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Ayn Rand's Definition of Music

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Andrew Grathwohl

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So, let me see, unless it's verified to have the same intervals as measured by an atomic clock, it's not periodic?

Don't be ridiculous. The context is people listening to it; if they perceive it being equal intervals, it's periodic within the context. Any attempt to measure it with an atomic clock and say it's not periodic for that reason is sheer rationalism.

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So, let me see, unless it's verified to have the same intervals as measured by an atomic clock, it's not periodic?

Don't be ridiculous. The context is people listening to it; if they perceive it being equal intervals, it's periodic within the context. Any attempt to measure it with an atomic clock and say it's not periodic for that reason is sheer rationalism.

If you still refuse to believe that Ayn Rand was speaking on a physical level - as opposed to a psychophysical level - then you simply have not read my provided evidence in the proper context. Ayn Rand refers to this same periodicity characteristic that she says defines music, when she attempts to disprove music made from "machine gears" and other "aperiodic" sounds. If she meant that music is made up of sounds that are perceived as periodic to the human brain then she would be wrong as well, because the JND for frequency interval perception among humans is around 0.5%. A concert violinist can get off tune by that much in a matter of minutes depending on his/her instrument. Your defense would amount to the falsity that music has a different definition to every person, because people are, by nature or by choice, able to utilize and recognize this perceptive strength in different amounts. Despite one's ability to recognize it, even the most prestigious of musical performances are likely to sound aperiodic to such an extent that the trained ear can identify it.

The next fallacy would be that only "good" music is defined as music, because it would have to be so well-performed that the perceived output sounds periodic to the listener. The more one would know about music - and the better one's sonic perceptions - the fewer pieces of "true" music one can actually listen to.

I would suggest rereading the essay yourself if you need clarification, but I think the evidence has already been provided to show that Ayn Rand speaks of periodicity in a physical context - not a psychophysical one.

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How is this a strawman?
Because holding that there is a difference between 'periodic' to refer to 'frequency of vibration' specifically and 'periodic' in a more general sense does not at all depend on demanding that the frequency of vibration be measured to within the accuracy of an atomic clock and no one who has pointed out that what is at issue is frequency of vibration has suggested that such frequency must be measured within the accuracy of an atomic clock.

Ordinary musical instruments that involve playing various pitches are enabled by the fact that pitches are the frequencies of waves that have a regular interval between the high points of the wave. In contrast are other other sounds whose pitch is not distinct as it is for such aforementioned musical instruments. That such other various sounds can be produced periodically (such as stomping one's foot on the ground every two seconds) doesn't diminish the fact that such events are a distinct kind of phenomenon from the periodicity of such waves that are involved in musical pitches. And even if the period of a wave from such pitch-based musical instruments might not be within atomic accuracy, still, within some margin of error, there is a constant period, unlike certain other sounds that don't have such distinct pitch. (Of course, there may matters of degree, such that sounds may have indistinct pitch, some getting closer to the distinctness as from a musical instrument; and, from the other side, musical instruments are imperfect and my have distortions and compromise in pitch. However, that is not what is at stake here, as surely we all recognize that in various classifications there are gray areas that don't necessarily lead us to conclude that our basic classifications are not well conceived. It is clear enough the difference between, on the one hand, for example, the sound of a flute and its specific pitches from waves that are periodic in the specific sense of regular interval in the heights and, on the other hand, for example, making a thud sound every two seconds. And that, for example, has been the point here, not some irrelevancy about precision of measurement.)

Edited by Schmarksvillian
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Because holding that there is a difference between 'periodic' to refer to 'frequency of vibration' specifically and 'periodic' in a more general sense does not at all depend on demanding that the frequency of vibration be measured to within the accuracy of an atomic clock and no one who has pointed out that what is at issue is frequency of vibration has suggested that such frequency must be measured within the accuracy of an atomic clock.

I don't mean to get into a pissing contest, but it really is fascinating how different people can read the same words and come away with different meanings. Here is the evidence for my point of view:

From post #1

The fact is that sounds fluctuate in frequency, amplitude, and timbrel quality, due to a number of both personal and environmental factors. The only way the average human being could ever be exposed to a sound that was even close to periodic would be to employ a digital sound oscillator, which featured a VERY high sampling rate and bit depth, and then played through VERY high-fidelity playback equipment, in an acoustically-sound room.

From post #5

A periodic wave would never deviate from its starting frequency. ... It should be clear that if frequency changes, its period changes as well - making it aperiodic.

From post #14

Sounds from instruments are never periodic. They may always sound the same to you, but by nature, their sonorous output will never be periodic.

