From the course: Learning Modular Synthesis: Eurorack Expansion

Waveforms, harmonics, and voltages

(electronics hum) - [Instructor] The way a synthesizer works is by creating voltages or electric currents, sending those out through its audio output, which eventually get routed to your speakers, which eventually vibrate the air to make sounds that you hear. I personally think a great way to learn how to use the synthesizer, particularly a modular synthesizer, is to get some insight on what's happening with those voltages moving around inside your system. To peer inside your machine, I like to use something like an oscilloscope. Think of it as a stethoscope or something they can see the oscillations of voltages happening inside your instrument. You can get an oscilloscope that's a big external device. You can get one that connects to your computer. I like using an oscilloscope module such as the Mordax Systems' DATA. This module has a lot of functions including acting as a tuner, acting as an oscillator, acting as a master clock, monitoring voltages in the system, but also looking at the waveforms of the voltages being created, as well as what harmonic spectra are being created by those. So let's go into oscilloscope display and look at some of these moving voltages. Now some voltages oscillate up and down at an audible rate, from 20 times to as many as 20,000 times a second. That's why we can hear them. So I'm going to plug in directly into an output of the sawtooth wave on the oscillator in my Moog Mother-32, and plug that into the input on one channel of my data. And there is a nice clean, sawtooth waveform. Now the way the data works is that below each input to its four channels is a jack that exactly replicates what's coming into that input. That way you're not losing the signal. You can still patch it somewhere else. So I'm going to take that output, run it to my audio output on my system, and now I can hear that sawtooth wave. Different wave shapes produce different sounds. They vibrate the air in different ways. The way we can analyze this is to look at the harmonic structure of a sound. Harmonics are individual components of a sound, similar to the way individual notes make up a chord. Typically, but not always, harmonics are spaced what are called integer intervals, where the second harmonic is at twice the frequency of the first, or the fundamental. And the third harmonic is three times the frequency, et cetera. The sawtooth wave has every harmonic present. So if I go ahead and measure the frequency of that fundamental harmonic, it's right around 131 hertz, an octave below middle C. The second spike which is not quite as tall, is around 262 hertz, that's the second harmonic. Three times that is right around indeed 390 hertz or so. And you notice that each of these harmonics get weaker as the frequencies go from low to high. That's why the fundamental, or the base, is a little bit more powerful than the high frequencies. Playing a different pitch results in the wave form being drawn more quickly. It also moves the harmonic spectrum up the frequency scale. As I mentioned, different waveforms have different sounds, and therefore different harmonic structure. Let's move over to the pulse or square wave. We see a nice square wave displayed on the oscilloscope, and over here on the spectrograph, we see gaps in between the harmonics being displayed. There's our fundamental again, right around 131 hertz or so, but the second harmonic is barely present at all, and actually, in a perfect square wave, there's no second harmonic present. You go straight to the third harmonic which is three times that fundamental frequency. No fourth harmonic present. The next one we see is the fifth harmonic, five times that fundamental frequency. That's why square waves have a more open, more hollow sound. And again as we change the wave shape, we'll change the character of the sound. I'll alter my pulse with making it a bit skinnier. As I do so, you hear the sound change. It becomes a bit more treble-ly. As we look at our spectrograph display, I'm using Audiofile Engineering's Spectre program, you'll notice that the fundamental eventually is suppressed in strength, and strange little humps start appearing in the higher harmonics. This creates this nasally tone we're hearing right now. Back to a square wave. Now the sawtooth and the square are indeed the most common waveforms you'll find in the synthesizer. Those are the two offered by the audio oscillator inside the Moog Mother-32, but different oscillators can provide different waveforms and therefore different sounds. Example, I have my Expert Sleeper's Disting set to an oscillator mode right now. I'll plug in one of its outputs, and there we're getting a very pure tone, a sine wave. This is the most pure sound a synthesizer can make. A perfect sine wave would only have one harmonic, its fundamental. This one has a slight bit of distortion and probably through the audio system that I'm running through here, therefore we're seeing a little bit of second harmonic present as well. I'll switch this to a different mode. Now we have a triangle wave which is a straightened up sine wave. Indeed, it's slightly brighter, and now we're seeing some additional odd harmonics present in the spectra. Changing the