Application of Tessendorf's Interactive Wave Algorithm to Music Composition
Prof. Bruno Degazio
Sheridan College, School of Animation
Oakville, Ontario, Canada
ABSTRACT:
Interactive Waves, or iWaves, is a computer algorithm developed by Jerry Tessendorf of the Los Angeles motion picture effects studio, Rhythm and Hues, for the realtime graphic simulation of moving water waves. This paper gives some background to the subject of computer simulation of water waves and of Tessendorf's elegant solution to the many problems involved; briefly addresses the aesthetic questions of such a simulation; describes an implementation strategy suitable for musical research; discusses different methods of mapping the simulated waves to musical parameters; and proposes a composition based on the ideas discussed.
1) INTRODUCTION
This paper attempts to survey both the technical and the aesthetic issues around a particular application of algorithmic composition. Unlike life, it moves from the general to the particular. It first explores some questions on algorithmic composition in general, followed by a discussion of the symbolic value of water in works of art, with a concentration on musical applications. It then discusses a particular problem, the computer graphic simulation of water waves, and a solution known as interactive waves. It concludes with a proposal for a musical work based on the ideas explored.
ALGORITHMIC COMPOSITION IN MUSIC HISTORY
ALGORITHMIC COMPOSITION IN CONTEMPORARY MUSIC
WATER AS AN AESTHETIC FACTOR IN MUSIC HISTORY
Water as a Symbol - Life and Death
Water in various forms, such as the sea, rivers, lakes, meteorological phenomenon, etc. as an aesthetic element in music and the other arts is intimately connected with its diverse symbolic meanings. Because water is essential to life it tends to function symbolically in its most undifferentiated state simply as a symbol of life. More specifically, because it is a pre-condition to life, it can mean symbolically the origin of life. “The Spirit of the Lord moved over the Waters” (Genesis 1) and in Hindu myth the World Egg, Brahmanda, hatched upon the water. And in fact the oceans were, some three billion years ago, probably the first playground of life on this planet.
Because it is the fundamental substance of life, out of which all life forms have grown and become differentiated in time, water can also function as a symbol of the unconscious, out of which consciousness emerged in childhood, and emerges each morning from sleep. Because of this connection with the unconscious water is also associated with wisdom, as in Apsu, the Mesopotamian watery abyss at the center of the world, the source of wisdom. In the Biblical tradition, the water of Wisdom dwells in a man’s heart and is like a fountain or a spring (Proverbs 20:5). And in the New testament, Jesus says to the Samarian woman, that the water he will give her is a “well of water spring up into everlasting life.” (John 4:14)
Because of its importance as a matrix of life, water is symbolically feminine - the Mother. Hence the long association of goddesses with the Sea, extending even to our own time, with the Christian Mary in her role as “Maris Stella” and traditional benefactor of sailors and all who live by the sea. The Moon because of its connection with the tides and with the female fertility cycle is traditionally feminine and watery.
As a symbol of life it is also connected with other fluid substances, such as Wine, Amrita, Soma, Ambrosia, Mead. and especially with the vital bodily fluids - tears, blood, semen, and milk. The last of course also confirms the feminine aspect of the symbol.
These vital substances point to the dynamic aspect of the symbol, since life is by definition dynamic and subject to change “animal” - that which moves, related to anima, soul). The dynamic quality of the libido as experienced psychologically is perhaps the most important connection of these symbols with the aesthetic application in works of art. The fountain at the center of the garden in medieval legend is a symbol of the ever flowing, watery quality of the libido. In contrast to its ever-moving restlessness, still water can symbolize peacefulness (Psalm 23.20)
Because it flows, waves, and is otherwise characteristically in motion, water also can symbolize time, as with “the river that you step into is not the same river you step from”. the river of life, etc.
Water, though essential for life, can also in be dangerous and the cause of death. Floods, storms, drowning, are examples of this aspect of water. The River Lethe, from which the dead drink, brings forgetfulness of life. The Flood of Noah brought death to all mankind except a select few, the reason being the wickedness of the many. Here the symbolic role of water spreads out into another cleansing and rebirth. Water in rough or violent motion carries the meaning of disorder and chaos (Ezekial 57.20).
Water as A Symbol of Cleansing and Rebirth
Immersion in water is a worldwide symbol of purification and regeneration. In the Christian tradition this is accomplished via the rite of baptism (second birth into the life of the spirit) and in a smaller way with the use of holy water for various cleansing and purification.
