************************************
Main Group 50: Subtractive Synthesis
************************************


Sub Id  Contents

01      Basic Design RESON
    1   RAND source
09      Continuous Control of Bandwidth bw
    1   variable center frequency cfq
11      Continuous Control cfq and bw
    1   Glissandoing noise bands
51      Spectrum Proportional to Amplitude
    1   Bandwidth is 10% of amplitude
71      Two Constant Formant Regions
    1   BUZZ pulse as source

------------------------------------------------------------ next

Overview

RESON

So far we have used in this main group the general purpose filter
RESON, which has a control on the center frequency of the filter
and its bandwidth. A third optional input determines the mode of
functioning of RESON with respect to input/output ratio. The
signal will not be scaled (mode 0), have a peak response factor
of 1 (mode 1) or an overall response factor such that the overall
RMS value is raised to 1 (mode 2).

------------------------------------------------------------ next

Suggested Reading

Dodge, C, and T.A. Jerse 1985.
"Subtractive Synthesis."
Computer Music: Synthesis, Composition and Performance. 
Schirmer Books. pp. 155-194.

Moore, F.R. 1990.
"Digital Filters."
Elements of Computer Music.
Prentice-Hall, pp. 111-148.

Moore, F.R. 1990.
"Time-varying Digital Filters."
Elements of Computer Music.
Prentice-Hall, pp. 264-270.

Slawson, Wayne 1981.
"The Color of Sound: A Theoretical Study in Musical Timbre."
Music Theory Spectrum 3:123-141.

Slawson, Wayne 1982.
"The Musical Control of Sound Colour."
Canadian University Music Review 3:67-79.

Slawson, Wayne 1985.
Sound Color.
Berkeley: University of California Press, 266 pp.

Smith, J.O. 1985.
"An Introduction To Digital Filter Theory."
in J. Strawn, ed. 1985. 
Digital Audio Signal Processing: An Anthology. 
A-R Editions. pp. 69-136.

Smith, J.O. 1985.
"Fundamentals of Digital Filter Theory."
Reprinted in C.Roads, ed. 1989. 
The Music Machine. MIT Press, pp. 509-520.

------------------------------------------------------------ next

50_01_1
additional parameters: iperc


This simple design shows the basic idea of subtractive synthesis,
where a rich source is filtered to produce sounds.

The white noise form RAND's output is here filtered with a narrow
bandwidth (5% of the center frequency) RESON. This results in
evenly pitched noises for the whole range of audio frequencies.
(Dodge 1985: p.170)


(flowchart)
(.orc and .sco files)

------------------------------------------------------------ next

50_09_1
additional parameters: ipeakbw, iratebw


The instrument gives continuous control over the bandwidth of a
noise with a simple, but ingenious use of an LFO oscillator. A
sinus is taken from its lowest point at 270 degrees. By addition
of 1 and dividing by 2, the sinus takes on an all positive and
normalized bell shape. Applying the peak bandwidth value
completes the bandwidth controlling contour. The contour will run
at irate times a note, as irate is duration dependent.
The four notes played by this instrument show four different
settings that lead to very different tone qualities. Sounds can
be described as "rustling", "thumping", "scurrying",
"ringing","blowing", etc. (Dodge 1985: p. 171)

(flowchart)
(.orc and .sco files)

------------------------------------------------------------ next

50_11_1
additional parameters:


This design carries the idea of 50_09_1 a little further: center
frequency and bandwidth are both subject to continuous changes.
The instrument produces glissandoing noise bands.

The amplitude target of EXPON is set to the ratio of the highest
to the lowest center frequency. Then, multiplying the output of
EXPON with the center frequency lets icfq vary from the minimum
to the maximum frequency during the duration of the tone.

The right oscillator (playing a line function from 0 to 1) is fed
a peak deviation in percentages. A minimum percentage is added
before this control signal is scaled by the value of kcfq, thus
making bandwidth dependent on center frequency.

Three notes are played: 1 1/2 octaves up in 4 sec
                        2 1/2 octaves up in 4 sec
                        7 octaves down in 6 sec

The minimum bandwidth is in all case 5% of the center frequency
(thus starting with a pitched noise) and finishes at a maximum of
50% (35%) of the center frequency (coloured noise). (Dodge 1985:
p. 172)

(flowchart)
(.orc and .sco files)

------------------------------------------------------------ next

50_51_1
additional parameters:


Here the spectrum is varied, in proportion to the amplitude of
the tone, a situation commonly encountered in  "natural" music
instruments. The technique is frequently used by musicians and
referred to as harmonic enveloping.

Care has to be taken to choose the correct scaling factor
mediating between amplitudes and bandwidths. In this case the
bandwidth is 10% of the amplitude value of the tones. Some
different amplitudes values are presented in the score, ranging
from 4000 to 160000.

Note also: If RESON is used as a low pass filter (icfq=0), the
actual cutoff frequency of the filter will be .707 times the
value of kbw. (Dodge 1985: p. 174)


(flowchart)
(.orc and .sco files)

------------------------------------------------------------ next

50_71_1
additional parameters:


This subtractive instrument is based on a buzzy source,
containing harmonics in equal strength up to the Nyquist.
After being filtered by two RESON filters (scaling mode 0:
no scaling of the signal) at respective center frequencies of
1000 Hz and 3000 Hz, the input of RESON 1 is balanced with the
output of RESON 2.

The first section plays a scale in C major, the second section
plays a dominant seventh chord in C major.

(flowchart)
(.orc and .sco files)
