Bill Thibault, Dept. of Mathematics and Computer Science
Scot Gresham-Lancaster, Dept. of Music
California State University, Hayward Hayward, CA 94542
email: firstname.lastname@example.org email@example.com
"The song still remains which names the land over which it sings." -- Heidegger
All civilizations create artifacts that are manifesta- tions of their relationship with the land [Chat87]. The `dragon lines' of feng-shui, or traditional Chinese geo- mancy are an instance of this. The Nazca `lines' of the central Peruvian Desert and the `ley-lines' of `Cities of Revelation' in Ancient Britain are both totemic maps that link humanity to the land. One of the most inspirational instances of this phenomenon is the songlines of Australia. The songlines are built of the land and manifest the time when the world was "sung" into existence. In this case the music of the land is the primordial manifestation of exist- ence. In order to transcend the `modern' urge to conquer nature, the message from our ancestors is clear. We are the song of the land.
The initial inspiration for the current installation, "Songlines.DEM," comes from the work of Rich Gold [Bisc85]. The "Terrain Reader" used the height cross-sec- tion of a "traveller's" path as an audio waveform. The traveller traveled on an imaginary land stored as a grid of elevations in the memory of a KIM-I computer (in 256 bytes of a total 1K of RAM). As the traveller moved to a new position on the grid, the elevation of that point was sent to a DAC driving a speaker. The traveller's speed determined the sampling rate of the resulting digital sig- nal.
The idea of applying Gold's technique to a large dataset describing "real" terrain came to one of the authors (Gresham-Lancaster) in the context of the Pleiades project: a large, privately-owned radio telescope to be built in the desert near the Grand Canyon [Cope90]. The antenna functions as both receiver and transmitter, and would be used to beam music to other worlds. A transmis- sion of music generated from applying Gold's technique to the terrain in and around the antenna was conceived.
2.0 TERRAIN DATA
Recently, the United States Geological Service has made available data in a form that makes realizing the con- cept relatively straightforward. The USGS DEM (Digital Elevation Model) format consists of a grid of elevations. There are actually two DEM formats [USGS87], one cov- ering a 7.5 degree quadrangle with a sampling interval of 30m, the other a 1 minute quadrangle with a sampling interval of 3 arc seconds (~90m).
For efficient audio processing, the ASCII floating point data are converted to binary integers. These are stored at the resolution of the audio hardware (e.g., 8 bits/ sample for the Amiga, 16 for the NeXT) and normalized to maximize dynamic range. The massaged binary data are loaded into RAM. A full 1201x1201 1-degree DEM occu- pies about 1.5 Mbytes of 8-bit values (~3Mb of 16-bit val- ues). This is practical on modern personal computers. Conversion to binary form also eases the task of manipu- lating it. The data can easily be stored in a format used for images, making it possible to use image processing and data visualization tools for operations like cropping, past- ing, and viewing the data.
3.0 WAVEFORM GENERATION
We have implemented a waveform extraction algo- rithm that is efficient for today's hardware. We have gener- alized the specification of a path as a series of line segments described by their endpoints. We use a modified version of Bresenham's Line Algorithm [Fole90], used in computer graphics to determine which pixels lie along a line between two points. The line drawing algorithm was modified to visit pixels in the order of travel. Space limita- tions preclude a detailed presentation of the algorithm. Contact the authors (preferably via email) for an ANSI C implementation.
The waveform produced from any closed path (a path that has the same start and end point) will have no discon- tinuities when looped, unless there are discontinuities in the terrain. The simplest closed path is from point A to point B and back. The waveform consists of the cross-sec- tion for the line segment AB followed by a mirror image.
If the looped waveform is output for audition at a fixed sampling rate, the pitch will be determined by the number of samples in the waveform. This is directly related to the length of the path. The number of samples along a line segment AB, where A=(x,y) and B=(x',y') is: max(dx, dy)+1, where dx=|x-x'|, dy=|y-y'|. To ensure the line is connected, the line drawing algorithm produces a pixel for each value of the "driving axis," i.e., the axis along which the endpoints coordinates are farthest apart. The "+1" can be thought of as the last pixel along the line. When constructing paths of multiple, connected line seg- ments, we prefer not to include the datum for a given pixel more than once, and thereby do not include the last pixel's value in the output waveform. This pixel will be accounted for in the waveform since the next line segment along the path will include it as its first pixel. So, we can drop the "+1" term from the calculation of the number of samples for a multi-segment path, which is simply max(dx,dy) summed over all line segments.