WATER AS AN AESTHETIC FACTOR IN CONTEMPORARY MUSIC
- Thomas Ades - The Tempest m.498 “Tempestoso” - very like old Silent Film “Storm at Sea”
- Michel Redolfi - Underwater Series, 5th Installment: - Sonic Waters (Hat Art, USA) 1984
- French Spectralists:
- Horaţiu Rădulescu - Clepsydra (1983) for 16 players with sound icons
- Michel Redolfi - Underwater Music
- Silver Waves
- Pacific Waves
WAVE MOTION AS A MUSICAL MOTIF
In this section I would like to examine a number of representations of water wave motion in musical literature.
- Musical Theater and Opera connected to Water
- John Adams --- The Death of Klinghoffer
- Wagner - Das Rheingold
- Britten - Peter Grimes, esp. Sea Interludes
- Gilbert and Sullivan
- --- Gondoliers
- --- Gondolier
s
- --- H.M.S. Pinafore
- --- Pirates of Penzance
- Pietro Mascagni --- Iris
- John Adams --- The Death of Klinghoffer
- Cole Porter--- Anything Goes
- Rodgers and Hammerstein --- South Pacific
- Silent Film Stock music- Storm at Sea
- Encyclopedia of Music for Pictures, Belwin, NY, 1925. Reprinted in 1974 by the Arno Press. ISBN 0-405-01634-4
- Motion Picture Moods for Pianists and Organists, G. Schirmer, NY, 1924. Reprinted in 1974 by the Arno Press. ISBN 0-405-01635-2
- Musical Imagery of Water
- Beethoven: storm from Symphony No.6
- LISZT: Les Jeux d'eaux a la Villa d'Este
- Frederic Chopin
- - Prelude, op. 28, no. 15, "The Raindrop"
- Claude Debussy
- - La cathédral englouté
- - La Mer
- - Reflets de l'eau
- - Jardins sous la pluie
- - Poissons d’Or
- - Ondine
- GRIFFES: The Fountain of the Acqua Paola
- Ferde Grofe - Mississippi Suite
- Virgil Thomson - The River, from The Plow That Broke the Plains
- Jacques Ibert - Escales
- Todd Levin --- Swirl
- Maurice Ravel --- Jeux d'eau
- Ottorino Respighi --- Fountains of Rome
- Richard Rodgers --- Victory at Sea
- Giacchino Rossini --- Overture to William Tell
- Camille Saint-Saëns --- "Aquarium" from Carnival of the Animals
- Virgil Thomson --- Suite from "The River"
- Ralph Vaughan Williams --- Sea Symphony
- Antonio Vivaldi --- 2 concerti, RV 253 and 433, "La Tempesta di mare"
- Pieces that represent the flow or movement of Water:
- Bach - BWV 26 - Ach wie flüchtig, ach wie nichtig
- MacDowell - Sea Pieces Op. 25
- Rimsky Op. 46 - By the Sea *esp. songs 3 and 5
- Elgar - Sea Pictures - esp. no.4 - From the Depths, no.6, In Mid Ocean
- Grainger - Spoon River
- Wagner - Rheingold
- Debussy - La Mer (splashes)
- Frederic Chopin --- Prelude, op. 28, no. 15, "The Raindrop"
- Claude Debussy--- La cathedral engloute
- --- La Mer
- --- Reflets de l'eau
- Ferde Grofe --- Mississippi Suite
- Jacques Ibert --- Escales
- Matin sur l'eau
- Todd Levin --- Swirl
- Maurice Ravel--- Jeux d'eau
- Ottorino Respighi --- Fountains of Rome
- Richard Rodgers --- Victory at Sea
- Giacchino Rossini --- Overture to William Tell
- Camille Saint-Saens --- "Aquarium" from Carnival of the Animals
- Virgil Thomson --- Suite from "The River"
- Ralph Vaughan Williams--- Sea Symphony
- Antonio Vivaldi--- 2 concerti, RV 253 and 433, "La Tempesta di mare"
- Ludwig van Beethoven --- Symphony No. 6, movement 4 "The Thunderstorm"
- Jonathan Green --- Symphony No. 3, movement 4 "Water"
- Bedrich Smetana --- "The Moldau" from Ma Vlast [My Country]
- Jonathan Green --- Symphony No. 3, movement 4 "Water"
2) COMPUTER SIMULATION OF WATER WAVES
i) History, 1986-2010
This topic has been researched since the late 1980’s because of the enormous practical application to, initially, animated and simulated cinema and, later, interactive computer games. Two approaches have been dominant in that timeframe:
a) Gerstner Waves
This method is derived from a long-standing oceanographic theory, known as the Gerstner-Rankine wave model or simply Gerstner waves. Simplistically described, this model states that individual water “particles” move in circular or elliptical orbits around a resting position. There is an interesting Canadian connection with this method, in that the two seminal papers describing it were published by Canadians in the 1986 - Darwin Peachy, of the University of Saskatchewan, and William Reeves, at the time working at animation company Pixar in San Francisco, but formerly of the University of Toronto, Department of Computer Science.
