Enchanting Instruments 114 - U-he Zebralette3 BETA2 Review Part 3

Additive Synthesis in Zebralette3

This time I’m going to talk about the additive mode of Zebralette3.

Additive synthesis isn’t particularly common, but it is one of the classical sound synthesis methods. The stop levers used for tone control in pipe organs can be thought of as a type of additive synthesis. Various waveforms can be created by playing sine waves from the fundamental simultaneously to any desired integer overtones and adjusting the amplitude of each overtone.

In the video below, we are going to start with a sine wave of just the fundamental tone in Zebralette3, then add one overtone at a time, layering them up to the 128th overtone to form a sawtooth wave. Mathematically, the amplitude of each overtone is the reciprocal of its harmonic number, but Zebralette3 allows for the selection of several different methods.

This is what it sounds like. It starts as a sine wave, but as you add overtones, you can hear it transform into a sawtooth wave.

Display

There are several ways to perform additive synthesis in Zebralette3, but if you want to directly draw the harmonics, the following method is recommended.
The horizontal axis displays the harmonics on a logarithmic scale and the vertical axis represents amplitude. Each harmonic’s amplitude is controlled using vectors.
The display size can also be enlarged and the harmonic numbers are shown, allowing for detailed editing with a feel similar to using a drawing application.
Compared to the traditional bar graph, this display is smarter and easier to handle.
The number of harmonics is specified separately in the Harmonics section.
Only the first harmonic has maximum amplitude and all other harmonics are set to zero in the figure below.
In other words, only the fundamental tone is output, resulting in a sine wave.

Unique Additive Mode

The additive mode in Zebralette3 is a rather unusual form of additive synthesis. While the phase of each harmonic is initially aligned, it quickly becomes disordered.
The video below shows a sawtooth wave, but the waveform begins to collapse and seems unlikely to ever return to the shape of a sawtooth wave.
This means it is difficult to identify the waveform using an oscilloscope.

The following sample uses the above sound, and although it continues to play the same sawtooth wave, it still sounds consistent.

This is because human hearing is not very sensitive to changes in phase.
It may seem questionable why an additive mode with such phase disorder was intentionally implemented, but it appears this is the result of balancing computational cost.
Because of this, attempting to check the waveform with an oscilloscope can be confusing, so it's a point worth knowing in advance.

Controlling 16 to 1024 Harmonics

Zebralette3’s additive synthesis handles harmonics in steps, from 16 up to 1024.
With fewer harmonics, the computational load is reduced, resulting in lower CPU usage. However, when playing low-pitched sounds, the lack of high-frequency content tends to become noticeable.
When using the maximum 1024 harmonics, even low-pitched sounds generate overtones up to the Nyquist frequency. This often yields better results for bass or percussion sounds, though at the cost of increased processing.
Therefore, in Zebralette3, it’s important to be conscious of the optimal number of harmonics for the sound you're aiming to produce.

In the next sample, the number of harmonics in a sawtooth wave is increased every 0.5 seconds to: 16, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, and 1024.
Beyond 192 harmonics, the differences become less noticeable.

Zebralette3 allows various manipulations of each harmonic. However, with a maximum of 1024 harmonics, manually adjusting the level of each one isn’t practical.
To address this, it offers bulk control features. A few of these methods are introduced below.

Control of Even and Odd Harmonics

By using an effect in Zebralette 3 called FX Spectral Focus, you can adjust even and odd harmonics.
For example, in the video below, increasing the Odd (odd harmonics) component of a sawtooth wave eventually results in only odd harmonics remaining, making the waveform resemble a square wave.
Additive synthesis requires understanding the relationship between harmonics and waveforms, but it offers great flexibility.

Spectral Dist – Stretching and Compressing Harmonics

When the Renderer is set to Additive, a parameter called Spectral Dist appears, enabling operations unique to additive synthesis.

Harmonics that define pitch are generally integer multiples of the fundamental frequency and appear evenly spaced in a linear frequency spectrum display.
By disrupting this spacing, the harmonics become non-integer multiples, and the sense of pitch is gradually lost.
While this might seem like a disadvantage at first glance, it actually allows for the emulation of percussive sounds and other tones with a weak sense of pitch.

As an example, applying Expansion to a sawtooth wave that includes clean integer harmonics causes the higher harmonics to stretch upward when Spectral Dist is turned from 0 to 100.

Next, applying the opposite effect, Compression, to the sawtooth wave results in the harmonics collapsing toward the fundamental. Eventually, the waveform settles into a sine wave.

The following sample is an example of applying Expansion, removing the sense of pitch to emulate a percussive sound.

Spectral Dist and More

In additive mode, there are various parameters such as Random, Chaos, and Noise, which support the creation of sounds that are difficult to achieve using only integer harmonics.
Among these, Random Seed is a unique feature that allows you to specify the starting point of a pseudo-random sequence, enabling reproducibility of random behavior.
This parameter may be confusing for users unfamiliar with programming, but it’s useful for controlling the tonal character.
Finally, I created a glockenspiel-like sound using these parameters.
It's a sound that can be difficult to produce using analog synthesizers or FM synthesis.

Next time, we’ll be covering Zebralette3’s powerful spectral effect FX.

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