FM synthesis on the Modular

Author: Rob Hordijk

FM synthesis is a way of generating musically interesting sounds by rapidly changing the basic frequency of a sound in a repetitious way. The pattern of change comes from another waveform with a frequency in the hearing range. In practice it just means connecting the audio output of e.g. an oscillator to a frequency input of another oscillator. But there is a lot to say about which waveforms and which frequency inputs to use.

The good news is that the Nord Mordular is capable of doing all FM sound-generating techniques possible. In this chapter we will sum up all these possibilities and present you with some more indept information about the how and why. We will NOT go into the complex mathematics of FM or soundspectra, only the directly practical and musical aspects will be covered. If you're interested in the theory look at the writings of people like Dr. Chowning or Barry Truax.

Frequency modulation of a waveform is originally a radiotechnique in use for a very long time. Dr. Chowning is credited for first exploring the musical capabilities of frequency modulation. To do frequency modulation we start with two oscillators. One is used to modulate the frequency of the second oscillator and the output of the second one is used to listen to. Mostly sinewaves are used, but on the Modular you are by no means limited to sinewaves. Actually we can use any waveform and even sounds coming in at the audio input. However the more complex the modulating waveform the more complex the resulting waveform, and the most complex waveform of all is actually noise. So the trick of FM is not to end up with only noise, as for those purposes you can directly use a noise generator.

(A japanese manufacturer known for building sythesizers based solely on the FM priciple, doesn't use the name oscillator but carrier and operator instead.)

Two types of FM

There are two basic types of FM, namely true FM and PM. In true FM it is the actual frequency parameter that is manipulated. In PM the frequency parameter is fixed but it is the phase of the waveform that is manipulated, so that's why the proper name should be P(hase) M(odulation). PM is only available on digital synthesizers as it requires rock-stable oscillators. Sonically they both generate the same type of sound, FM however is such a common acronym that you will read FM in most papers although PM might be the real technique used. Actually the mentioned japanese manufacturer uses PM instead of FM, but they always name it FM.
There are two advantages of PM over FM. The first is that it allows selfmodulation of an oscillator without changing the fundamental frequency of the resulting waveform. The second is that the fundamental of the resulting waveform doesn't drift if the modulating waveform contains a DC component (DC as opposed to AC), meaning that the average energy of the waveform is slightly positive or negative instead of true zero.

Modulation index

The amount of modulation or volume level we apply to the second oscillator is commonly known as the modulation index. It's difficult to calculate the actual spectrum of the resulting sound from the modulation index, this involves mathematics with Bessel-functions, but the rule of thumb is that the more modulation you apply the brighter the sound gets, resulting in noise if the modulation index is very high. If we increase the modulation index of a sinewave modulating another sinewave, the resulting waveform changes from a sinewave at modulation index 0, through an increasingly more complex and brighter waveform, to noise at a very high modulation index. The change into noise is quite sudden and this can be used in many creative ways.

Linear versus logaritmic

The frequency of an analog oscillator can be controlled in a linear or logarithmic fashion, commonly known as Volt/Hz or Volt/Octave. Most analog sythesizers work with Volt/Octave to control the pitch from a keyboard. The Modular uses the same system on the Pitch inputs of the master oscillators, increasing the signallevel on the pitch-input with one unit raises the pitch with one semi-tone. Internally, however, analog oscillators work with Volt/Hz and the grey slave inputs of the slave oscillators on the Modular need the digital equivalent of the Volt/Hz signal. Such a signal is generated by the master oscillators grey outputs.

Volt/Octave or logarithmic type of signals can be manipulated much more predictable if used for general modulation from LFO's and Sequencer modules to play and bend notes. For FM however using the Volt/Hz type or linear signal gives the most predictable results, it also produces less easily unwanted inharmonic material. So extra inputs for linear FM are needed on the oscillators and these are the FMA and FMB inputs.
The difference between the FMA and FMB is that the FMA input modulates the actual frequency and FMB modulates the phase of the modulated oscillator, thus FMB actually being PM. FMA is currently present on most oscillators, FMB only on the FMB slave oscillator.

Frequency ratios and fixed formants

Last but not least, it also makes a difference if we modulate an oscillator with a specific frequency in a given ratio to the frequency of the modulating oscilator, or if we modulate an oscillator with a basic frequency of zero Hertz. If an oscillator is set to zero frequency it doesn't generate sound at all. This can be done by feeding a signal of zero units into a slave oscillators grey input. Modulating a frequency of zero Hz means that we will sweep the frequency around zero Hz. This will in effect give fixed formants in the resulting waveform. In addition to these fixed formants the frequency of the resulting waveform will also be the same as the frequency of the modulating oscillator. As we modulate "silence" in the rhythm of the modulating oscillator, it is only the modulating oscillators fundamental frequency that defines the resulting fundamental frequency in the mathematics. This also opens up the possibility to FM an oscillator with an outside audiosignal in a more or less predictable way. The resulting waveform will inherit its resulting fundamental frequency from that outside signal. This subject is also described in the Softsync workshop.

To my knowledge, at the moment of this writing, only the Modular possesses all of the mentioned features in a freely programmable way.

