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B.4 FM RATIOS

APPENDIX B: THE FM TONE SYNTHESIS > B.4 FM RATIOS · PDF 第 107–108 · OS 1.10D

# B.4 FM RATIOS

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:

APPENDIX B: THE FM TONE SYNTHESIS
C which always works like a carrier, is limited mostly to integers since it is generally used for carrying the
base note of the sound. For more information, please see “A.2.1 FM TONE” on page 89.
A has a more extensive number of ratio values to allow for more inharmonic relationships. For more informa­
tion, please see “A.2.1 FM TONE” on page 89.
B (B1 and B2) controls both operators at the same time. The minimum value for B1 and B2 is .25. As you
turn the encoder, B2 increases until it reaches the max (16). It then starts over from .25 and B1 increases to
the next value (0.5). This revolving behavior continues until both operators reach the maximum value. This
parameter behavior is similar to the movement of the hands on a watch. For more information, please see
“A.2.1 FM TONE” on page 89.
B.5 OPERATOR ENVELOPES
If you modulate one oscillator directly with another it creates very harsh harmonics, so you need to limit the
modulation level to control the amount of modulation. In Digitone II you use an envelope and a LEVEL pa­
rameter control to attenuate the amount of how much the modulator affects the carrier. The envelopes also
give the possibility to control the modulation over time. A piano for example, when first struck, the timbre is
sharp but quickly fades to a softer tone. Envelopes and modulation level are vital elements in FM synthesis
and are the tools that you use to shape the sounds you want to achieve.
The Digitone II FM engine has two operator envelopes that are designed to be practical and easy to use.
One envelope is for operator group A, and one is for group B (B1 and B2).
The envelopes are essentially expanded AD (Attack Decay) envelopes, but with an added adjustable end
level (the amplitude level the sound reaches at the end of the decay stage). Normally, an AD envelope al­
ways ends at zero level, but with FM you often want to retain some modulation after a short pluck or fade in
for example. For more information, please see “A.2.1 FM TONE” on page 89.
Please note that operator envelope B controls the output from both B1 and B2.
The envelopes can be either triggered or gated - making it either an ADE (Attack Decay End) or an ASDE
(Attack Sustain Decay End) envelope. The sustain phase does not have an envelope level. It is instead the
LEV parameter that sets the sustain level. The note length defines the length of the sustain phase. For more
information, please see “A.2.1 FM TONE” on page 89.
Trigged (ATRG/BTRG ON)
Attack
End level
Decay
Note on
Gated (ATRG/BTRG OFF)
Attack
Decay
End level
Sustain
Note on
Note off
You can also set if the envelopes should reset or not when they are retrigged. For more information, please
see “A.2.1 FM TONE” on page 89.

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