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␈↓"∧␈↓ α∧␈↓␈↓ β!␈↓βSOUND SYNTHESIS AND CONTROL OF TIMBRE␈↓


␈↓"∧␈↓ α∧␈↓␈↓ ε_PROBLEM 1


␈↓"∧␈↓ α∧␈↓␈↓α1. Step through the first five pages (1-1 to 1-5) of USEMUS.␈↓

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

␈↓"∧␈↓ α∧␈↓An␈αalternative␈αis␈αto␈αmake␈α
use␈αof␈α␈↓αfiles␈↓␈αwhere␈αparameter␈αdata␈α
is␈αtyped␈αinto␈αa␈αfile␈αwhich␈α
is␈αthen
␈↓ α∧␈↓read␈αby␈αMUS10.␈α As␈αan␈αexample,␈αthe␈αinformation␈αon␈αline␈α18700,␈αpage␈α1-4␈αof␈αUSEMUS,␈αcan␈α
be
␈↓ α∧␈↓entered in the following way:

␈↓"∧␈↓ α∧␈↓␈↓ αT.␈↓↓CREATE PSIMP␈↓∧

␈↓"∧␈↓ α∧␈↓∧␈↓ αT00100␈↓ βT ␈↓↓PLAY;SIMP 0 .2 C;SIMP .5;FINISH;␈↓∧
␈↓"∧␈↓ α∧␈↓∧␈↓ αT00200␈↓ βT ␈↓↓<ALT>␈↓∧
␈↓"∧␈↓ α∧␈↓∧␈↓ αT*␈↓↓E␈↓∧

␈↓"∧␈↓ α∧␈↓∧␈↓ αTEXIT
␈↓"∧␈↓ α∧␈↓∧␈↓ αT↑C
␈↓"∧␈↓ α∧␈↓∧␈↓ αT.


␈↓"∧␈↓ α∧␈↓Now␈α
the␈αparameter␈α
data␈α
is␈αon␈α
the␈αfile␈α
"PSIMP".␈α
 When␈αMUS10␈α
askes␈α
"␈αINPUT?␈α
"␈αyou␈α
respond
␈↓ α∧␈↓by typing the filename

␈↓"∧␈↓ α∧␈↓␈↓ αT␈↓∧INPUT? ␈↓↓PSIMP␈↓

␈↓"∧␈↓ α∧␈↓which␈α
instructs␈α
MUS10␈α
to␈α
find␈α
a␈α
file␈α
by␈α
that␈α
name␈α
and␈α
then␈α
read␈α
the␈α
contents␈α
of␈α
the␈α
file␈α
as␈αif␈α
it
␈↓ α∧␈↓had been typed directly to the program.

␈↓"∧␈↓ α∧␈↓In␈αthe␈αcase␈αof␈αfunctions,␈αrather␈αthan␈αsimply␈αtype␈αinto␈αa␈αfile␈αthe␈αinformation␈αas␈αit␈αis␈αrepresented
␈↓ α∧␈↓at␈α
line␈α∞21400,␈α
USEMUS␈α
page␈α∞1-4,␈α
we␈α
will␈α∞make␈α
use␈α
of␈α∞a␈α
special␈α
program␈α∞which␈α
allows␈α∞us␈α
to
␈↓ α∧␈↓make␈α⊂direct␈α⊂use␈α⊃of␈α⊂graphics.␈α⊂ After␈α⊃a␈α⊂function␈α⊂is␈α⊃specified␈α⊂it␈α⊂is␈α⊃given␈α⊂a␈α⊂name␈α⊃(F1-15)␈α⊂and
␈↓ α∧␈↓entered␈αinto␈α
a␈αfile␈α
"NAME"␈α.␈α
 As␈αmany␈α
as␈α15␈αfunctions␈α
can␈αbe␈α
entered␈αonto␈α
one␈αfile.␈α
 To␈αrun
␈↓ α∧␈↓this program type

␈↓"∧␈↓ α∧␈↓␈↓ αT.␈↓↓R FUNC␈↓


␈↓"∧␈↓ α∧␈↓(The operation of FUNC will be learned at the console)