Combining with oscillator syncronisation

It is very interesting to combine FM with the use of the sync input of the oscillators that have one. Besides the frequency ratio and the modulation index of the two or more oscillators, a difference in phase can also influence the resulting waveform and hence make a patch sound different on each new keypress. Syncing the modulated oscillator(s) to the modulating oscillator(s) or keyboard gate signal can solve this, if this is an unwanted feature of your patch.
Next to this, combining sync and FM opens up a whole new range of soundspectra, in sound more predictable then FM alone, as there is no chance of the modulating oscillators fundamental drifting away when increasing or decreasing the modulation index, due to a modulation index dependent DC-component in the resulting waveform when using the FMA inputs or using the logaritmic Pitch inputs. Also the resulting wave is less likely to become inharmonic. More on this subject is in the Softsync workshop.

Summary

1. We can modulate either the frequency or the phase of an oscillators waveform by using the FMA/Pitch or FMB inputs
2. We can modulate in a logarithmic or linear fashion
3. We can modulate an oscillator with a given frequency ratio to the modulating oscillator or we can modulate a zero frequency oscillator which gives fixed formants
4. We can additionally use oscillator sync to overcome detuning problems with FM or to generate an additional range of soundspectra

The workshop

Now we will give simple examples of all the combinations possible. There is a good reason to keep it simple, for using FM without the mathematics, its good to experiment a lot with the different possibilities to acquire an intuitive feel for the type of sounds possible. And if you do want to apply the mathematics involved, be warned, they are highly complex.
The examples can be used as basic building blocks for you experiments.

The basic two oscillator linear FM building block

Opening the FMA knob will increase the modulation index resulting in a brighter sound, opening it very far will result in noise. As the modulation index is also dependent of the volumelevel of the OscC1 we can control the sound by modulating the AM input on OscC1. With the partials setting on OscSlvE1 the frequency ratio can be set. If this setting is not a whole number the sound will contain inharmonic components, useful for metallic sounds.

The basic two oscillator PM building block

You can hear a slight difference in sonic development when playing with the FMB control, compared to the first example.

The basic logaritmic FM building block

Changing the Pitch controlknob will sound very much like a ringmodulator. Lots of inharmonic components can easily be heard. There is also a change in basic pitch when changing the modulation index.

Selfmodulation

Only the FMB input offers the possibility of selfmodulation without changing the fundamental frequency. On all other oscillators the fundamental frequency will drift away if the modulation index is increased.

Controlling the modulation index by e.g. an envelope

To control the modulation index by another module we can insert a gain controlling module like an envelope generator or a gain controller from the mixers section.

An alternative way of controlling the modulation index

The AM input is a built-in gain controller so applying a signal to the AM input controls the modulation index as well.

In the previous example we hear the sound gradually changing as a result of phasedrift between the two oscillators. This can be overcome by connecting the output of the modulating oscillator to the sync input of the modulated oscillator. Note that from the slave oscillators only OSC SlaveA, OSC Sine bank and OSC Slave FM have sync inputs.

Fixed formant FM

In this example we force the slave oscillator to a fundamental frequency of zero Hz by connecting a constant value of 0 units to the grey input. If the knob on the FMB input is closed we will hear no sound, gradually opening the FMB knob will result in a increasingly bright sound. If we play notes on the keyboard we will hear that the sound has strong formants that remain fixed in the sound spectrum. This is especially obvious with a bright sound and playing low notes. Regrettably the structure of the formants is pretty complex, its not straightforward to impose the formant structure of a specific acoustic realworld instrument, this would require more oscillator sets and some pretty complex mathematics. So experiment with this patching to get some intuitive feel for usable settings.

Alternative way to control fixed formant FM

As the average mean of e.g. a sine waveform is zero we can immediately connect the output of an oscillator to the grey input of a slave oscillator. We can control the sound by either increasing or decreasing the volume level of the modulating waveform and/or playing with the Partials or Detune controls on the slave oscillator.

Note that the FMB input is now free to be modulated by another source.

Percussive formant FM

In this patch we use a percussive oscillator to modulate a slave oscillator. Connecting the trigger that goes to the PercOsc1 also to the sync input of the modulated slave oscillator will prevent the sound from slowly drifting.

Combining different ways of FM

Here we added an envelope that rhythmically modulates the selfmodulation of a fixed formant FM patch, modulated by a percussive oscillator. Interesting for generating industrial noise kind of sounds.

Logaritmic FM of a zero frequency oscillator

Compared to linear FM, logaritmic FM gives a different, more ringmodulator-like sound. Its interesting to see what happens if we do this with a modulated oscillator set to a zero frequency. What we do is generate two grey signals and subtract them from each other. This will result in a zero value, setting the slave oscillator to a basic frequency of zero. Now we can use a pitch input of one of the masters to modulate the grey signal in a logaritmic way. As we need to do this with audio material we use only red input and output modules, to insure the highest sound quality. The modulation index can be controlled by the AM input on OscSlvE1 or the pitch input on OscC1. Note that applying a signal to the FMA input on OscC1 will not affect the sound in any way, as the FMA input does have no effect on the grey output signal of a master oscillator.

FM'ing the Sinebank

As you might have noticed the Sinebank oscillator can be used for much more purposes than drawbar organ patches.

Using the audio input for FM

In this patch we use audio material to frequency modulate a zero frequency oscillator to make the result inherits the audio materials basic pitch. This works best with not to complex, single pitched sounds. Connecting a guitar and playing with the Overdrive1 and Mod. Index knobs will give effects not found on common guitar stomp boxes.
As there might be noise on the input and the Modulars AD converters might have some slight DC-offset, the output might not be silent without an input signal. In this case we can add a noise gate patching in the following way. CompareLev1 sets the noise gates treshold.

This concludes our overview of the FM possibilities of the Modular. Hopefully there has been enough material to ignite your imagination and creativety.