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Godfried-Willem Raes: Fuzzy Harmony StudiesSince melody is -after all- not much more than a decorated musical scale, for many of these pieces we renounced the use of any other kind of melody than merely scales. This to reveal better the characteristics of the harmonic structures underlying each of these pieces. Put in another way: these pieces are not harmonisations of thematic (melodic) material, but rather pieces where melody and harmony are fully integrated in a single unifying compositional thought. Many of these studies are intended to be performed by humans. However, a few of these studies go beyond what humans can play and thus call for the player piano for their performance. Although they are abstract musical forms in time, they should be played and interpreted in an utmost �traditional� musical way, i.e. not mechanically!Warren Burt: A tENT aTTRACTOR for tENT and Probable Occurances (in Layers)These two pieces were composed using a series of non-linear function generators I made for John Dunn�s �ArtWonk� algorithmic composing software. They are essays in exploring how one can use the output of mathematical equations to make a stream of pitches, loudnesses and durations � that is, making music with them, music which, hopefully, has a sense of energy and inner life. They were realized by sending midi files of the pieces to Logos, where they were realized on the player piano at Logos. They were part of a larger series of works I made for the Logos Robot Orchestra in 2004-05, a series of works I hope to add to in the future. A tENT aTTRACTOR for tENT:One of the first families of functions I investigated while creating my package of random composing routines were the one dimensional attractors. Of these, the Logistic attractor, also known as the Bifurcation diagram, or the Feigenbaum attractor is the best known. Much simpler than the Logistic attractor, and with much wilder results at some settings is the Tent attractor. Like the Logistic attractor, this is a feedback equation, where the results of each generation are fed back into the equation as parameters for the next generation. The Tent equation is x(next) = s*(0.5 Abs[x(current) 0.5]), where s is a value between 1 and 2 and Abs indicates the absolute value of the expression in brackets. For values of S between 1 and 1.414 (the square root of two), regular or irregular alternations between two or more values occur. For values between 1.414 and 2.0, many kinds of random-like sequences, but with repeating elements are found, and when used, for example, to control pitch, produce melodies with many exciting patterns in them. In making the piece, I used two simultaneous versions of the Tent attractor, each controlling a piano over a separate pitch range, and at different tempi (in order to get polyrhythms), and dynamics. A button was placed on the control screen, and when this button was pushed, new values of S and X were generated, as well as new dynamics. Pushing this button can potentially throw the equation into completely different behavior, producing a radically different kind of melody. With grim wartime humor (this was at the beginning of the Iraq war), I labeled this button �Regime Change.� Finally, I doubled each of the two voices in fourths � this gave a much richer harmonic sound and resulted in a wide variety of chords between the voices. The use of doubling in fourths or fifths also seems to change the piano timbre in slight ways, producing a timbre with more depth, to my ears at least. Finally, in homage to my friend, the Pittsburgh based multiartform explorer tENTATIVELY, a cONVENIENCE, I changed the typography of the Tent attractor to match the inverse typography of his name. It is now the tENT aTTRACTOR, and I am pleased to report that tENT does, indeed, find the output of this equation quite attractive. Probable Occurrences, In Layers: In this piece, I wanted to explore the idea of different voices progressing in different registers at different tempi. My desire for a complex sound reached its peak here. In Probable Occurrences, In Layers, I made an ArtWonk patch with four layers, each of which was in a different pitch register (low, mid-low, mid-high, and high), and each of which was controlled with a different random function. The lowest register was controlled with the tENT aTTRACTOR. In fact four different tENT aTTRACTORs were used, one each for pitch, duration, velocities, and length of notes. Each of the other voices similarly used four instances of its function to control the different parameters. The mid-low register was controlled by the Burr Distribution, a random distribution with more low values than high values, but one which is highly shapeable and controllable. The mid-high register was controlled by the Pareto Distribution, another distribution with more low values than high, but one with a totally different shape than the Burr Distribution. The highest register was controlled by the Sine Attractor, another one-dimensional nonlinear attractor with results that are somewhere between the wildness of the tENT aTTRACTOR, and the more sedate randomness of the Logistic Attractor. Further, each of these four voices are also controlled by two function generators, which produce slowly descending ramp waves. These control the overall tempo and loudness of each voice, so each voice also has within it a gradual acceleration and crescendo, which then snaps back to a slower, softer articulation at the end of the ramp cycle. For performance, there are only 4 controls: on-off buttons for each of the four voices. A successful performance results from the judicious choice of which registers to combine in real time, bringing out different polyrhythmic and multi-registral textures as the performance progresses. The performance on this CD is the result of one performance of this patch. |
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