Another form of expectation arises when listeners learn to expect the unexpected. In a famous passage outlining his method of composing with twelve tones, Schoenberg claimed that repeating a pitch has a tendency to raise the tone to the status of the tonic. Given his avowed aesthetic goal to avoid tonality, Schoenberg proposed a remarkably simple system of constructing a tone-row where all twelve pitch-classes are sounded one after another. In effect, Schoenberg advocated creating music where the aggregate distribution of pitch-classes shows a "flat" or uniform
distribution. Notice that this compositional approach is very much
consistent with the view that the perception of pitch stability tends to be related to an unequal pitch-class distribution where one or another pitch becomes more predictable.
Of course, tonal implications are hard to eliminate. As we have seen, playing just a single tone is apt to evoke a sense of tonic for most
listeners. In the construction of a tone row, a composer might well choose ensuing pitches so that they tend to erase any latent tonal implications. For example, beginning with the pitch `C', an ensuing `G' would tend to reinforce a C-major key implication; an ensuing `C#' or `F#' would tend to contradict the tendency to assume a C-major key context.
Huron and von Hippel (2000) carried out a detailed study of the
construction of 12-tone rows from the classic "Second" Viennese school composers: Arnold Schoenberg, Anton Webern, and Alban Berg. Using some 80 twelve-tone rows, Huron and von Hippel examined the moment- to-moment key implications using the Krumhansl and Schmuckler
key-estimation algorithm. The moment-to-moment unfolding of the tone rows were shown to exhibit strong contra-tonal organizations. By way of illustration, consider the first four pitches in Schoenberg's tone-row for Opus 27, No. 3: G, F#, D, and E. Given these four notes, there are eight possible choices for the ensuing (fifth) pitch-class. Table 4 shows the maximum Krumhansl and Schmuckler key correlations that arise for each
of the eight possible continuations for the fifth pitch-class. For example, continuing the row with pitch-class `A' causes a high maximum key correlation (r=+0.81 for D major), whereas continuing the row with `F' produces a low maximum key correlation (r=+0.43 also for D major). Table 4
Initial Row Possible Continuation Maximum Key Correlation
G, F#, D, E C +0.64 G, F#, D, E C# +0.50 G, F#, D, E D# +0.47 G, F#, D, E F +0.43 G, F#, D, E G# +0.46 G, F#, D, E A +0.81 G, F#, D, E A# +0.55 G, F#, D, E B +0.79
If Schoenberg wished to circumvent this key implication, the best (lowest) key correlation would arise for the pitch F -- according to the Krumhansl and Schmuckler algorithm. The actual fifth pitch selected by Schoenberg is indeed F. In Huron and von Hippel, this contra-tonal tendency is evident throughout the twelve-tone rows used by these Viennese composers. In another study of twelve-tone rows, Krumhansl, Sandell and Sergeant (1987) asked listeners to judge the "goodness" of various probe tones at successive points in a twelve-tone row. Interestingly, Krumhansl et al's listeners divided into two distinct groups. Some listeners tended to rate "highly" tones which tended to reinforce some latent possible key. That is, the most highly rated tones tended to be those which maximized the
aggregate correlation for the passage with the Krumhansl and Kessler key profiles. The second group of listeners responded in a completely opposite fashion. That is, they rated most highly those continuation pitches that minimized the aggregate correlation for the passage with the Krumhansl and Kessler key profiles. In other words, this second group of listeners thought the most appropriate pitch continuations are those that create the most contra-tonal effect.
Fascinatingly, Krumhansl and her colleagues found that the two groups differed in their musical experience. The group that rated highly the most atonal continuations were the more musically experienced or trained
listeners. This suggests that these listeners had internalized the
contra-tonal organization underlying this music and were able to form expectations that correspond both with the aesthetic goal, and with the
pitch-related statistics exhibited by the music. In other words, the bifurcation in listening strategies reflected the combination of the
bifurcation of composing strategies, and the experience of the listeners. The phenomenon of "expecting the unexpected" has repercussions for understanding musical enjoyment. Earlier it was claimed that the exposure effect may simply be an artifact of a postive affect evoked by accurate anticipation of stimuli. If this is the case, then the frequency of occurrence of a stimulus does not, by itself, engender a positive affect. The more pertinent issue is the degree of predictability. To the extent that
knowledgeable listeners are better able to predict the behavior of 12-tone music, then it should not be unexpected that knowledgeable listeners might enjoy 12-tone music more than other listeners.
On the other hand, it might be noted that the expectations of
knowledgeable listeners when encountering 12-tone music are rather vague. Knowledgeable listeners have a higher than chance ability to
predict which pitch-classes are unlikely to occur next. But there may very well be a difference between knowing which two or three stimuli are most likely to occur next, and which two or three stimuli are least likely to occur next. It may be that expectation-evoked pleasure arises foremost when an expected stimulus is realized, not when an unexpected stimulus in not realized. It is possible that this hypothetical asymmetry limits the expectation-related pleasure that can arise from listening to 12-tone music.