wave shape does indeed change the character of the sound that we hear. However, we have to be careful not to get too hung up on the details inside this wave shape. We're looking at overall changes. Example, if I was to go back and look at just my pure square wave again, you'll see how clean it looks on the data, but if I look at it after it's gone through the audio output in my synthesizer, through my mixing board and into my audio interface, you'll see what finally hits my computer looks considerably different than what's moving around inside my synthesizer. These little details indicate a little bit of the higher frequencies of a perfect square wave being removed, thanks to analog electronics not being perfect. There's also a phenomenon known as ringing that can happen after sharp transitions. So we can't get too hung up on details. We're just more interested in overall shapes. For example, if I was to go back to the sawtooth, indeed I'll take the output of my synthesizer here, switch to a sawtooth wave, turn the output amplifier on, I can start to shape that waveform using a filter to cut off some of the harmonics. I'll switch to a low pass mode, which only lets low harmonics through, and raise that cutoff frequency. I'll turn down the resonance for now. Now we have a softened sawtooth wave, and indeed, back in Spectre, those high harmonics have been suppressed. They have been filtered out or cut off. As I increase the resonance or the feedback in the circuit, you'll notice on this display, some additional humps will appear. That shows the filter is emphasizing some of the harmonics in the sound, rather than merely cutting them off. So I go ahead and move this frequency around. You can count how many humps we have in our waveform. I see basically, one, two, maybe about three humps per cycle of the sawtooth, and indeed, first, second, third harmonic is being emphasized due to this increased resonance. Maybe a little but of the fourth as well. It looked like I'm right in between the frequencies, so I can either dial-up to the fourth harmonic, and there you'll see four humps in the waveform. Or dial down to emphasizing the third harmonic. So that's how processing a sound inside the synthesizer not only changes its wave shape, but changes the harmonic makeup of the sound that we hear. Now just a quick techy side note, you'll notice that my oscilloscope display is a little bit unstable here. The more complex or the lower in level your waveform gets, the harder it's going to be for your oscilloscope to lock onto it. Fortunately, most scopes have the ability to synchronize to an external signal. So I've created for myself a preset in data that synchronizes to the input at jack number four. Let's load that up. Initially, nothing at jack four, waveforms just wandering across the screen. If I choose a pure waveform that hasn't been filtered and run that into the input four, you'll see my display suddenly get rock solid. So throughout this course, if you see this little black cable running into data, don't worry about it. It's not part of the patch. It's not changing the sound. I'm just using it to synchronize my oscilloscope, so you get a cleaner, more stable display. Now not all voltages inside a synthesizer move at audio rates. Sometimes they move much more slowly, just to change the pitch of the oscillator or to vary parameters such as the cough of the filter. We can also look at those on the oscilloscope by slowing things way down. I'm going to go ahead and turn this off for now, enter DATA's menu, press the fourth button to bring up the user presets, choose preset three which I created using a slower timescale and load that. Let's go back to the oscilloscope display, and I'll patch in some slowly moving voltages. For example, the output at a low frequency oscillator to modulate, something like a filter. You'll see it draws very closely across the screen there. That's the voltage going up and down in the synth which I can use to change the parameter inside it. I can even change to something like an envelope output. Trigger that envelope, and you can see the voltage rays, go back down to my sustain level, and then release back down to silence. So we'll also be using the data to analyze some of these more slowly moving voltages inside the synthesizer. Now the last note I'll throw in, you'll notice I'm using different colored patch cables, and throughout all of my courses, I color code my cables. Yellow cables carry audio signals. Blue cables carry the slower modulation signals, like envelopes and low-frequency oscillators. I'll also be using red cables for gates or trigger signals, things that initiate events inside a synthesizer, and white cables whenever I'm carrying a voltage that's supposed to define the pitch that I'm playing, what note my oscillators are supposed to be playing at. I'll distinguish that from other modulation voltages that are not necessarily related to pitch. So now that you have a basic idea of how voltages are moving around inside your synth, let's start exploring what support modules I consider to be essential, help extend the capabilities of your core synth or semi-modular synth and allow it to interface more easily to other modules you might want to add later on.

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