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What is (TZFM) Through-Zero Frequency Modulation?

Through-Zero Frequency Modulation (TZFM) is a synthesis technique used in various musical and sound applications, particularly in electronic music. The concept can be a bit complex, but I'll try to explain it in a clear and accessible manner.

Firstly, let's start with basic Frequency Modulation (FM). FM synthesis involves changing the frequency of one waveform (the "carrier") in accordance with the amplitude of another waveform (the "modulator"). This process can generate a wide variety of sounds, from complex harmonic tones to simple sine waves.

But there's a catch in traditional FM synthesis. When the modulator tries to push the carrier's frequency lower than zero Hz, it instead "wraps around" and becomes a very high frequency. This effect can produce unexpected and sometimes undesirable results, particularly a harsh, inharmonic sound as the carrier rapidly shifts from very low to very high frequencies.

Visual graphic courtesy of imgur.com.

Through-Zero Frequency Modulation is a Solution to This Problem

In Through-Zero Frequency Modulation, when the modulator pushes the carrier's frequency down to zero Hz and below, it will continue smoothly into negative frequencies. It may seem strange to talk about "negative frequencies", but in the realm of signal processing, a negative frequency is just a waveform phase-inverted (mirrored) and moving backward in time.

By allowing frequencies to pass through zero and go negative, Through-Zero Frequency Modulation creates a wider and smoother range of sonic possibilities, avoiding the harsh "frequency wrapping" of traditional FM synthesis. The result is more consistent, balanced, and musical sounds, particularly when creating complex, evolving tones such as those used in electronic and experimental music.

It's important to note that not all synthesizers, especially older or simpler models, support Through-Zero Frequency Modulation. However, many modern digital and software synthesizers do, and it's a feature sought after by sound designers and electronic musicians for the extended sonic palette it offers.

Through-Zero Frequency Modulation Oscillators Available at Patchwerks

Through-Zero Frequency Modulation Patch Example

Let's use a general modular synthesizer as an example to create a Through-Zero Frequency Modulation (TZFM) patch. Please note that the specifics can vary depending on the particular synthesizer or software you're using.

  1. Set up your carrier oscillator: This is the main sound source that you'll be hearing, so start by selecting the type of wave you want (sine, triangle, etc.), and set its frequency to your desired starting pitch.
  2. Set up your modulator oscillator: This oscillator will be controlling the frequency of the carrier. Again, select the type of wave you want and set its frequency. Remember, the frequency of the modulator will dictate the speed at which the carrier's frequency changes, and the wave type will affect how those changes occur.
  3. Set up Through-Zero Modulation: Not all oscillators will have this feature built-in. If yours does, there should be a dedicated input and a knob or control for adjusting the amount of modulation. Plug the output of the modulator oscillator into this input on the carrier oscillator, and start with the modulation amount turned down.
  4. Begin to introduce modulation: Slowly increase the amount of modulation from the modulator oscillator on the carrier oscillator. As you do this, you should hear the pitch of the carrier start to change in complex ways.
  5. Adjust to taste: The beauty of Through-Zero Frequency Modulation is in the richness and variety of the sounds it can create. Play around with the frequencies of both oscillators, the amount of modulation, and the waveforms of each oscillator until you get a sound that you like.

Remember, through-zero modulation allows the frequency of the carrier to go "below" zero and become a negative frequency, which manifests as a phase inversion of the waveform. So, unlike traditional FM, where the timbre becomes harsh and noisy as you approach zero Hz, in Through-Zero Frequency Modulation, you should hear a smoother, more balanced timbre across the entire frequency sweep.

It's also worth noting that Through-Zero Frequency Modulation can create quite complex and intense sounds, so it's often a good idea to start with simple waveforms like sine or triangle waves, and then experiment from there. Also, be careful with your volume levels, as the amplitude can become quite large when the carrier frequency is modulated to high values.

Here's a video by ALM Busy Circuits on their oscillator module, the TAZM-O Analog Thru Zero Oscillator, where you can hear some applications and sounds a Through-Zero Frequency Modulation oscillator can create. 

I hope this short introduction to Through-Zero Frequency Modulation is helpful and gets you excited to use your oscillators in a fun and exciting ways.