Tapping a blue plastic sphere with a white wand, Robin Hayward releases the sound of a single sine wave. He reaches into the latticed framework of plastic tubes and touches a red sphere suspended above the blue. Another tone sounds, this time a Pythagorean 3rd above the first.
Each ball and tube, constructed of a children’s Zometool scientific modeling set, represents a tone and a prime number ratio. The device resembles an abacus; instead of moving beads, the white wand activates nodal overtones and undertones through RFID. The “Tuning Vine” is a 3d model of the harmonic relationships that make up the “just intonation” system of tuning.
In classical western music theory, the tonal system has been tempered, to create equal intervals between the notes in the scale. The keys on a piano represent these notes, altered from the algorithmic progression of ratios, to make it easier to transpose melodies in different octaves. Usually we read notes on stave instead of frequency numbers. Unlike the 12 tone tempered scale however, just intonation requires the calculation of ratios related to each central tone, with an infinite number of possible intervals: micro-tones.
Hayward, a tuba player, became interested in the idea of just intonation after reading Helmholtz’s ‘On the Sensations of Tone.’ When he discovered Martin Vogel’s micro-tonal tuba designs from the 1970s, he began to develop his own. The ability to play in just intonation is available on any fretless instrument. On the tuba it requires adding another valve. The “Tuning Vine” attempts to open a more intuitive channel to composing in just intonation as well as being an instrument in itself.
The understanding however is not immediate. During the master class, the group used a software version of the “Tuning Vine,” and did a lot of multiplying fractions. Then we listened to the vertical layering of sound. Every sound, besides a pure sine wave contains harmonics. This is how we hear timbre, from the layering and emphasis on different harmonics with a note. We practiced building up the harmonic series in overtones and undertones, learned to deduce common harmonic components of tones, and then sang along. Within one note of our singing, we listened to the overtones contained within it, and then learned what these ratios were.
The program helps in understanding the subtleties between Ptolemaic and Pythagorean intervals, La Consonance Anglais, and the minor 7th “blue” note, expanding compositional possibilities. Throughout the afternoons, we sang and droned, intuitively calculating while listening upwards and downwards, through tone to timbre and back again.
Robin Hayward plays with Tonaliens, a Berlin-based ensemble working with just intonation on the final day Sonic Acts.
