The Tensegrity Harp Project

Scot Gresham-Lancaster ongoing research ( since 1983 ) into the harmonic relationships suggested by the geodesic, synergetic, and tensegrity math of R. Buckminster Fuller.To See the lastest update click here

Prescript July 11, 2001: Last night while watching the PBS series "Building Big" there was an interview with sculptor and designer Kenneth Snelson in which it was revealed that R Buckminister Fullershould not be attributed with the actual conceptualization of the tensegrity structure, but rather blantantly took credit for work that Mr. Snelson had done. This sort of robbing of attribution is something that has plagued my own work as a technical assistant and digital music problem solver for many years and so I was very embarassed when in my excitement at discovering this fact I wrote to Mr. Snelson without taking the time to edit this page to reflect this truth. Those who are intererested are invited to read a full account of a corrected history in the form of a letterto R. Motro of the International Journal of Space Structures by Mr. Snelson that sets the record straight.
What follows is my text from June of 1999. I will be updating this page later in the summer to show the current work of the acoustic electromechanical hybrid instrument that I am currently working on.

Early in 1983 I was commissioned to write the music for a wedding reception of performance artist and art curator Evan Painter. At that time I was steeped in reading Synergetics by Buckminster Fuller and decided to work with these mathematics as a compositional determinate. I was particularly interested at that time, in the vocabulary of the geodesic dome that described the rational relationship of the length of strut members in a geodesic object as "Chord" factors. This obvious allusion to harmonic relationships prompted me to create a piece that mapped these specific frequency relationships determined by the lengths of an architectural structure to a harmonic lattice. These harmonic lattices are common among researchers in to intonation theory and so I based the research on combining my knowledge of geodesic math with the concepts of harmonic lattices put forward in modern intonation theory. My first project involved using the lattice created using the chord factors from a 6 frequency geodesic ellipsoid with foci proportioned at the golden mean. If the great ellipse of the defined structure was 2 units across, the distance between the foci would be 1.61803989... units ( the golden mean ). The lattice of chord factors that constructing such a geodesic elipsoid will generate. The main atribute of the lattice is that it is described by a triangular juxtaposition of members as opposed to the quadrille or quadralateral dispalcement of cartesean based mathematics.

By multiplying each of the chord factors of the representative architectural strut members by the fundamental frequency of the intended scale the frequency relationship of each chordal member is established. These chord derived frequency sets are ordered in matrices based on each struts placement in the original structure. By collecting the parameters of adjacent matrix members to the in ordered grouping, isorhythmic chord groupings and polyphonic melodies determined by these relationtionships are generated. This complex set of predetermined systems generated a sweet and pleasing sound field that had inherent symetries of motion and confluence and yet was complex enough to afford continuous gentle variation.

The sequential playing of groupings in the matrices could actually be visualized as planes that were passing through the elipsoid. Sticking strictly to these intersections as a means of timing lead to thinking of the vertices of the structure as being "strings" of a conceptual harp that was being played by the planes as they passed through each vertici. truncated octahedron tensegrity This concept of the vertices being strings, led to the next phase of the research. This type of structures based on the work of Keneth Snelson lent itself to being the basis for a playable instrument appeared to be the tensegrity structures. The question was how was this new proposed instrument to sound: acoustically or in more challenging way as a means of playing the multiple parameters needed for the control of digital synthesis algorithms. By tranducing the net stress of each of the faces of a tensegrity structure ( such as the truncated octahedron in the illu. ) then one could intuitively control multiple parameters associated with processes suchas vocoding, resynthesis, etc. Also, if one could distinguish between the act of stretching and the act of plucking, more useful musical information would be generated by the instrument.This intuitively interesting project is fraught with technical difficulties, however.
The problems associated with the work are both of a hardware and software nature. Addionally, there are considerations that add to the look of the instrument as an aesthetically beautiful object. A transducer needed to be found that would translate the information regarding the stretching and plucking of the suspension mebers without interupting the look of the instrument. My association with STEIM and its cadre of instrument designers lead me to many potential solutions. First Bert Bongers suggested a transducer that was linked to a spring that was in a machined part that held a magnet and a hall effect sensor. This is a problematic solution mostly because of the non-linearity of the hall effect sensor. In thinking about the problem more carefully, I came across al ine of inquiry that seemed very interesting.

In electronics magazines I spotted a company called Instrument Specialities Inc.. which specialized in making special purpose gaskets for electromagnetic isolation of components in microwave electornics. One of their products was called "Conductive Siicon Elastomers". The short description included the information that the material could be doped with carbon, copper, aluminum, nickel, etc. It occured to me if this string like material was stretched that there was a chance that the metal particles suspended in the silicon would contact more their changing any resistance that was created. Upon talking to the field representatives this was indeed the case. I then went over the specification sheets and selected the carbon/nickel combination as having the best conductivity with at least some resistivity. After some phone work iwas able to acquire a six foot sample of a fabricated 130 mm length of this material. It met and exceed my expectations. At rest it has almost no resistivity with about 100 ohms at 12 cm. when stretched this resistance increases linearly with stretch to about 4 M ohms. Quite good for my purposes.

By using this material with a votage across the members of a tensegrity structure can be connected to an A/D convertor and the stretch can be congruently converted into a digital number based on the resolution and sampling rate of that conversion. With the backing of the MultiMedia masters degree program at CSUhayward and the support of Microchip Inc. I have acquired a PicMaster emulator and a Picstart plus programmer. For my initial experimentation, I am using the PIC 16C77 embedded processor which has integrated into it eight 8 bit A/D channels. With this system I can read the stretching of the structure and in that way create a dynamic vector model that can be remapped to abstract parameters associated with one or many DSP algorithms that are generating, delaying, filtering or in some other way modyifying sonic material.

The most, initially, unclear aspect of the reason for this construction can be summed up in a historical perspective of my experiences with various types of alternative controllers.

Update February 2002
I have decided to take another approach on the construction of this instument and not use the Conductive Silicon Elastomers. While they produced promising results they were not stable and required constant recalibration. I spent more time on the recalibration routines thatn working on the routines to make the construction a viable musical instrument. So there are now two prototypes using two different approaches.

One is based on the Tensegritoy model. By building this model I was given an elastic version of the structure I intended to work with then I simply attached linear potentiometers to the members and took the output of those potentiometers directly into a voltage to midi conversion box ( the STEIM sensorlab ) and input the midi conversion into a Macintosh computer running Max software. I use Max to message the data for the particular application that I am working on.

The second model is more elaborate. I built struts out of oak and mounted guitar tuning machines on one end and added a bridge on the other. Then i constructed a real stringed harp using the tension created by the tuning pegs to tighten and tune up the construction. This phase is now finished and I have what i would describe as a multi dimensional Berimbau. The next phase of the building of this instrument is to add six single coil pickups to the bridge of each of the struts and then not only amplify the unique string vibration and sounds that they prduce, but also do a real time spectrum analysis and geneal acoustical analysis of each of the pickups and use that as a performance determinate. i am currently working on the best pickups and mountings for those pickups on the instrument.