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B.2 OPERATORS

APPENDIX B: THE FM TONE SYNTHESIS > B.2 OPERATORS · PDF p. 106–107 · OS 1.10D

# B.2 OPERATORS

APPENDIX B: THE FM TONE SYNTHESIS
APPENDIX B: THE FM TONE SYNTHESIS
B.1 OVERVIEW
The Digitone II's FM TONE machine is a four operator Frequency Modulation (FM) synth in the style of the
classic 80s implementations. However, unlike the early FM synths, the Digitone II use its FM engine more
like a complex tone generator than a complete synthesizer voice (although it does have this capability too).
The Digitone II signal path is more similar to a typical subtractive synth than a classic FM voice.
FM
Overdrive
Multimode
Filter
Base-width
Filter
Amp
The idea of this design is to harness the raw, and often complex, soundscapes of FM synthesis and use a
more well-known and approachable subtractive method for the overall sound shaping.
FM is a synthesis method where you add harmonics to the timbre by using modulation or layering to shape
the sound. You add harmonics by modulating one oscillator’s pitch with the output of another oscillator. FM
works similarly to how you would apply vibrato via an LFO. At slower modulation rates, it is simply vibrato,
but when the modulating frequency reaches audio rate, the vibrato effects becomes a part of the sound and
becomes a timbral effect instead.
B.2 OPERATORS
In FM synthesis the oscillators are called operators. Unlike the analog oscillator, the operator also contains
an envelope and specific input and outputs, making it a sort of macro oscillator. FM combines two or more
operators to generate a more harmonically rich output. An operator that is used to modulate another opera­
tor is called a modulator. The operator that generates, or carries, the resulting tone is called a carrier.
Feedback is used to increase the sharpness of a sound and is usually only applied to modulators. The
output of the operator is fed back into itself, resulting in added harmonics. For example, have a look at the
Sounds B001 and B002 in the Digitone II to see how feedback is used to create a basic square and saw
waveform. For more information, please see “A.2.1 FM TONE” on page 89.
Operator
Waveform
Envelope
Feedback
Modulation
input
Output
Amplitude
Wavelength
(frequency)
Output
Modulator
(ratio: 8)
Carrier
(ratio: 1)

APPENDIX B: THE FM TONE SYNTHESIS
In some instances, an operator can be both carrier and modulator. This means that it outputs its result as a
tone while also using it to modulate another operator. We have divided the operators into three groups: C, A,
and B (B1 and B2) to lessen the complexity and make the Digitone II easier to use. Since group B consist of
two operators, the parameter controls for B are macro mapped to both operators.
B.3 ALGORITHMS
An algorithm is a set routing, or combination, of the operators. Routing the modulation in different ways
gives you several different methods of applying modulation and naturally different results.
Carrier
Envelope
Modulator
Feedback
Feedback
Modulator
Envelope output
Carrier
Direct output
Output
Algorithm
Modulation
Level
Pictured above is a 2 operator algorithm, which is FM synthesis in its most basic form. The Digitone II has
four operators available which can be routed in many different ways. Different algorithms dramatically
changes the characteristics of the output - for example stacking four operators can lead to very complex
timbres.
The Digitone II has eight different algorithms where the four operators are routed in different ways. For
more information, please see “A.2.1 FM TONE” on page 89. Each algorithm has two carrier outputs (X
and Y) that come from two different operators depending on what algorithm you chose. It is possible to
use the MIX parameter to mix between these outputs so that you can cross-fade between two separate
timbres. For more information, please see “A.2.1 FM TONE” on page 89.
The lines going to X and Y indicate the output from a carrier. There are two different ways a carrier output
is sent to the X/Y outputs: 1. Its amplitude is unaffected by the operator envelope (dotted line). 2. Its ampli­
tude is affected by the operator envelope (filled line). The sound from the X/Y outputs is then routed via the
overdrive to the filters.
B.4 FM RATIOS
Frequency modulation is applied in multipliers of the principal frequency to retain the sounds tonality. These
multipliers are known as ratios. Each operator group’s ratio is a multiplier of the input pitch (note value). The
higher the ratio, the higher the pitch frequency. For example, when applying modulation with a ratio of 1:2
(carrier:modulator), the carrier output resembles a square wave. A ratio of 1:1 sounds like a sawtooth, and
odd numbers can be used for various metallic or other “natural” sounds. In Digitone II, the FM ratios for the
different operator groups works like this:

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