Mind, Body, World- Foundations of Cognitive Science, 2013a

simulations also revealed new phenomena that have typically not been explored in
the reorientation task that relate to the difference between excitatory cues, which
indicate the presence of a reward, and inhibitory cues, which indicate the absence of
a reward. In short, perceptrons have been used to create an associative, nonmodular
theory of reorientation.
4.17 Perceptrons and Jazz Progressions
We have seen that a particular type of network from Old Connectionism, the perceptron,
can be usefully applied in the studies of classical conditioning and reorientation.
In the current section we see that it can also be used to explore musical
regularities. Also illustrated is the interpretation of the internal structure of such a
network, which demonstrates that even simple networks can reveal some interesting
algorithmic properties.
Jazz progressions are sequences of chords. Consider the C major scale presented
earlier, in Figure 4-8. If one takes the first note of the scale, C, as the root
and adds every second note in the scale—E, G, and B)—the result is a four-note
chord—a tetrachord—called the C major 7 th chord (Cmaj7). Because the root of this
chord is the first note of the scale, this is identified as the I chord for C major. Other
tetrachords can also be built for this key. Starting with the second note in the scale,
D, and adding the notes F, A, and C produces D minor 7 th (Dm7). Because its root is
the second note of the scale, this is identified as the II chord for the key of C major.
Using G as the root and adding the notes B, D, and F creates the G dominant 7 th
chord (G7). It is the V chord of the key of C major because its root is the fifth note
of the C major scale.
The I, II, and V chords are the three most commonly played jazz chords, and in
jazz they often appear in the context of the II-V-I progression (Levine, 1989). This
chord progression involves playing these chords in a sequence that begins with the
II chord, moves to the V chord, and ends on the I chord. The II-V-I progression is
important for several reasons.
First, chord progressions are used to establish tonality, that is, to specify to the
listener the musical key in which a piece is being played. They do so by setting up
expectancies about what is to be played next. For any major key, the most stable
tones are notes I, IV, and V (Krumhansl, 1990), and the most stable chords are the
ones built on those three notes.
Second, in the perception of chord sequences there are definite preferences for
the IV chord to resolve into the V chord and for the V chord to resolve into the I chord,
producing the IV-V-I progression that is common in cadences in classical music
(Bharucha, 1984; Jarvinen, 1995; Katz, 1995; Krumhansl, Bharucha, & Kessler, 1982;
Rosner & Narmour, 1992). There is a similar relationship between the IV chord and
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