Digital Sound & Music: Concepts, Applications, & Science, Chapter 6, last updated 6/25/2013
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These basic waveforms turn out to be very important in subtractive synthesis, as they serve as a
starting point from which other more complex sounds can be created.
To be able to create a sound by additive synthesis, you need to know the frequency
components to add together. It's usually difficult to get the sound you want by adding
waveforms from the ground up. In turns out that subtractive synthesis is often an easier way to
proceed.
Subtractive Synthesis 6.3.3.3
The first synthesizers, including the Moog and Buchla’s Music Box, were analog synthesizers
that made distinctive electronic sounds different from what is produced by traditional
instruments. This was part of the fascination that listeners had for them. They did this by
subtractive synthesis, a process that begins with a basic sound and then selectively removes
frequency components. The first digital synthesizers imitated their analog precursors. Thus,
when people speak of “analog synthesizers” today, they often mean digital subtractive
synthesizers. The Subtractor Polyphonic Synthesizer shown in Figure 6.19 is an example of one
of these.
The development of subtractive synthesis arose from an analysis of musical instruments
and the way they create their sound, the human voice being among those instruments. Such
sounds can be divided into two components: a source of excitation and a resonator. For a violin,
the source is the bow being drawn across the string, and the resonator is the body of the violin.
For the human voice, the source results from air movement and muscle contractions of the vocal
chords, and the resonator is the mouth. In a subtractive synthesizer, the source could be a pulse,
sawtooth, or triangle wave or random noise of different colors (colors corresponding to how the
noise is spread out over the frequency spectrum). Frequently, preset patches are provided, which
are basic waveforms with certain settings like amplitude envelopes already applied (another
usage of the term patch). Filters are provided that allow you to remove selected frequency
components. For example, you could start with a sawtooth wave and filter out some of the
higher harmonic frequencies, creating something that sounds fairly similar to a stringed
instrument. An amplitude envelope could be applied also to shape the attack, decay, sustain, and
release of the sound.
The exercise suggests that you experiment with subtractive synthesis in C++ by
beginning with a waveform, subtracting some of its frequency components, and applying an
envelope.
Amplitude Modulation (AM) 6.3.3.4
Amplitude, phase, and frequency modulation are three types of modulation that can be applied to
synthesize sounds in a digital synthesizer. We explain the mathematical operations below. In
Section 0, we defined modulation as the process of changing the shape of a waveform over time.
Modulation has long been used in analog telecommunication systems as a way to transmit a
signal on a fixed frequency channel. The frequency on which a television or radio station is
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