Today we’ll begin our journey into BRENSO’s FM circuit, and we will start… From FALISTRI. Relax, take a breath, and prepare to dive into the world of exponential frequency modulation.

Most analog oscillators provide a stock of really cool waveforms like triangle, sawtooth, or pulse waves. However, some techniques can help us achieve many more wave shapes and timbres. One of these is frequency modulation, and we’ll talk about it in this video. Coming up!

1. Understanding FM

Every time we modulate an oscillator’s frequency with another oscillating signal, we are doing frequency modulation. If our modulating signal is an LFO, we call this modulation “vibrato.” We can easily create a vibrato with FALISTRI and the 321 utility module.

Let’s set the green oscillator to Loop and its time scale to Fast to obtain an oscillator. Then let’s patch its bipolar output to our CGM. It will be our carrier oscillator. For now, we can keep the wave shapes to linear, and achieve a classic triangle wave.

Then, let’s apply the same settings to the yellow oscillator, patch its bipolar output to a 321 input, and its output to the green V/oct input. It will be our modulator oscillator.Make sure that the inverter and the offset switches are off!

If we gently increase the signal level with the 321 knob, we can start hearing a vibrato effect, like the familiar modulation wheel on keyboard synthesizers. The timbre, though, still sounds like a triangle wave.

Now, let’s make the modulator faster and faster. At this point, it no longer sounds like a tremolo. What happened is that the modulating signal became faster than 20 Hz, and it became an audio signal. We can no longer perceive its individual oscillations, but we hear it as a sound. In fact, if we patch it to the CGM, we can hear a low triangle wave.

We must note that there is no physical difference between an LFO and an oscillator; the only difference is in our ears and our subjective hearing range. So they’re both vibrating air.

When we modulate an oscillator’s frequency at audio rate, we hear the interaction of both frequencies that results in a new timbre. This is the frequency modulation, and to understand what’s going on, we need to do some math, so brace yourself!

What FM does is create sidebands. Remember? We talked about them when discussing AM and RM.

Both ring modulation and amplitude modulation introduce external elements in the audio signal, called sidebands. In AM and RM, the sidebands are the sum and difference of the two oscillators’ frequencies. In FM, this is not always the case, for two reasons.

The first one is that the frequency of the sidebands depends on whether our FM is exponential or linear: more on this later on.

The second one is that the number of sidebands depends on a third parameter that we need to consider: the modulation amount.

When we do a vibrato, we can choose how fast it goes (which is its frequency), but also how “wide” it must be, which is how much it shifts our oscillator’s frequency up and down.

In this patch, we change this modulation amount through the 321 amplifier. Let’s bring our modulation signal back to audio rate. Even in this case, a different modulation amount creates different timbres because it generates more or fewer sidebands.

So, to sum up, we have two main parameters that change our sound through FM synthesis: the oscillator frequencies and the modulation amount.

At this point, it is worth noting that the new sidebands subtract energy from the Carrier’s frequency and the other sidebands so that the overall signal’s amplitude stays the same.

BUT! Some of you may have noticed something strange: the original pitch changes as we increase the modulation amount. How so? The key is in this symbol here or the very topic of this video.

2. Exponential FM

This symbol marks a V/oct input. The V/oct standard increases an oscillator frequency by one octave per volt. In other words, every positive increment of 1 volt doubles the oscillator’s frequency. This behavior is exponential and corresponds to the musical intervals that we generally use to make music.

When we apply a bipolar modulation to a V/oct input, the frequency will change more going up than going down. As a consequence, when we apply a bipolar LFO to a v/oct input, it modulates our oscillator by the same musical interval up and down, but the frequency increment and decrement are completely different.

For example, if our modulating oscillator goes up and down by one volt, the frequency of an A 440 will oscillate between A 880 and A 220. Our ears will thus perceive a central frequency of 880-220 Hz, therefore 660 Hz.

Since the way our modulation is applied is exponential, this technique is called exponential FM.

Exponential FM also has another quirk, which becomes evident once we start to play with the oscillators.

Let’s make a variation of this rudimentary FM patch that allows us to control both oscillator’s pitches.

First, we need to duplicate our V/oct signal by the first section of our 333. So we will patch the first one to the yellow V/oct input and the second one to the green one.

But the green oscillator is already receiving a signal! We’ll thus use another section of the 333 to combine the V/oct signal with the FM modulator.

The 333 sections are semi-normalled, so it is sufficient for us to just patch the yellow bipolar output to the second input of the second section to combine it with the V/oct signal patched to the first one.

Now we can patch the second section’s output to the green V/oct input. Again, if we keep our modulation amount at 0, we can hear the two oscillators play.

Once we increase the modulation amount, we can hear the frequency detuning that we talked about. If we keep increasing the modulation amount, we can come up with consonant sounds. Yes!

But here’s what happens once we change our notes. It is dissonant again! How so? The reason is that, with exponential FM, the modulation amount is different for every note.

We saw that if we modulate an A 440 by +/- 1 octave, its modulation bandwidth will be the average of 880 and 220, so 660 Hz.

However, if we modulate a B 4 493.88 Hz by +/-1 octave, its modulation bandwidth will be much higher, from 246.94 to 987.77, so 617,355 Hz, and so on.

The first result is that the perceived pitch will get higher and higher than the note’s nominal value.

The second result is that the frequency of the sidebands is much harder to calculate, being the modulation amount unbalanced across the carrier’s frequency.

The fact that we cannot play musical intervals with exponential FM shouldn’t refrain us from using it in our patches. We can obtain some fascinating eerie sounds that lead us to unpredictable territories.

For example, we can use SAPÈL’s sample and hold circuit to change the modulator’s frequency, and its fluctuating random voltages to control the modulation amount via FALISTRI’s four-quadrant multiplier.

Then, we patched SAPÈL’s clock output the slew limiter to obtain a very simple envelope.

We can also replicate this exponential FM patch with the BRENSO oscillator. We can use either oscillator as Carrier or modulator and activate the exponential FM circuit through these knobs here. This defines the amplitude of the modulator, which by default is the other oscillator’s sine wave. This other is deviation control, which defines the modulation bandwidth.

The cool thing about BRENSO is that we can voltage-control the modulation amount, so we can start with a consonant sound and make it more and more dissonant through an envelope.

Another cool thing is that we have several waveforms that we can use both as Carrier and modulator. The default one, as we said, is the sine wave. You may have noticed that the timbre is mellower than FALISTRI’s one: it’s because the sine waves have just one harmonic. They are the simplest available waveform, and their sidebands are pretty easy to calculate.

With BRENSO, however, we can use other waveforms, both as Carrier and modulators, and even process the modulated sound through the wavefolder. In this case, the timbre will be richer, even sharp and dissonant, because the FM rule now applies to every spectral component of the Carrier and modulator’s waveforms.

We can also use an external sound to modulate any of BRENSO’s oscillators, like FALISTRI, or even some of SAPÈL’s noise.

Now you may wonder: what if I do want to play melodies with FM just like I’d do with AM or RM?

The answer is that Exponential FM is not the only FM: there’s also Linear FM, where we can calculate the sidebands in a much more predictable way and achieve a modulation that lets us keep any pitch information, but we’ll talk about that in the next video, so see you there!