␈↓"∧␈↓ α∧␈↓By␈α∞typing␈α
the␈α∞monitor␈α∞command␈α
␈↓↓DIR␈↓␈α∞you␈α
will␈α∞notice␈α∞that␈α
whatever␈α∞␈↓↓NAME␈↓␈α
you␈α∞gave␈α∞to␈α
the
␈↓ α∧␈↓function␈α∞file␈α∞now␈α∞has␈α∞the␈α∞extension␈α∞DAT.␈α∞ When␈α∞reading␈α∞the␈α∞function␈α∞file␈α∞into␈α∞MUS10␈α
you
␈↓ α∧␈↓must include the extension, for example

␈↓"∧␈↓ α∧␈↓␈↓ αT␈↓∧INPUT? ␈↓↓NAME.DAT␈↓α

␈↓"∧␈↓ α∧␈↓2.␈αUsing␈αthe␈αprogram␈αFUNC␈αand␈αthe␈αinstrument␈αSIMP,␈αexperiment␈αwith␈αvarious␈αwave␈αshapes.
␈↓ α∧␈↓On␈α⊃a␈α⊃piece␈α∩of␈α⊃paper,␈α⊃you␈α∩should␈α⊃systematically␈α⊃keep␈α⊃a␈α∩graphic␈α⊃record␈α⊃of␈α∩every␈α⊃frequency
␈↓ α∧␈↓contained␈α⊃in␈α⊂the␈α⊃wave␈α⊂and␈α⊃its␈α⊃relative␈α⊂amplitude.␈α⊃ This␈α⊂is␈α⊃the␈α⊃line-spectrum␈α⊂representation
␈↓ α∧␈↓discussed␈α∞at␈α∞the␈α∞last␈α∞session␈α∂yesterday␈α∞(see␈α∞FIG␈α∞1A␈α∞and␈α∂FIG␈α∞2A␈α∞handed␈α∞out␈α∞by␈α∂John␈α∞Grey).
␈↓ α∧␈↓Also␈αon␈αthe␈αpaper,␈αrecord␈αyour␈αimpressions␈αof␈αthe␈αresulting␈αeffects␈αon␈αtimbre␈α(and␈αpitch)␈αin␈αthe
␈↓ α∧␈↓examples you generate.

␈↓"∧␈↓ α∧␈↓Recently,␈α∃a␈α∃young␈α∃scholar␈α⊗by␈α∃the␈α∃name␈α∃of␈α⊗Helmholtz␈α∃(1863)␈α∃found␈α∃the␈α⊗following␈α∃rules
␈↓ α∧␈↓concerning␈α⊃the␈α∩perception␈α⊃of␈α∩steady-state␈α⊃periodic␈α∩tones:␈α⊃ sinusoidal␈α∩tones␈α⊃sound␈α∩sweet␈α⊃and
␈↓ α∧␈↓pleasant,␈α∂without␈α∂any␈α∂roughness,␈α∂but␈α∂dull␈α∞at␈α∂low␈α∂frequencies;␈α∂complex␈α∂tones␈α∂with␈α∞moderately
␈↓ α∧␈↓loud␈αlower␈αharmonics,␈αup␈αto␈αthe␈α6th,␈αsound␈αmore␈αmusical␈αand␈αrich␈αthan␈αsimple␈αtones,␈αbut␈αthey
␈↓ α∧␈↓are␈αstill␈αsweet␈α
and␈αpleasant␈αif␈α
the␈αhigher␈αharmonics␈α
are␈αabsent;␈αcomplex␈α
tones␈αconsisting␈αof␈α
only
␈↓ α∧␈↓odd␈α⊂harmonics␈α∂(1st,␈α⊂3rd,␈α⊂5th,␈α∂etc.)␈α⊂sound␈α⊂hollow␈α∂and,␈α⊂if␈α⊂many␈α∂harmonics␈α⊂are␈α⊂present,␈α∂nasal;
␈↓ α∧␈↓predomination␈α⊂of␈α⊂the␈α∂fundamental␈α⊂(1st␈α⊂harmonic)␈α⊂gives␈α∂a␈α⊂full␈α⊂tone,␈α∂in␈α⊂the␈α⊂reverse␈α⊂the␈α∂tone
␈↓ α∧␈↓sounds␈αempty;␈αcomplex␈αtones␈αwith␈αstrong␈αharmonics␈αbeyond␈αthe␈α6th␈αor␈α7th␈αsound␈αsharp,␈αrough
␈↓ α∧␈↓and␈α
penetrating.␈α
 He␈α
also␈αconcluded␈α
that␈α
the␈α
phase␈αrelationships␈α
between␈α
the␈α
harmonics␈αdid␈α
not
␈↓ α∧␈↓have a significant effect on the timbre of the resulting complex tones.

