Structure and Interpretation of Music Concepts

                  Chapter 2 -- Music Primitives
                     Homework no. 1 

Due: Nov. 7th, 2002

This homework assignment is your first "meeting" with Scheme.
You can consult with the notes of class1-scheme.txt.
The book is always a great source. The POP notes follow the book chapters
(found in the bib link in the course site).

1. Define a procedure named 'square-dif-pitch' that takes 3 numbers as
   arguments and returns a note whose pitch, duration, and loudness values are
   the square of the difference of the 2 smaller numbers.

2. Given the following two procedures:
   (define (increase-pitch pitch)
     (increase-pitch
        (make-pitch (add1 (pitch-class pitch))
                    (pitch-octave pitch))))

   (define (test-pitch p q)
     (if (= (midi-pitch p) 60)
         0
         q))

   What is the result of evaluating the form
    (test-pitch (make-pitch 0 4) (increase-pitch (make-pitch 5 3)))
   under applicative-order evaluation and under normal-order evaluation?

3. Suggest an appropriate note-value for a rest. Note that it must have
   a duration property.

4. The pitch linear upward curve given in class results a simultaneous play
   for all notes. In order to repair the problem we need to enable some
   delayed play.
   a. Write a procedure for delayed play of a note.
   b. The delayed play can be used within two different accounts for the
      machine clock:
      1. The machine clock, sampled by applying
         > (midi-get-time)
         2233299029
         is computed prior to every play -- and the delayed play is computed
         relative to it.
      2. The machine clock is sampled only once -- in the beginning,
         and the desired delayes are accumulated relative to it.
      Write two different procedures that demonstrate the two approaches.
      Discuss  and demonstrate the advantages/drawbacks of each.
      If you need a time-consuming procedure, you can use the recursive
      Fibonacci procedure defined in SICP (1.2 -- see also POP notes,
      class2).

   Always, take care to use the embedded procedures style of writing,
   taking advantage of lexical scoping to remove unnecessary parameters
   from the embedded procedures.

5. Suppose that we replace the primitive procedure "if" by a compound
   procedure "new-if", defined using "cond" as follows:

     (define (new-if predicate then-clause else-clause)
       (cond (predicate then-clause)
             (else else-clause)))

   For example: (new-if (= 5 5) 0 1)
   evaluates to 0, and (new-if (= 5 6) 0 1) evaluates to 1. Try it!

   Consider the following procedure for computing the factorial function:

      (define (factorial n)
        (new-if (= n 1)
                1
                (* n (factorial (- n 1) ) )
                           ))

   Try this definition of factorial. Explain what happens.