expected that particular transition and adding it to the running total
score for the song.Thus,songs that contain more of the individual tran-
sitions that the female expects (e.g.,with many C-G transitions,if she
expects Cs to be followed by Gs very often) will be scored higher,and
she will prefer to mate with males who sing these songs.We call this the
local transition preferencescoring method.
In the second method,the female listens to a whole song first,count-
ing the number each type of transition occurs (e.g.,she might tally up Gs
following Cs four times and other notes following Cs two times).Then
from these counts she constructs a transition matrix for that particular
song (e.g.,with an entry of .66 for the C-G transition,because that is what
occurred two-thirds of the time after a C).Finally,she compares that
song’s transition table with her expected (preferred) transition table,and
the closer the tables match on an entry-by-entry basis,the higher score
and preference she gives to that song.
Thus,this method means that a female will prefer songs that match
the overall statistical pattern of transitions in her transition table.We call
this the global transition preferencescoring method.Continuing with our
example,if the female has a value of .75 stored in her own transition
table for the C-G transition,she will like songs most that have a C-G
transition exactly three-fourths of the time (along with other C-x transi-
tions,where x will be notes other than G,for the other quarter of the
time that C appears).In contrast,with local transition scoring,she would
prefer C-G transitions after every C,because they give a higher local
score than any other transition from C.
The third scoring method produces females that enjoy being surprised.
The female listens to each transition in the song individually as in the
first method,looks up how much she expected that transition,and sub-
tracts this probability value from the probability she attached to the tran-
sition she most expected to hear.Consider our female from the previous
paragraph.Whenever she hears a C,she most expects a G to follow it
(75% of the time).Imagine she instead hears a C-E transition.This is a
surprise to her,because it violates the C-G transition expectation,and
she likes this song more as a consequence.
But how much of a surprise was this note,and how much does it
increase her preference for this song? To find out,the female critic first
looks up the C-E transition in her table and finds she expected that tran-
sition 15% of the time (for example).Thus,this C-E transition was not
a complete surprise,because she had some expectation for it,but it was
a reasonably large one.We quantify the surprise level with a score of .75- .15 =.6 for that transition (i.e.,probability(C-G)—probability(C-E)).
This expected-minus-actual transition probability score is summed for all
transitions in the current song,and the final sum registers how much
377 Simulating the Evolution of Musical Behavior