From post #16

Rhythms are only periodic in theory. They never are precisely the same repetition in spacing of time, and when swing gets involved, all hope is lost in making a rhythm truly "periodic."

These quotes, especially the last one, make clear that Andrew Grathwohl takes for granted a theory-practice dichotomy. Whatever Ayn Rand was writing about it couldn't possibly capture what actually happens in music because theory is limited to words that do not refer to reality but perfect Pythagorean mathematical constructs, such as a perfectly unwavering frequency.

(Once again, a dispute comes down to epistemology. Here, the relation between a concept and its referents.)

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These quotes, especially the last one, make clear that Andrew Grathwohl takes for granted a theory-practice dichotomy. Whatever Ayn Rand was writing about it couldn't possibly capture what actually happens in music because theory is limited to words that do not refer to reality but perfect Pythagorean mathematical constructs, such as a perfectly unwavering frequency.

You've actually succeeded in over-complicating my ideas, in a rather shallow way. The conflict is simple: in reality, Ayn Rand tried to connect the physical properties of musical sounds to the definition of music psychologically - that exclusive property being periodic sonorous activity; in reality, rarely are musical sounds sonorously periodic.

If anybody is ignoring reality, it is the one who is apologizing for this factual error by incorrectly stating that Ayn Rand's use of the word "periodic" was meant perceptually, when in reality, it was meant physically. There's no getting around this, and your suggestion that a perfectly unwavering frequency is not possible in reality shows your lack of credibility. Periodic frequencies are easily obtained by anybody who possesses mid-grade consumer audio equipment nowadays.

Edited by Andrew Grathwohl
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Periodic frequencies have always easily been obtainable by anyone making a taut string vibrate.

Your lack of precision in this sentence is astounding, and makes your argument vague and worthless. Humans don't have the potential to play instruments periodically, and humans don't have the potential to design acoustic instruments that sound periodically. In what way do you claim periodicity? Physically? Then you're simply wrong. Psychoacoustically? Then you're not giving people credit who actually have discerning ears. Either way, you're absolutely not correct, and your entire defense is based on context-dropping.

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Grames is right here. Period is inversely proportional to frequency. A pluck of a string has a frequency. Therefore, it has a period. Q.E.D.

It has a period, but that doesn't mean that the sound itself is periodic. Period as it relates to frequency is a measurement of the number of cycles as a result of time (time/cycle). In other words, period is only a measurement of how long it takes to complete a single revolution. That has no bearing on the periodicity of a wave, and certinly doesn't influence the revolution that preceeds or proceeds it.

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It seems that most of the members who have responded don't have any understanding of how sound moves through air, nor how it is perceived. I also suspect just about everyone that responded did not actually read the essay, either.

Just because something has a period - that doesn't make it periodic. And just because something sounds the same to the listener doesn't make it periodic either. And furthermore, if anybody actually read the essay before responding, then they'd know that Ayn Rand makes a direct connection between the physical properties of a sound and its musicality. These three facts need to be addressed in order to go anywhere meaningful with this discussion.

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Wikipedia

Subjective aspects

Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called "sound". Most sound that people recognize as "musical" is dominated by periodic or regular vibrations rather than non-periodic ones (called a definite pitch), and we refer to the transmission mechanism as a "sound wave". In a very simple case, the sound of a sine wave, which is considered to be the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very "pure" tone. Pure tones can be produced by tuning forks or whistling. The rate at which the air pressure varies governs is the frequency of the tone, which is measured in oscillations per second, called hertz. Frequency is a primary determinate of the perceived pitch. Frequency can change with Altitude due to changes in air pressure. This is called the Adiabatic Lapse Rate.

Periodicity, illustrated. The fundamental and first 6 harmonic modes of a vibrating string.

Moodswingerscale.jpg

Periodicity is fundamental to the concept of a musical scale, which is derived from ratios of the pure tones.

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Periodicity is fundamental to the concept of a musical scale, which is derived from ratios of the pure tones.

You would do best to give this up. You have a lot more reading to do about sound.

What that picture demonstrated wasn't periodicity. It merely demonstrated the first six harmonic modes of a vibrating string (fixed or unfixed is unclear, clearly showing how much validity your source truly holds). Periodicity, in the context of the physics of sound, is unrelated to the modal systems of vibrating bodies. The only way in which periodicity comes into play is that it is required for a resonant modal response, but that is only necessary for as long as the harmonic is being sounded. And considering pretty much all sounds made by humans have a plethora of partials to select from to create resonant tones (not just harmonics) it is easy for a vibrating string to play a non-harmonic upper-partial with a resonant response. Simply put, this means that upper-partial resonance can be obtained without periodicity on the part of either the resonant force or the initial vibration.

