Atrium Display, Visual Harmony: The Interval Rotors of Siemen Terpstra & Interval Diagrams by Yuri Landman
The Interval Rotors of Siemen Terpstra
These rotors are tools used to simplify harmonic analysis of musical scores in unusual temperaments. They allow one to quickly calculate any pattern (type of harmony, set of intervals) to any pitch or function. Siemen Terpstra made examples for the tuning systems that he uses most (i.e. 12-et, 31-et, 53-et) but the approach can be adapted to any system. Even though the intent is strictly practical, he designs them to be pleasing to look at, to embody aesthetic values, while the connective geometry indicates thirds, fourths or fifths from any given tonic in a given pitch set.
Siemen Terpstra was born in 1948 in the Netherlands. As a baby he immigrated to Canada and grew up in Ontario. In 1970 after attending university he moved to the west coast. Having dual citizenship he returned to the Netherlands in 1993. He now lives in Amsterdam.
Terpstra came from an artistic family; his father painted seascapes and his mother sang and directed choirs. As a teenager artistic interests dominated but when he grew older musical matters came to the fore. He developed a keen interest in musical intonation during the 1960’s but his active research in the field covers the 1970’s to the 90’s. Having a high aptitude in mathematics, he explores many avenues and developed his own models to clarify issues. As a teenager he wanted to be an architect, but then as an adult the architecture of resonance systems proved more fascinating. Subjects that came in for special attention include: monochord arithmetic, alternative just intonations, multiple divisions, irregular temperaments and new instrumental resources. Having a long-time interest in musical conceptions of order, he thoroughly explored the interplay between music and ancient philosophy, cultural history and possible futures.
Interval Diagrams by Yuri Landman
As a former graphic designer, Yuri wanted to make a visual diagram to clarify intervals, like the periodic table clarifies chemistry. He developed a color code for the harmonic series where the denominator is the dominant factor of the sound composition (re: string lengths; in frequencies: it’s the numerator). The color legend on diagrams explains number-color relation. In his words:
The Third Bridge
Adding a third bridge in the middle of the strings of a harp creates a multiphonic timbre consisting of the vibration of the left string part, the right string part and their shared harmonic. To illustrate this I came up with a symbol consisting of a circle (the denominator of the fraction), and three squares rotated 45°. The left square mentions the key of the left string part, the right square the right string part and the upper square is the shared harmonic (1/denominator). The cluster of the three mentioned keys all together are the composition of the multiphonic.
Utonality & Otonality
From White Consonance to Dark Dissonance, both diagrams feature more subtile colors; both start with white for the fundamental. Then the octave is again white and the 3rd overtone or undertone has a soft color. The fourth overtone or undertone is again an octave and white. I continue that process with darker colors for each newly appearing overtone or undertone in an octave interval. This is a binary coloring method used in cellular automata. Notice that the two systems are symmetrical though inverted; the remainder of one indicates the other and this is also evident in the tonality diamonds.
Yuri Landman (1973) is a musician and an inventor of musical instruments. Based on prepared guitar techniques, he built his first instrument in 2001 to solve the inaccuracy of instant preparations. He has build experimental for acts such as Sonic Youth, dEUS, Melt-Banana, Rhys Chatham, Ex-Easter Island Head, Half Japanese, Kaki King.
In the past seven years he has given over 100 DIY-instrument building workshops in Europe and the US at music festivals, music academies, art academies, concert venues and art spaces. In 2012 Yuri Landman and Bart Hopkin published Nice Noise, a book about string preparations and extended techniques for guitar. In the same year he started his band Bismuth with Arnold van de Velde followed by an album in 2014 Bismuth.
Institutes such as MIM (Phoenix), Muziekgebouw aan ’t IJ, WORM, Extrapool, Sonoscopia own collections of his instruments. Articles about his work have appeared in Pitchfork, The Guardian, CNN, Libération, El País, Frankfurter Algemeine, and many others.