This method had the advantages of allowing a time-based description, hence of being adaptable to moving images. The basic formulae have several parameters that relate directly to interesting aspects of the wave surface, such as wave height and steepness of slope. It also allowed for effective simulation of such secondary wave phenomena spray and interaction with partially submerged obstacles.
b) Almost simultaneously with (a), another approach was being developed at several places, based on two-dimensional Fourier Synthesis. Briefly, real ocean surfaces were analyzed via Fourier methods to determine the relative weights of the various frequencies. This data could then be applied to a two -dimensional computer graphic surface to “synthesize” analogous wave surfaces.
TESSENDORF’S SOLUTION
Jerry Tessendorf, of the Los Angels special effects company Rhythm and Hues, bypassed the existing approaches and instead devised a simulation based on the two dimensional convolution.
IMPLEMENTATION IN THE TRANSFORMATION ENGINE
MUSICAL PARAMETER MAPPINGS
COMPOSITION PROPOSAL - WAVELENGTH
BIBLIOGRAPHY
N. Collins, Musical Form and Algorithmic Composition
M. Edwards, Algorithmic Composition: Computational Thinking in Music
J. Harley, Generative Processes in Algorithmic Composition: Chaos and Music,
Leonardo, Vol 28, #3
A. Fournier, W.T. Reeves, A simple model of ocean waves, in: Proceedings of SIGGRAPH’86, Comput. Graph. 20 (4) (1986) 75–84.
D.R. Peachey, Modeling waves and surf, in: Proceedings of
SIGGRAPH’86, Comput. Graph. 20 (4) (1986) 65–74.
Taruskin, Richard - Does Nature Call the Tune? The Danger of Music and Other Anti-Utopian Essays - University of California Press, 2008.
Keiji Hirata and Tatsuya Aoyagi, Computational Music Representation Based on the Generative Theory of Tonal Music and the Deductive Object-Oriented Database, Computer Music Journal, 27(3), pp.73-89, 2003.
Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo, Implementing "A Generative Theory of Tonal Music", Journal of New Music Research, 35:4, pp.249-277, 2007.
Marsden, A. (2005). Generative Structural Representation of Tonal Music, Journal of New Music Research, Vol. 34, No. 4, pp. 409-428.
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( from http://witcombe.sbc.edu/water/music.html )
Water has had surprising prominence in the musical world. It has served as a tool, as inspiration, and even as a performing venue.
Water as a Musical Tool
The Hydraulis, or Water Organ, was a musical instrument that produced sound using pressure generated by falling water as the energy source.
Water Drums exist in various cultures. The native populations of the Americas constructed a drum within a drum, with the inner instrument being filled with various amounts of water to affect the timbre of the sound. In some areas in Africa and New Guinea, hollow gourds were placed in larger vessels and struck.
Water Gong is the name attached to a modern use of traditional gongs and tam-tams. the instrument was struck and then lowered into a tub of water which lowered the pitch.Likewise, it could be struck while suspended in water, and then removed to raise the pitch.
Water as Inspiration in Music
Water has served composers as musical inspiration for a number of reasons: as the backdrop for opera and musical theater, as an image to be represented in musical sound, as a source of natural sound to be imitated in music, and as a cultural icon.
Water as Musical Venue
The most celebrated piece of such music was composed in England, by Handel, for a 1717 party for George I upon the Thames.
Throughout history, composers have been asked to write music to be "played upon the water." Venetian musicians composed much brass music for barges.
