Luisa Pereira
Manuela Donoso Lamas

The Harmonic Series

A series of objects (software, print, plastic, tuning-forks+mirrors+laser) that explore the rendering of Lissajous figures, which represent harmonic musical intervals and chords.

Cooking With Sound,Designing for Digital Fabrication,Materials and Building Strategies,Tech Crafts

In the nineteenth century Jules Lissajous, a French mathematician, made an experiment: he aimed a beam of light at two successive, perpendicular tuning forks with small mirrors attached to their tips. If their frequencies were related by simple integer ratios, beautiful figures would be projected on a dark screen.
Fascinated by the relationship between musical and visual harmony that these images suggest, we decided to generate them ourselves, hoping to get a better understanding of how harmony works.
A specific application was at hand: designing the poster for the NIME show. We had already talked about making a NIME poster that was a NIME itself, and these figures seemed to be perfect for our the idea of a high-low tech poster where people could both see and hear a sound.
We created an application that draws 3d Lissajous figures based on three frequencies input by the user, and renders them in different ways. We generated images representing musical intervals (a minor third, a minor second), and used them for our design of the poster for the NIME show.
Still curious about these figures, we plan (and hope) to explore them further in the next couple of weeks through the following experiments:
1) Executing our initial concept for the poster –a poster for a NIME show that is a NIME itself. It will be standalone (no computer), and interactive: when a person gets near it, she will hear the musical interval represented by the figure on the poster. This will be Manuela\'s final project for theTech Crafts class.
2) Adding sound to the figure generating application: we\'d like people to be able to hear the sound that each figure they make represents. We imagine that, by playing with the app, people (and us!) will discover that simple frequency ratios generate both harmonic figures and sounds. Another step would be to add two microphones, and make the figures represent the ratios of the singers\' voices (and perhaps also two recorders placed in front of them). This is not a final for any class, and will probably have to wait until the break to be executed…
3) Recreating Lissajous\' device. We have a set of tuning forks, a laser pointer and a little disco ball full of mirrors, and will try to generate the images using them. This will be Manuela\'s final for the Cooking with Sound class, and Luisa\'s final for the Materials and Building Strategies class.
4) Creating 3d prints of figures representing minor, major, diminished and augmented chords (a major chord, for example, has frequency ratios of 4:5:6). This will be Luisa\'s final for the Designing for Digital Fabrication class.