5 lf combinations of one sound source and one sound manipulator are

considered

the

number

of

sound manipulators should

equal the

number

of

sound sources

to

^g

íve the

maxîmum number

of

^permu.tat

ions.

l^/hen

combinations

of

one sound,source and two

or

more sound manipulators

are considered, the

^number

of

avai

lable

combinations increases

considerably,

and

the

number

of

sound manipuìators shouìd actuál ly exceed

the

number

of

sound sources

to give the

maximum number

of combínations. ln fact,

according

to the

assumptions,

the

greatest

number

of available

sounds occurs when

there is onìy

one sound source and

the

remaining resources

are

devoted

to nine

sound manipulators.

This Îs

because

the

number

of

arrangements

of nine

sound manipulators

is so Iarge.

However

there are

compìementary

factors to

be considered,

It is

convenient

to

produce more than one independent sound

at a

time.

This _requires

_{more than one sound source.}

Also it is

possible

to

use more than one sound source

to

produce

a given sound.

The

more

units

introduced

involved

^producing

a

sound,the,more

difficult is the operation of the synthesizer.

Completely

different

sounds

are

avai

lable

from

different

sound sources and would increase the range

of

avai

lable

sounds, whereas sound manipulators

give

some

similarity in the

sound produced.

It

was decided

to

use

six

^sound manipulators compared

with four

sound sou rces ^.

\.2.1

Operator Con

trol

The

re'lationship

between

the input

and

óutput of

most

of the

sound

manipulators can be

controìled

by

a voìtage. ln this

way

the

^operator can use

a control unit to

^produce

the sound.

For example

the

passband

frequency

of the filter

can be determined

by the positîon of a

ìever.

This is to allow real time control over the

sound produced.

4,2.2 Diversity

The

units are

^designed

to ^give very different effects on the

^sound.

The Harmonic Generator and

the

Frequency

Divider

add frequency components

which

are

above and predominantly below

the input

frequency

respectively.

The

multipì ier

adds frequency components which depend upon

two

inputs.

The Fi

lter

and Reverberation

units

do

not

add frequency components,

but

change those

present in very different ways.

^There

is

provision

for position control of the signal

by determining

the ratio of the

^ampì

itudes in

two channels, and

this is voltage

control led.

Each

un¡t ¡s

designed

to

have outputs which

are

capable

of a

wide range

of sound.

The

fi lter

has

hîgh,

low and band pass outputs;

the output of the

Frequency

Divider

preserves components

of

the

input

waveform

rather than the

uniform square wave

of logic circuitry

which

is

used

for the

frequency

division.

\-7

\.2.3 Predictabil ity

lJhen

a synthesizer is

used by a, musician

¡t is

^necessâry

for

^{him to}

be

able to

^assess

its

^{scope and}

its linlitations,

^{ancl bc}

ablc

[o achieve

an

intended resul

t.

The sound manipulators

are

des igned

to ^give predictîble transformations.

The

effect of a fi

^I

ter

^on

a

sound can be

predicted,

dnd

this allows the

musician to

systemmatically use

this facil ity.

^{A number}

of interesting electronic effects are

almost impossible

to set

uP

again.

These

effects

^may

depend upon some

critical triggering conditions, or perturbations

to

a

cômpìex

oscillatory conditìon. ln

each

of

these sound manipulators

a specific input to output relationship

^{has been} achieved.

A

filter is a very useful

sound

manipulator in a synthesizer. lt is a

powerful technique

for

modifying sounds, and

the effect

can

be readi

ly

appreciated

by the musician.

The

objective is to

design

a versatile filter

which can be

controìled by the musician.

The

filter for the

synthesizer

has high pass,

low pass and band pass outputs, and

its transfer characteristics are voltage

control led.

4.

¡. t

Second Order Fi I

ter

A

f¡lter

based on

the

biquad

principle

t was used

in this application.

A

simplified circuit of this

second

order filter

and

the

correspondíng

block

diagram

are given in diagrams lr.3.n.

_and

4.3.8. ln

^general th,is

fí lter

has

a transfer function of 2

poles and

2 or l.r, ,"ror.2

r(s) "2t

2

^{*"lt *"o}

brt' ⁺ brs *

^bo

where

^Zr.1,"oU

^O

b2'b'oot

o

Diagram

4.3.c

shows

the high pass,

low pass and band pass

transfer functions, the

corresponding

s plane

representations and

the

Bode

magnitude

plots. ln

^general

the

zeros can be on

the real axis

or complex

conjuqates. This

ci

rcuit is

^chosen

to ^locate the

zeros at

the origin

because

this gives a

more

su¡table

magnitude response

in the

bandpass and

high

pass

filters.