So, for a fixed sampling rate, we vary pitch by chang- ing the path length: long paths have lower pitches than short paths. For the closed path between points A and B, the number of distinct integer path lengths is small for grids on the order of 1Kx1K, making an equal tempered scale hard to tune. The restriction to small integers is best suited to a just tuning. The installation uses (in one mode) a set of line lengths from 30 to 120 pixels, almost giving two octaves of a 5 limit scale:
1/1, 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4, 9/5, 11/6, 2/1.
(The 5/4 and 7/4 cannot be realized in the high octave, since they require a line segment 37.5 or 52.5 pix- els long.)
A timbrally evolving pitched tone is created by mov- ing a fixed path geometry over the surface. "Flat" regions produce low amplitudes (silence in the case of completely flat regions like bodies of water); hills or canyons produce louder signals. The effect of an amplitude envelope is obtained by moving the path through regions of different "roughness."
Rotating a set of endpoints to achieve timbral varia- tion is made difficult by the unusual distance metric asso- ciated with sample lengths. For a rotation of a path to keep the same pitch, the rotated path must have the same length. We are unaware of a general solution for multi-segment paths, though one probably exists. For the simple case of a rotating line segment, the sample length metric can be held constant by constraining the endpoints of the line segment to the opposite sides of a square.
4.0 BEHAVIORAL MODELING
The terrain is perhaps more interesting at a higher level, as a place. We can define processes in terms of rules or goals stated in terms of the terrain. For example, one traveller might want to always go uphill. Another might like to travel in straight lines, but slows down when going uphill and speeds up going downhill. We implement these processes as separate executing programs using a multi- programmed operating system. The time-scale of such activities is more suitable for MIDI output, with events occurring in "macro-time," as opposed to the "micro- time" scale of the waveform extraction algorithm.
The terrain context immediately suggests a wide range of possible behaviors. Elevations encountered can be output as MIDI messages: one traveller sending pitch- bend, another modwheel, another notes, etc. We have also used travelers that circle a moving point, that "roll down- hill", that take a "drunken walk" by moving in a random direction for each step, etc.
One traveller embodies the physics of a particle mov- ing in a gravitational field and interacting with the terrain through elastic collisions. The force of each collision is output as MIDI velocity. Particles are introduced into the terrain at a sequence of points above the surface (deter- mined by a Sierpinski plane-filling curve), accelerate downward until colliding with the surface, rebounding from the surface to fall again. The computational demands of this physical simulation preclude real-time implementa- tion on current PC-class machines, but this will soon change.
In the installation, users interact with travellers and the terrain in a variety of ways, none of which involve direct physical contact. This emphasizes the ephemeral quality of "information" in contrast to the ultimately hard reality of the place itself, and how this ephemeral, sensory- mediated connection is the only contact we have with real- ity in the first place. We can "be there" in one sense by interacting with data describing it. We prefer the term "telepresence" to "virtual reality" in this setting, as we are bringing the distant but real place to us "here" in new ways, rather than creating a new place.
The techniques can be applied to any data organized on a grid, and may find application to auditory analysis (sonification) of medical or scientific data.
We've found using terrain data as source material to be a rich context for creative investigations and play. We look forward to playing with terrain from various regions on this planet and others (e.g., recent detailed radar map- pings of the surface of Venus).
[Bisc85] John Bischoff, Rich Gold, and Jim Horton, "Music for an Interactive Network of Microcomputers," in Curtis Roads and John Strawn, eds., Foundations of Computer Music, MIT Press, 1985.
[Chat87] Bruce Chatwin, "The Songlines", Penguin Press, 1987.
[Cope84] David Cope, Prospectus for the Pleiades Project, 1984.
[USGS87] USGS, "Digital Elevation Models: Data Users Guide 5," Dept. of the Interior, U.S. Geological Survey, 1987.
[Fole91] Foley, Van Dam, Feiner, and Hughes, "Computer Graphics: Principles and Practice," Addison- Wesley, 1990.