Periodicity of sounds is dependent on looking at at least two full cycles of a wave of sound. You haven't presented one bit of evidence to suggest you even know what periodicity means in the context of the physics of sound travel.

It is just about impossible to hear a pure tone, as even the purest of tones suffer from spectral splatter (which is only minimized by having attack and release times beneath 200 milliseconds - not eliminated). Musical scales, just like pure tones, are ideas that can only be put into practice (on a human being playing a musical instrument) by means of estimation. Periodicity only applies to musical scales because, like all aspects of the science of sound, its ideas are mathematically-derived, and unrealistic assumptions are made when formulating these ideas. Periodic sounds have to be assumed in order to carry out the concept of a musical scale, because otherwise you couldn't mathematically-justify them. But even if your auditory nerve fibers have incredibly poor tuning curves, or if you have bassilar hearing damage, you can still detect changes in timbrel and harmonic quality despite the fact that the sounds may be played at agreeable (psychoacoustically-speaking) intervals to the listener.

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You would do best to give this up. You have a lot more reading to do about sound.

What that picture demonstrated wasn't periodicity. It merely demonstrated the first six harmonic modes of a vibrating string (fixed or unfixed is unclear, clearly showing how much validity your source truly holds). Periodicity, in the context of the physics of sound, is unrelated to the modal systems of vibrating bodies. The only way in which periodicity comes into play is that it is required for a resonant modal response, but that is only necessary for as long as the harmonic is being sounded. And considering pretty much all sounds made by humans have a plethora of partials to select from to create resonant tones (not just harmonics) it is easy for a vibrating string to play a non-harmonic upper-partial with a resonant response. Simply put, this means that upper-partial resonance can be obtained without periodicity on the part of either the resonant force or the initial vibration.

Yes every instrument and even every Stradivarius violin is different in its sound because of the vibrations which are not exactly on the pure tone, and yet they are all still instruments capable of being tuned to the same standard. It is not the differences that make music possible but the similarities.

Periodicity of sounds is dependent on looking at at least two full cycles of a wave of sound. You haven't presented one bit of evidence to suggest you even know what periodicity means in the context of the physics of sound travel.

Physics is actually irrelevant to philosophizing about music. No comprehension of physics is necessary to hear or compose music, and ancient music predates physics.

It is just about impossible to hear a pure tone, as even the purest of tones suffer from spectral splatter (which is only minimized by having attack and release times beneath 200 milliseconds - not eliminated).

It is ironic that you would make such an error immediately after attacking my own level of knowledge. This is backwards. Long attack and release times reduce spectral spread, short times necessarily broaden it. Review Fourier analysis to understand why. But this is a distraction. It is no more impossible to hear a pure tone than to see a pure color, and even colors produced by lasers suffer from finite spectral spread.

Musical scales, just like pure tones, are ideas that can only be put into practice (on a human being playing a musical instrument) by means of estimation. Periodicity only applies to musical scales because, like all aspects of the science of sound, its ideas are mathematically-derived, and unrealistic assumptions are made when formulating these ideas. Periodic sounds have to be assumed in order to carry out the concept of a musical scale, because otherwise you couldn't mathematically-justify them. But even if your auditory nerve fibers have incredibly poor tuning curves, or if you have bassilar hearing damage, you can still detect changes in timbrel and harmonic quality despite the fact that the sounds may be played at agreeable (psychoacoustically-speaking) intervals to the listener.

With this last paragraph you once again parade your idealism before the world and take it for granted that it is correct and that all reasonable people agree with you. Your 'pure tone-real sound' dichotomy is just a form of the theory-practice dichotomy. It is wrong and explicitly rejected in Objectivism, and is the real issue that must be overcome before any progress can be made in this thread. Musical scales are not just mathematically justified, they sound right. The mathematics of musical scales is an explanation, a story told in hindsight, not a cause of what is musical.

Consider this quote from the Ayn Rand Lexicon

[Consider the catch phrase:] “This may be good in theory, but it doesn’t work in practice.” What is a theory? It is a set of abstract principles purporting to be either a correct description of reality or a set of guidelines for man’s actions. Correspondence to reality is the standard of value by which one estimates a theory. If a theory is inapplicable to reality, by what standard can it be estimated as “good”? If one were to accept that notion, it would mean: a. that the activity of man’s mind is unrelated to reality; b. that the purpose of thinking is neither to acquire knowledge nor to guide man’s actions. (The purpose of that catch phrase is to invalidate man’s conceptual faculty.)

