provided and computed in SNARK to derive state values
matching combinations of 3-tuples of musical features. However, again, in cases
where precomputed information is unavailable Handle is designed to make an “intu-
itive leap,” by using one of a number of possible heuristics to guide its judgment.
We note at this point that for the given three-player scenario we may represent
each state as a color corresponding to the most extreme coordinates for a feature
3-tuple. For example, a solo for player A corresponds to red (6, 0, 0 255, 0, 0),

Solo B is 0, 6, 0, which encodes to green, and Solo C is 0, 0, 6, blue. Low-tension tutti
is represented by grey (calculated by finding the centroid of the state), high-tension
tutti is white, end is black, and uncertainty is determined by the coordinate values
themselves. After computing all state combinations, such a representation appears
as in Fig. 14.9 .
Our approach for resolving an unknown state at runtime is to use a nearest-
neighbor algorithm. Given the (safe) assumption that the states for all 8 corners of
the state cube are absolutely known ab initio, the value of any unknown state may
be derived by taking the average of the sum of the distance vector between it and
each (fully known) corner. As more and more states are derived and the knowledge-
base becomes progressively more complete, however, we would prefer to use more
accurate information; that is, state values which are more proximate to the unknown
state. These 8 cubes, nearest to the unknown state in diagonal distance, are determined
using a simple vector approach and the mean of their values returned. Thus, given
an unknown state

→

α α x , α y , α z ) and

with coordinates ( x , y , z vectors of the

co-ordinates of all known states, the 8 nearest neighbors of α can be found as follows:

index 1 = find( x[i] ≥ α x & y[i] ≥ α y & z[i] ≥ α z
index 2 = find( x[i] ≥ α x & y[i] ≤ α y & z[i] ≥ α z
index 3 = find( x[i] ≥ α x & y[i] ≤ α y & z[i] ≤ α z

Fig. 14.9 Chromatic representation of complete 3D state cube for tension B