Participants. We used 68 participants who were students at the University
of Sussex. Twenty-eight participated in the training conditions, in which
each participant was trained and tested on one transform. An equal number
of training participants were randomly assigned to each transform. Forty participated
in the control conditions, in which each participant was tested on a transform
but not trained on it. An equal number of control participants were randomly
assigned to each transform.
Materials. The order of pitch classes in the first hexachord was determined
by randomly choosing a starting (white) pitch class, then randomly picking
a direction (clockwise or anticlockwise) and moving round the clock face systematically
in that direction, picking out the whites in order. For example, consider
the whites consisting of the set {0, 2, 7, 9, 10, 11} again. If the random
starting note was 9, and the random direction was clockwise, the first hexachord
would be: 9, 10, 11, 0, 2, 7 (A, Bb, B, C, D, G). Thus, for a transpose, the
second hexachord would be 3, 4, 5, 6, 8, 1 (Eb, E, F, F#, Ab, Db). Each note
was played in the octave that ensured the interval from the last note lay
within the range -5...+6 semitones (for the nonoctified materials only). This
procedure ensured that the second hexachord was a literal pitch transformation
of the first (for the nonoctifed materials); that is, the transforms respected
normal arithmetic rather than modulo arithmetic. The two hexachords were separated
by a delay of one second to help draw attention to the hexachord structure
of the tone row. Also, unlike experiment 1, the distractor items were not
randomly scrambled: In nongrammatical tone rows, the second hexachord was
a cyclic permutation of what the grammatical one would be (cyclic permutation
has "ecological validity" in that it is a devise employed by Stravinsky
and Krenek in their serialist pieces); specifically, the first tone of the
hexachord was moved to become the last tone of the hexachord. So for the example
being used in this paragraph, the second hexachord would become 4, 5, 6, 8,
1, 3 (creating the non-grammatical tone row: 9, 10, 11, 0, 2, 7, 4, 5, 6,
8, 1, 3).
Procedure. The procedure for the trained participants was the same
as in experiment 1, only the materials differed. The control participants
participated in only the test phase.
Results
To our surprise, trained participants once again performed at chance for each
transform. The means and standard errors are shown in Table 1.
Table 1.
Percent correct classification (standard errors in parentheses).
| Trained participants: | Control participants: | |||
| Transform: | Nonoctified: | Octified: | Nonoctified: | Octified: |
| transpose | 50.6 (4.5) | 60.0 (5.0) | 53.1 (3.0) | 54.6 (4.9) |
| inversion | 44.1 (3.4) | 60.0 (8.2) | 57.7 (3.3) | 56.6 (4.5) |
| retrograde | 42.0 (3.5) | 45.7 (6.7) | 47.4 (2.8) | 59.7 (3.6) |
| inverse retrograde | 45.7 (3.0) | 63.8 (7.9) | 45.9 (3.7) | 55.8 (4.9) |
A three-way (training (trained vs control) by transform (transpose vs inversion
vs retrograde vs inverse retrograde) by octave displacement (octified vs non-octified))
mixed model ANOVA indicated no main effect of training, F(1, 60) = 0.98, p
= .33, MSe = 0.019, and no interactions involving training (all p's > .10).
The upper limit of the 95% CI on the difference between trained and control
scores is 1%. That is, the lack of learning of the trained participants is
established to a high degree of sensitivity.
The only significant effect was the main effect of octave displacement, F(1,
60) = 13.86, p < .0005, MSe = 0.018, with all participants performing better
on the octified rather than non-octified stimuli. Because there was no octave
displacement by training interaction, F(1, 60) = 1.71, p = 0.20, MSe = 0.018,
the effect of octave displacement is not due to anything learnt in the training
phase but due to pre-existing biases people bring to the test phase.
Six of the 28 trained participants had achieved grade 5 or better on a musical instrument; the rest had very little or no musical training. Comparing these two groups, on the non-octified material the "musically experienced" participants classified 45% (SD = 11%) of the materials correctly and the musically inexperiened classified 46% (SD = 10%) of the materials correctly, the difference was not significant, t(26) = 0.23. For the octified materials, the musically experienced scored 50% (SD = 18%) and the musically inexperienced scored 59% (SD = 19%), t(26) = 1.07.
In summary, there is no evidence for learning with these materials.