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!group skip 2
!begin center
≡4SOUND SYNTHESIS AND CONTROL OF TIMBRE≡1


PROBLEM 1
!end

!begin fill adjust
≡31. Step through the first five pages (1-1 to 1-5) of USEMUS.≡1

In these examples parameters and functions are entered directly
into the MUS10 program.  A difficulty here is that one has no record
of the typed information.  An error in playing the instrument SIMP or
in defining functions means that the information must be re-typed.

An alternative is to make use of ≡3files≡1 where parameter data is
typed into a file which is then read by MUS10.  As an example,
the information on line 18700, page 1-4 of USEMUS, can be entered
in the following way:
!END

!BEGIN NARROW 5,0
.≡2CREATE PSIMP≡5

00100    ≡2PLAY;SIMP 0 .2 C;SIMP .5;FINISH;≡5
00200    ≡2<ALT>≡5
*≡2E≡5

EXIT
↑C
.
!END

!BEGIN FILL ADJUST
≡1Now the parameter data is on the file "PSIMP".  When MUS10 askes
" INPUT? " you respond by typing the filename

!BEGIN NARROW 5,0
≡5INPUT? ≡2PSIMP≡1
!END

which instructs MUS10 to find a file by that name and then read the contents
of the file as if it had been typed directly to the program.

In the case of functions, rather than simply type into a file the
information as it is represented at line 21400, USEMUS page 1-4, we
will make use of a special program which allows us to make direct use
of graphics.  After a function is specified it is given a name (F1-15)
and entered into a file "NAME" .  As many as 15 functions can be entered
onto one file.  To run this program type

!BEGIN NARROW 5,0
.≡2R FUNC≡1
!END

(The operation of FUNC will be learned at the console)

By typing the monitor command ≡2DIR≡1 you will notice that whatever ≡2NAME≡1 you
gave to the function file now has the extension DAT.  When reading the function
file into MUS10 you must include the extension, for example

!BEGIN NARROW 5,0
≡5INPUT? ≡2NAME.DAT≡3
!END

2. Using the program FUNC and the instrument SIMP, experiment with various
wave shapes.  On a piece of paper, you should systematically keep a graphic 
record of every frequency contained in the wave and its relative amplitude.
This is the line-spectrum representation discussed at the last session
yesterday (see FIG 1A and FIG 2A handed out by John Grey).  Also on the
paper, record your impressions of the resulting effects on timbre (and pitch)
in the examples you generate.

Recently, a young scholar by the name of Helmholtz (1863) found the following
rules concerning the perception of steady-state periodic tones:  sinusoidal 
tones sound sweet and pleasant, without any roughness, but dull at low
frequencies; complex tones with moderately loud lower harmonics, up to the
6th, sound more musical and rich than simple tones, but they are still
sweet and pleasant if the higher harmonics are absent; complex tones consisting
of only odd harmonics (1st, 3rd, 5th, etc.) sound hollow and, if many harmonics
are present, nasal; predomination of the fundamental (1st harmonic) gives a
full tone, in the reverse the tone sounds empty; complex tones with strong
harmonics beyond the 6th or 7th sound sharp, rough and penetrating.  He also
concluded that the phase relationships between the harmonics did not have
a significant effect on the timbre of the resulting complex tones.

We shall be interested in looking at this budding scientist's findings in
our waveform synthesis today.  Here are a few suggestions to start with:

≡1a. Generate a wave composed of the first 5 harmonics all having the
same phase and relative amplitudes equal to 1/harmonic number.
Play SIMP at pitches C1, C2, C3, C4, and C5 for 1/2 second each, P2 equals .5,
(remember to create a file
for the play commands, we can use it for several experiments).

b. Now change the function such that there is no fundamental and play at 
the same five pitches as in (a.) above.

c. Add back the fundamental but with a change of phase of 90 degrees.  Also
change the phase of the 4th harmonic to 45 degrees.  Give this function a
new name and compare with the original wave.

d. Now add in some higher harmonics to the waveform, at amplitudes equal to
1/harmonic number, say up to the 12th harmonic.  Play at the pitches in (a.).

e. Increase the amplitudes of the highest harmonics quite a bit (from the 8th 
to the 12th harmonics) and play at the same pitches.  

f. Play waveforms that consist only of these higher harmonics (8 to 12th), 
and do not have harmonics 1 through 7.

g. Play waveforms that have only odd harmonics (1st, 3rd, 5th, etc.).

h. Play waveforms that consist only of three adjacent harmonics, from the
4th + 5th + 6th  to as high as the 18th + 19th + 20th.  What happens to
the timbre?  What to the pitch?  Play only at the pitch C3.

!END