Connectionist Representations of Tonal Music

List of Tables

Tables

Table 3-1 Pitch-class representation (for an artificial neural network) of 12 different major and 12 different harmonic minor scales.

Table 3-2 The connection weights from each input unit to each output unit for a perceptron trained to identify the tonic pitch-class of an input major or harmonic minor scale pattern.

Table 3-3 The rearranged connection weights from Table 3-2.

Table 4-1 Properties of the 12 harmonic minor scales and their position in hidden unit space.

Table 5-1 The three sets of key profiles used in key-finding algorithms.

Table 5-2 The three sets of mean-centred normalized key profiles used to train different key-finding perceptrons.

Table 5-3 The average percent accuracy of classification of the three perceptrons trained on three different mean-centred and normalized key profiles.

Table 5-4 Weights from input units to typical output units of the three perceptrons.

Table 6-1 The 13 possible distances between pitches that can be used to create interval cycles.

Table 6-2 Musical properties of each type of tetrachord in Figure 6-21.

Table 6-3 The different patterns of hidden unit activity produced by different subsets of each type of tetrachord.

Table 6-4 Example pitch-class representations of two major seventh tetrachords and three minor seventh tetrachords, along with the net input they provide to Hidden Unit 1 (Net) and its resulting activity.

Table 6-5 Example pitch-class representations of two dominant seventh tetrachords and two minor seventh flat five tetrachords, along with the net input they provide to Hidden Unit 1 (Net) and its resulting activity.

Table 6-6 The four major seventh tetrachords and then the four minor seventh flat five tetrachords that produce moderate activity in Hidden Unit 2.

Table 7-1 The names and formulas for twelve different types of tetrachords.

Table 7-2 The activity produced in Hidden Unit 6 by all possible pairs of different input pitch-classes.

Table 7-3 The activity produced in Hidden Unit 5 by all possible pairs of different input pitch-classes.

Table 7-4 The activity produced in Hidden Unit 2 by all possible pairs of different input pitch-classes.

Table 7-5 Correlations among activities of three hidden units to the 144 input patterns.

Table 7-6 The types of tetrachords found in each band in each jittered density plot that was presented in Section 7.3.

Table 7-7 The types of tetrachords found in each band to which the first single pattern presented to the network belongs.

Table 7-8 The types of tetrachords found in each band to which the second single pattern presented to the network belongs.

Table 8-1 The three tetrachords that define the ii-V-I progression for each major key.

Table 8-2 The mean number of sweeps required for a network to converge (with standard deviations) for perceptrons trained using four different encodings of the ii-V-I progression problem.

Table 8-3 The eight patterns in the ii-V-I training set that cause the A output unit to activate when signals are sent through the weights illustrated in Figure 8-8.

Table 8-4 The probability structure of the ii-V-I progression problem in the context of the A output unit whose connection weights were presented in Figure 8-8.

Table 8-5 The correlations between each of Krumhansl’s tonal hierarchies for major keys and the connection weights illustrated in Figure 8-8.

Table 8-6 The Coltrane changes for each major musical key.

Table 8-7 The various chord forms used to achieve efficient voice leading for the Coltrane Changes.

Table 8-8 The connection weights for a perceptron that has learned the Coltrane changes in lead sheet notation.

Table 9-1 Examples from previous chapters of identifying tritone relationships in a variety of network interpretations.

Table 9-2 Examples from previous chapters that discovered use of strange circles in different network interpretations.

Acknowledgements