... it1.1
Even though this thesis has many graphs and an accompanying audio tape, for the sake of simplicity, let us only talk about the words of this thesis. 
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... them1.2
The question of whether information exists when there is no perceiver for it is up for discussion; however, we believe, there is little content in that question. 
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... judgment1.3
This is the largest flaw in being judgmental about the world, and above all, about the people around us. 
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... more2.1
If we assume more than two entities we will have to think about the three body problem, which is still a hard problem for human beings to think about. 
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... channel2.2
The words ``channel'' and ``linear'' have very precise technical definitions. In this chapter we have used these words in contexts in which it is difficult to be scientifically precise. These words should be taken in their technical sense, but not with a scientific precision. 
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... ``vertical''2.3
The words ``vertical'' and ``horizontal'' are used to show two orthogonal axes. In this section, their orientation in space may not have any meaning; however, later they will be used for the time/frequency relationships where they have more literal meanings. 
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... listen2.4
Such a choice means that one has to be able to go into the state of ``not thinking'' when listening. 
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... matter.2.5
Spiritual concepts, especially those concerning life and survival, are important to us. Inquiring into the reason for that importance is philosophy, and that itself is a spiritual concept in the life of the one who inquires about that issue. 
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... singer2.6
We use a singer here rather than an instrumentalist, as many believe that one has learned a melody only when one can sing the melody. 
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... tonality2.7
Or is it the other way around? Do these rules come from tonality, or is it these rules that shape tonality itself? 
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... comprehensible2.8
Please note, if we question the meaning of comprehensibility, which after all is what Schoenberg is emphasizing, then neither our explanation nor his comment have any meaning. 
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... theory!2.9
Would Schoenberg say the same thing, if he had computers to help him create and control new timbres? And would he still feel the same way, if he had heard the contemporary computer music of today? 
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... comprehensibility.''2.10
These two ideas are really portraits of the same concept; however, since they have been used in different contexts in the music of 20th century, we will discuss them as separate entities. 
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... communicated2.11
The mentality that creates the music and the way it is communicated are all apparent in what lies in the music. 
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... sound2.12
Schoenberg believed that there were similarities between historical situations, but he says: ``I am no Bach''[40, page 119]. Schoenberg was inclined to call Bach the first twelve tone composer[page 117]. 
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... timbre''2.13
This idea was first introduced to me by Marc-André Dalbavie during late-night discussions when I stopped him from working at IRCAM. 
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... style2.14
The term ``Le Son Boulez'' is familiar among the composers and scientists of IRCAM (Institut de Recherche et Coordination Acoustique/Musique), the computer music research institute in Paris. 
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... conceived2.15
For an interesting discussion on conception, as opposed to composition, of music refer to[40, page 166]. 
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... blood2.16
Schoenberg would have been even more excited if he had known about DNA. 
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... UNIT.2.17
The capitalization of this sentence is Schoenberg's. 
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...fig:square-limit3.1
This drawing was coded in Post Script by John Pratt. 
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... variables3.2
The three variables are the angular velocity of the wheel, and the first sine and cosine coefficients of first harmonics of the fourier series of the amount of water in the buckets. 
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... fractal3.3
The name fractal was coined by Mandelbrot to bring together many mathematical shapes and ideas which prior to that were called with names such as monsters, wobbly, twisted, or crooked because of their infinite amount of details[29]. 
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...fig:hilbert3.4
This illustration was created by Jin Choi. 
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... exists3.5
Start with: ``nothing'' exists. 
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... created4.1
All the audio examples for this chapter were created using Csound[49]. 
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... micro-structures4.2
Customarily, micro-structures in music refer to structures which happen in the sound domain in frequencies above 20 or even 100 Hz. However, we are using this as a relativistic term in reference to the structures in the region of our inspection. 
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... method5.1
We would like to point out that this work started before we had any formal knowledge of the L-system, fractals or chaos. 
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... hierarchy5.2
Mammad Zadeh developed the initial parser. 
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...seed5.3
The name, seed, was suggested by Gerhard Eckel during discussions on the subject in summer of 1989. 
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...fig:barkspec5.4
All the spectrograms for this theses as well as the soundfile interface tools were written by Dan Ellis. These tools were indispensable to development of this project. 
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... hardware6.1
Miller Puckette's MAX is an excellent example of such efforts[33]. 
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... self-referential6.2
This sentence is not just a figure of speech, self-referentiality is as simple and profound as this situation. 
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...chap:self)6.3
It is also no surprise that Gödel's incompleteness theorem connects itself with the computer science halting problem and the non-computability of Kolmogorov complexity[6, page 162]. Kolmogorov complexity is the extension, or actually a superset, of the classical information theory. 
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... errorA.1
Stan Sclaroff provided the code for the algorithm. 
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