The second appearance of the JACK Quartet this season is dedicated to one single work: over the course of her 90-minute piece divisio spiralis, the American composer Catherine Lamb, resident in Berlin since 2013, creates a multi-dimensional harmonic space of extreme fragility. Effortlessly shimmering and defying the laws of gravity, Lamb’s spiral-shaped sonic architecture gradually shifts the parameters of musical perception.
Overtone series, numerical ratios, logarithmic spirals, tuning systems—when talking to Catherine Lamb about her string quartet divisio spiralis, things quickly get complicated. For Lamb does not compose with the familiar material of the twelve-note scale, nor with quartertones or other microtones, but in pure tuning. The entire piece is an infinitely slow, meditative measuring-out of this spiral harmonic space—but it is not essential to understand the complex mathematical background in order to experience Lamb’s harmonic spirals as something inherently beautiful.
When I first began to count, I imagined a long thread extending upwards and when looking up, at some point I began to see a curve forming in the line until eventually the line transformed into an infinite spiral, with my foot planted at the number one. Catherine Lamb
Also known as overtone series. A theoretically infinite series of tones that resonate (usually inaudibly) above every instrumentally or vocally produced fundamental tone and relate to the fundamental’s frequency in whole-number ratios, e.g., 2:1 for the first overtone (= octave) or 3:2 for the second overtone (= pure fifth) etc. The harmonic series can be visualized as a logarithmic spiral: https://superparticular.com/spiralsynth/
Tempered tuning system that became the standard for Western music in the 19th century and is most widely used today. It divides the octave into 12 equal semitones. Equal temperament only approximates the frequency ratios of the natural harmonic series (instead of 3:2, the fifth, for example, has a ratio of 12√128: 1 to the fundamental). At the same time, equal temperament makes all 24 keys available for the Western major-minor tonality, albeit in equal impurity.
In contrast to tempered tunings, pitches and intervals in just intonation correspond to the harmonic frequency ratios of the natural overtone series and are determined in relation to a fixed fundamental. On an instrument with fixed pitches, such as the piano, it is therefore impossible to apply just intonation to more than one key—all others remain impure. Equal temperament is a compromise that distributes impurity evenly across all keys.