+ ^{+ +}

h i gh pass

Damping feedback loop

band pass

¡ npu

low pass

\oI

DIAGRAM

4.¡.n.

S¡mpl

ified cîrcuit of the

second order biquad

fi lter.

T

S

I

¡

tnpUt + S

amping feedback loo

DIAGRAM

4.3.8.

Control system representation

of the

second order

fi lter.

ìow pass output

1

O

Transf'er function

r (s)

2

2

4-11

2

cL S S S

x x x

o

x x

X

r (s) ^SO

2

r(s)

+soß *q,

²

BAND PASS

tnlrl,an

*so,ß+o

^{2 2 2}

jw

S

+saß

^+cr

LOVJ PAS S

S plane representation

jw

Bode _{m¿q¡ i} tude

tnlrl,au

ln

^w

H I GH PASS

Jw

2 o o

n ^\¡J

tnlrl,au

Hiqh

pass,

band pass

and

_{low ¡rass}

transfer

funct ions

s

pìane represenIations and Sådc magnitucle

pìots.

D I/\GRAM II, 3. ^C

ln

^w

Voìtage

control is

used

to

^change

tlre position of the poìes.

This

movement must

suit the musician's requireÌncnts.

Diagrarî 4.3. D gives

suitable

and

unsuitable loci.

The

suitable locus is

^such

that the

damping

factor is

rrnch¡nqerl

as

t.he

cutol-l'

f rcqtrc'rrcy

is

clr¡rngccl

,

^Tlrcre

is

^a

second

control

volLagc

for the

danrping I'acl-<¡r wlrich can bc

conlrollcd

independently

of the cutoff

frequency.

The

transfer functions for the filter of

diagram

4.3.4

can be found

using

block

diagram

manipulation.

Diagram

4.3.E is

used

to

show

the

lov¿ pass

transfer function is,

2

r(s)

cL

z 2

S

+scrß +

0

where

cr

^and

^p are gain

parameters on

the block

diagram

of

4.3.D

The bandpass

output is

present

at the input to the integrator

which has

the

low pass

output, C(s). lt follows that the

bandpass

output

is

sC(s)/o, Similarly the high

pass

output ¡s

,2c

(r)/o2.

The corresponding

transfer functions

are;

Bandpass

sT (s) ^sct

2

+saß *cr

2

H i gh

pas, ,2t

^(. ) S

2 2

S

+sqß

+cr

These polynomial expressions

giving the

poles and zeros

of the transfer functions illustrate that the desired loci of the

poles

will

be achicved

if the term 'tÌ' is ^voltage

^control

ìed. Tlris

corrcsponds

to altering the

gains

of both the integrators

and resul

rs in a

Frequency shi

tt without a

change

in the A of ^the fi lter.

Sini

larly rhe

damping

2

S

4-13

SU ITABLE LOCUS

(2)

* f.

(2")*f

UNSU IT/\BLE ^LOCUS

(z) *

(r

) --

(r) *X

(l',t) -J,/

jw

I

)¿

I

x

jw

S

plane

representation

output

vol tage same overshoot

(1'.)* f

(2;,7

*

output _.l tage

o

same envelope.

(z)

o

x t

t(

I

(z) (r

Step Response

Ga

in

^(db)

(r ₎

/

/u,

t t

(r)

(r ₎

Ga i

n

^(db)

,-\

I

lr--

^{z)

I

,'(2) -\

n (*)

\

Bode magn i t ude ^cl i a q rams .

DIAGRAM

lr.3.0. Su¡table

ancl

unsuital¡lc ìoci [or thc polcs

of=

the

l<¡w

pass f i

ltcr a:; tlre

I'requcncy

corrtroì votìage is

clrangccl .

ln(w)

\

\

R+

^c

I

S

I

s

a/s q/s

1

+

_ußls

n R

R C

2 n 0,

2 2 2

2

r(s)

2

S

*scrß+cr

S

+

2s6w +

whe

re

^cr

and 2ß

rn

n n

0braining thc tran:;[er

I'r-¡lrction

ol'

Lhc f

iltcr

ln,

ln,l t,tlrìltol

l,y,,tr,nt lrlor

l.

.ll.r,¡r,rrrr trr,rni¡rrrl:rt lolt.

1 + o2/(t2 +

saß)

+

soß)

o2 / (r2

DIAcRAM ^I+.3.8

\-

¹⁵