linked to six chord units, chords that belong to the key. In addition, for the simulations
using chord sequences, the strength of the connections reflected the frequency of occur-
rence of chords in the sequences, and the tonic chord in a given key had stronger links than
the other chords. For the simulations with chord sets, all connections between chord and
key units had the same strength. In sum, specialized representational units were formed for
combinations of musical events (tones, chords) that occur with great regularity. The
self-organization leads to a hierarchical encoding in which tones occurring together are
represented by chord units, and similarly, chords occurring together are represented by key
units. Interestingly, the learned connections mirrored the pattern of connections that had
been hardwired in a previously proposed music perception network (MUSACT^73 ).
The trained HSOM networks were used as feedforward and reverberation systems. In a
feedforward system, activation consisted of bottom-up information only. Consequently,
activation of chord units reflected the number of component tones shared with the input:
the more tones are shared, the stronger the unit is activated. In a reverberation system, phasic
activation spreads between the units of the three layers until an equilibrium is reached.^73
After reverberation, the activation pattern reflects top-down influences of learned,
schematic structures, and respects tonal relations: the activation of major chord units, for
example, decreased monotonically with increasing distance on the circle of fifths. After
reverberation, top-down processes overwrote influences of coding richness and the
imposed activation pattern was analogous for sparse and rich input coding. Finally, activa-
tion patterns after reverberation for the four trained HSOM networks showed strong cor-
relations with activation patterns of MUSACT (0.984r0.999). This outcome suggests
that MUSACT’s hard-wired structure can emerge from self-organization.
The hierarchical self-organizing map thus manages to learn Western pitch regularities.
The input layer of the network was based on pitch classes, the 12 tones of the chromatic
scale. In Western tonal music, these pitch classes are repeated over octaves in different pitch
heights. The phenomenon of octave equivalence (i.e. tones separated by an octave are per-
ceived as similar in pitch) permits the presentation of the tonal system as based on
12 events. The abstract pitch-class coding in the network was based on previous simulations
of octave category learning. An SOM learned octave-equivalent pitch classes via mere
exposure to spectral representations of tones.^74 In addition, it has also been shown that
neural nets are able to learn the extraction of pitch height from frequency,75–77and to
transform a spectral representation of an acoustic source into a spatial distribution of pitch
strengths.^75 These models represent the application of neural nets to the learning of low-
level processes in auditory perception (pitch extraction, octave equivalence). The HSOM
model with its three organizational layers of tones, chords, and keys can be conceived of as
subsequent to these simulated phases of auditory preprocessing.
In the music perception domain, other neural net models have been proposed to sim-
ulate the learning of higher-level organizations. In contrast to the HSOM network presented
above, these models focused on either one or two organizational layers in music perception,
as for example, models of chord classification^78 or melodic sequence learning.79–81Griffith^82
and Leman72,83used SOMs to simulate the learning of key representations based on either
melodies,^82 chords^72 or recordings of real musical pieces which are preprocessed by an audit-
ory module.^83 After training, the specialized units of the SOMs showed a topological
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