Supplementary materials for the paper “Classical Music Composition Using State Space Models”.

We considered 15 models, M1-M15, to generate compositions: model M1 was a standard HMM with 25 hidden states, model M2 was a 2-HMM with 25 hidden states, M3 was a 3-HMM with 10 hidden states, model M4 was a LRHMM with 25 hidden states, model M5 was a 2-LRHMM with 25 hidden states, model M6 was a 3-LRHMM with 10 hidden states, model M7 was a ARHMM with 25 hidden states, model M8 was a HSMM with 25 hidden states, model M9 was a NSHMM with 25 hidden states, M10 was a TSHMM with 10 hidden states in the first layer and 5 in the second layer, M11 was a TSHMM with 5 hidden states in the first layer and 10 in the second layer, model M12 was a FHMM with three independent HMMs each with 15, 10 and 5 hidden states respectively, model M13 was a LHMM with three layers and 25 hidden states in each layer, model M14 was a TVAR with order between 7 and 14 and model M15 was a baseline model speci ed by a HMM with randomly assigned parameters.

Plot of the RMSE for various metrics for all 14 original models when trained on Pictures at an Exhibition, Promenade - Gnomus.

Plot of the average mutual information and average minimum edit distance for all 14 original models when trained on Pictures at an Exhibition, Promenade - Gnomus.

Table of the RMSE for various metrics for all 14 original models ordered from best to worst when trained on Pictures at an Exhibition, Promenade - Gnomus.

In addition to ranking each piece from favorite to least favorite for the second round of evaluations, each listener was asked to quantitatively score each piece on a scale of 1 to 5 according to:

  • how much the generated piece sounded like it was composed by a human, 1 = piece sounded completely random, 5 = piece sounded just like a human composition;
  • how harmonically pleasing each piece was, 1 = not at all harmonically pleasing, 5 = very harmonically pleasing;
  • how melodically pleasing each piece was, 1 = not at all melodically pleasing, 5 = very melodically pleasing.

The average rankings for each evaluated piece are here

The percentage of simple harmonic intervals that are thirds, perfect fourths or fifths and dissonant for the second round of evaluated pieces.

TSHMM Baum-Welch Algorithm

The Baum-Welch Algorithm for the two hidden state HMM.