Description:For this MAX patch, an mlp object (4 input units, 12 output units, 12 hidden units in one hidden layer) was trained using the tonal hierarchy data provided by C. Krumhansl in “Cognitive Foundations of Musical Pitch.”
Tonal hierarchies which were gained experimentally are characterized by high values for the tonic followed by the dominant, the mediant and other scale tones; non-scale tones have very low values. Applying multi-dimensional scaling to these data, the 24 minor and major keys can be represented as unique locations on the surface of toroid.
In my patch, I projected the endless surface of the toroid on the two dimensions of a plane. Nonetheless, the user can move the mouse pointer without ever reaching a border, creating continuous transitions between different key areas (modulations). Holding the mouse key while moving will suspend the mouse tracking and allow jumps between the areas.
The output of the network (profile) is a probability distribution for each chromatic tone, which can be adjusted by applying a non-linear function determining the tonality of the output (tonality index 0: all pitches are equally probable; tonality index 10: mainly the tonic is sounding). The output is fed into a random pulse generator in order to generate a rhythmic structure.
Tonal hierarchies which were gained experimentally are characterized by high values for the tonic followed by the dominant, the mediant and other scale tones; non-scale tones have very low values. Applying multi-dimensional scaling to these data, the 24 minor and major keys can be represented as unique locations on the surface of toroid.
In my patch, I projected the endless surface of the toroid on the two dimensions of a plane. Nonetheless, the user can move the mouse pointer without ever reaching a border, creating continuous transitions between different key areas (modulations). Holding the mouse key while moving will suspend the mouse tracking and allow jumps between the areas.
The output of the network (profile) is a probability distribution for each chromatic tone, which can be adjusted by applying a non-linear function determining the tonality of the output (tonality index 0: all pitches are equally probable; tonality index 10: mainly the tonic is sounding). The output is fed into a random pulse generator in order to generate a rhythmic structure.