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Tonal Space and the Human Mind
By P. Janata
Presented by
Deepak Natarajan
Background
• Simple musical stimuli used in the past to
measure expectancy violations
• Recently, neuroscientists prefer using more
natural stimuli (REAL music), causing a need
for modeling tonality in more sophisticated
ways
• Neural, perceptual, and cognitive constraints
of the human brain can provide more insight
to music theorists and musicologists
Background
• Major perceptual dimensions of music (tonality,
rhythm, timbre). Focus of this research is on
tonality
• Analysis must be conscious of the human mind
– Must establish short-term and long-term context of
tonality
– Need to consider other factors like human attention
span
• We can use physiological knowledge to inform
the models for music processing
Goal
• Develop models for tonal structure that are
suitable for analyzing behavioral and
neurophysiological data
(Janata, 2005)
Navigating Tonal Space
• The toroidal model links music theory,
cognitive psychology, and computational
modeling
(Krumhansl & Kessler, 1982)
Navigating Tonal Space
• Ability to use various distance metrics
between keys
• Different disciplines seek specific relationships
(eg. tonal/chordal relationships (circle of
fifths) vs. psychological values (relatedness)
• All of these relationships can be modeled
using self-organizing maps
Self-Organizing Maps
• An SOM is a type of artificial neural network
that is trained using unsupervised learning
– Unassuming of relationships among elements in
source data
– Produces a low-dimensional, discretized
representation of the input space of the training
samples
– Can uncover structure in source data
SOMs in music theory
• The approach assumes that nervous systems
learn to identify recurring patters of sensory
input; the brain is a statistical engine
• We can use similarities in the pitch class
distributions of input data and template data
to train the neural network
• The learning algorithm adjusts the weights
(ties) between input and output data to
determine the most probabilistic key
SOMs in music theory
• Three types
– Probe tone: Information on how well each of the
twelve pitch-classes is perceived to fit into a particular
key serves as an input to a SOM
– Pitch-class: Similar to probe tone, but uses music
theory (non-subjective) to create pitch-class
distributions to represent the importance of each
pitch in a key
– Acoustic Waveforms: Uses models of known
physiological mechanisms for defining transformations
of the auditory input and subsequent representations
Acoustic Waveform SOMs
(Janata, 2007)
Perception of Tonal Regions in a
Modulating Melody
• To perform key finding, a SOM was trained on
an 8 minute melody that modulated through
all 24 major and minor keys
– Resulted in an equal representation of PERCEIVED
key regions
• Model was probed with various timescales
using known stimuli and projected onto the
SOM to determine activation dynamics at
those different timescale
Input stimuli:
B-major scale + variations
(Janata, 2007)
Results: Activation Images
0.2 s
2.0 s
(Janata, 2007)
Results
• Activation consistently appears in the vicinity
of the B-major label
• However, activation is biased toward different
key regions, and the biasing depends on the
harmonic structure of the input stimuli
• The 2.0 s time-scale activation patterns
indicate the stable key. This analysis can be
extended to even longer time-scales
Video
(http://atonal.ucdavis.edu/projects/musical_spaces/tonal/torus_animations)
Brain Networks That Track
Musical Structure
• Identifying regions of the brain that invoke
tonal analysis (if at all!)
– Compare model data to fMRI data and look for
similarities. If matches are found, we can assume
we are essentially modeling this function of the
brain
– Use outside knowledge to raise/answer questions
concerning other brain functions occurring in
those regions
Attentive listening
• Music provides a complex soundscape for
attention to roam on
• We are interested in brain states that
correspond to attentive and engaged listening
• To achieve this, neuroimaging experiments
were performed where the subjects were
asked to identify some phenomenon (eg. tonal
expectancy violation)
Brain Activity
• fMRI data showed activity in premotor areas
of the brain, which are known to be active in
primarily perceptual tasks that have strong
and directed anticipatory components to
them
• This encourages the viewing of music in a
perception/action cycle framework. The task
demands shape the activity that we label as
the brain’s processing of music.
Tracking Movement Through
Tonal Space
(Janata, 2005)
Tracking Movement Through
Tonal Space
• Regions of high correlation between spherical
harmonic model data and brain activity
suggest other functions are linked to tracking
tonality
– Model data is extremely correlated with activity
from the Rostral Medial Prefrontal Cortex (RMPFC)
– This region is generally involved in the cognitive
control and evaluation of emotion
Tracking Movement Through
Tonal Space
(Janata, 2005)
Revisit Goal
• Develop models for tonal structure that are
suitable for analyzing behavioral and
neurophysiological data
(Janata, 2005)
Other Observations
• Rostral and ventral aspects of the MPFC are
among the last in which significant cortical
atrophy (weakening/degeneration) is observed in
Alzheimer disease (AD) patient
– (AD) patients have responded very positively to
familiar music from their childhood, often singing
along and readily detecting deviances implanted in
the musical stimuli
– Possibly suggests that the RMPFC is a locus at which
music and autobiographical memories are bound
together
References
• Janata, P. (2005). Brain networks that track
musical structure. In The Neurosciences and
Music II: From Perception to Performance (Vol.
1060): New York Academy of Sciences.
• Janata, P. (2007). Navigating tonal space. In E.
Selfridge-Field (Ed.), Tonal Theory for the Digital
Age (Computing in Musicology: Vol. 15, pp. 39–
50).
• Janata Lab (Center for Mind and Brain, UC Davis)
– http://atonal.ucdavis.edu/