Using Max to explore the Overtone Series

Fig. 1 — Overview of our patch, the overtones sequencer.

Fig. 2 — How the patch looks like when is loaded as a Live instrument, with native controls and midi mappings.

Overtone series on C, with deviations in respect to equal temperament.

Fig. 3 — Customisation of controls from the inspector window, setting units and ranges for the numeric boxes.

Fig. 4 — Demo video of the overtones sequencer in action.

Max for Live is a powerful environment, allowing to program audio and midi patches with a visual paradigm (similarly to TouchDesigner).

Since it’s built-in Ableton Live, it’s possible to create audio effects, midi effects and virtual instruments with GUI controls that look like Live’s native ones (sliders, buttons, knobs, etc.) and that can be midi mapped in the same manner as well (see fig. 2).

The Overtone Series

We created a patch that sequences, in a random manner, the natural overtone series of a note.

The overtone series exhibits an interesting phenomenon on how humans perceive sounds. While the frequencies increase linearly starting from a base, the perception of the music interval contracts, manifesting our logarithmic perception of sounds.

Nonetheless, while the perception of the first overtones sounds consonant (with just intervals like octave, fifth, fourth, major third), the upper overtones start to exhibit a more dissonant behaviour.

\begin{aligned} f_i &= i \cdot f_b \\ f_1 &= f_b \\ f_2 &= 2 f_b \\ &\dots \end{aligned}

The Patch

The environment of Max consists of blocks. Every block can have inputs and outputs, either in the form of data or signals, and represents a processing unit.

In our patch, the central block is the cycle~ which generates a sinusoidal signal as output by providing a frequency as first input.

The overtone series is built by multiplying a base frequency over

Using Max to explore the Overtone Series

The Overtone Series

The Patch

Our project