␈↓"∧␈↓ α∧␈↓We␈αshall␈αbe␈αinterested␈αin␈αlooking␈αat␈αthis␈αbudding␈αscientist's␈αfindings␈αin␈αour␈αwaveform␈αsynthesis
␈↓ α∧␈↓today.  Here are a few suggestions to start with:

␈↓"∧␈↓ α∧␈↓a.␈αGenerate␈αa␈α
wave␈αcomposed␈αof␈αthe␈α
first␈α5␈αharmonics␈αall␈α
having␈αthe␈αsame␈αphase␈α
and␈αrelative
␈↓ α∧␈↓amplitudes␈αequal␈α
to␈α1/harmonic␈α
number.␈α Play␈α
SIMP␈αat␈α
pitches␈αC1,␈α
C2,␈αC3,␈α
C4,␈αand␈α
C5␈αfor␈α
1/2
␈↓ α∧␈↓second␈αeach,␈αP2␈αequals␈α.5,␈α(remember␈αto␈αcreate␈αa␈αfile␈αfor␈αthe␈αplay␈αcommands,␈αwe␈αcan␈αuse␈α
it␈αfor
␈↓ α∧␈↓several experiments).

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

␈↓"∧␈↓ α∧␈↓c.␈α
Add␈αback␈α
the␈α
fundamental␈αbut␈α
with␈α
a␈αchange␈α
of␈α
phase␈αof␈α
90␈α
degrees.␈α Also␈α
change␈αthe␈α
phase
␈↓ α∧␈↓of␈α⊂the␈α∂4th␈α⊂harmonic␈α∂to␈α⊂45␈α∂degrees.␈α⊂ Give␈α∂this␈α⊂function␈α∂a␈α⊂new␈α∂name␈α⊂and␈α∂compare␈α⊂with␈α∂the
␈↓ α∧␈↓original wave.

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

␈↓"∧␈↓ α∧␈↓e.␈α⊃Increase␈α⊂the␈α⊃amplitudes␈α⊂of␈α⊃the␈α⊂highest␈α⊃harmonics␈α⊂quite␈α⊃a␈α⊂bit␈α⊃(from␈α⊂the␈α⊃8th␈α⊂to␈α⊃the␈α⊂12th
␈↓ α∧␈↓harmonics) and play at the same pitches.

␈↓"∧␈↓ α∧␈↓f.␈α∂Play␈α∞waveforms␈α∂that␈α∞consist␈α∂only␈α∞of␈α∂these␈α∂higher␈α∞harmonics␈α∂(8␈α∞to␈α∂12th),␈α∞and␈α∂do␈α∂not␈α∞have
␈↓ α∧␈↓harmonics 1 through 7.

␈↓"∧␈↓ α∧␈↓g. Play waveforms that have only odd harmonics (1st, 3rd, 5th, etc.).

␈↓"∧␈↓ α∧␈↓h.␈α
Play␈αwaveforms␈α
that␈α
consist␈αonly␈α
of␈α
three␈αadjacent␈α
harmonics,␈α
from␈αthe␈α
4th␈α
+␈α5th␈α
+␈α
6th␈α to␈α
as
␈↓ α∧␈↓high␈αas␈α
the␈α18th␈α
+␈α19th␈α+␈α
20th.␈α What␈α
happens␈αto␈α
the␈αtimbre?␈α What␈α
to␈αthe␈α
pitch?␈α Play␈αonly␈α
at
␈↓ α∧␈↓the pitch C3.