Are upward melodic leaps really more common than downward leaps?

Approach:

     First, we need to clarify what we mean by a melodic leap.
     For this demonstration, let's assume that a leap is any
     interval greater than 4 semitones.

     We'll use ten vocal lines from Lieder by Franz Schubert as
     the basis for this analysis.

     We can begin by transforming **kern representations to numerical
     semitone equivalents -- using the SEMITS command:

          semits -xt schub* > lieder.sem

     Next we need to calculate the semitone pitch difference
     between successive pitches (i.e. the melodic interval size).

     Avoid calculating intervals between pitches separated by rests:

          xdelta -s = -b r lieder.sem > intervals

     Now we can use the RECODE command to classify melodic intervals
     into one of five categories: (1) unison, (2) up-leap,
     (3) down-leap, (4) up-step, and (5) down-step.

     Here is an appropriate reassignment file for RECODE:

     	==0	unison
     	>=4	up-leap
     	<=-4	down-leap
     	>2	(undefined)
     	>0	up-step
     	<-2	(undefined)
     	<0	down-step

     Now run the appropriate RECODE command:

     recode -s '[]r=]' -i '**Xsemits' -f reassign intervals > classes.int

     Use the GREP -c command to identify and count the number of
     occurrences of each class of melodic interval:

          grep -c 'up-leap' classes.int
          grep -c 'up-step' classes.int  [etc.]

          upward leaps:  129
        downward leaps:  98
          upward steps:  163
        downward steps:  338
               unisons:  216

     Upward leaps appear to be about 30 percent more common than
     downward leaps.  (Downward steps are twice as common as upward
     steps.)