This is precisely the pattern of attack you have employed here. Ayn Rand's concept of music is invalid you say because periodicity does not actually exist and what does exist is not what she is referring to. Yet periodicity is an objective, specific, physical attribute and you want to replace it with "organized sound", a completely subjective 'eye of the beholder' type of standard. If "music is organized sound" extends so far as to cover "musique concrete" then there is no common denominator that distinguishes musical sound from any sound at all, except for the fact that it was recorded and placed into a composition which reduces to the explicitly subjective "music is whatever musicians do". You are advocating the disregard of a valid concept in favor of an anti-concept.

Definitions are covered in Introduction to Objectivist Epistemology, and are reviewed briefly in chapter 3 of Dr. Peikoff's OPAR. The principles of fundamentality and essence are also critical to understanding why Rand forms the definition in the way she does. A fundamental is that which makes possible the other attributes, or the most other attributes. Fundamental encompasses a variety of possible forms of relationships including: causes, underlies, makes possible, relation of an attribute to its exercise, leads to deductively; a cause which is necessary but not necessary and sufficient. An essence is that which constitutes the being of a unit; that by which something is the member of concept; that by which something belongs to a certain class. Essence as Objectivism uses it, is an epistemological term, not metaphysical. Metaphysically all attributes are equally important to an entity, there is no basis for discriminating among them. An essence is found by using the rule of fundamentality among the differentiating feature(s). Forming an essence accomplishes unit reduction by discarding nonessential attributes because they are non-distinctive and selecting the fundamental. {I'm mostly quoting here from my notes on Peikoff's Art of Thinking lectures, covering material left out of OPAR.}

Fundamentally periodicity is required because it is the basis for constructing any scheme of musical scale, and there has to be some musical scale at work for an abstract sequence of tones that don't particularly sound like anything else to evoke an emotional response. The definition Rand gives skips over this 'middle term' of the musical scale and isolates a fundamental, which I admit I did not follow at first but I'm on board with it now that I recall the relationship between tones and scales.

edit:

The only possibility 'musique concrete' has to be useful is a creation of a new set of sounds equivalent to a new musical instrument, as long as it can be reconciled to some musical scale.

Edited by Grames
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Humans don't have the potential to play instruments periodically, and humans don't have the potential to design acoustic instruments that sound periodically.

Andrew, what do humans have the potential to do with instruments? Do you have a defintion of music that you could offer in alternative to what you disagree with concerning Ayn Rand's statement? Most specifically, if real-world instruments are "aperiodic", do you think there is a defining or essential characteristic to aperiodic sounds that makes it possible to separate them into two categories: musical and non-musical?

My position is that any "auditory object" can be used to create music as long as it can be heard by a human ear and understandable to a human mind as pitch specific. So, you can create sounds from a violin, synth, or drums that are pitch specific enough to be musical in nature.

Also, I listened to your MP3s on your myspace page linked in your signature. Are all the sounds in those MP3s representative of what you regard as musical sounds? Can you provide an example of a sound that is not potentially musical in nature?

Periodicity is fundamental to the concept of a musical scale, which is derived from ratios of the pure tones.

In my estimation this is right on the money.

Your 'pure tone-real sound' dichotomy is just a form of the theory-practice dichotomy. It is wrong and explicitly rejected in Objectivism, and is the real issue that must be overcome before any progress can be made in this thread. Musical scales are not just mathematically justified, they sound right. The mathematics of musical scales is an explanation, a story told in hindsight, not a cause of what is musical.

Wow. Well stated. Grames, I've sincerely enjoyed your replies in this thread. :)

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With this last paragraph you once again parade your idealism before the world and take it for granted that it is correct and that all reasonable people agree with you. Your 'pure tone-real sound' dichotomy is just a form of the theory-practice dichotomy. It is wrong and explicitly rejected in Objectivism, and is the real issue that must be overcome before any progress can be made in this thread. Musical scales are not just mathematically justified, they sound right. The mathematics of musical scales is an explanation, a story told in hindsight, not a cause of what is musical.

I wouldn't call it a theory-practice dichotomy, though perhaps it's related. I would say that a more precise classification of his argument would be to call it a nominalist approach to concepts and definitions.

See:

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Physics is actually irrelevant to philosophizing about music. No comprehension of physics is necessary to hear or compose music, and ancient music predates physics.

According to Ayn Rand herself, the first statement is untrue.

Music employs the sounds produced by the periodic vibrations of a sonorous body, and evokes man’s sense-of-life emotions. - Ayn Rand

The second statement is outrageous. I would never wish to hear a composer's work who did not have a very sophisticated understanding of the timbrel qualities of different instruments. That's the basis of instrumentation. Not understanding the harmonic qualities of each instrument, and the ways that certain instruments will combine when sounded together, are huge pitfalls in music composition.

It is ironic that you would make such an error immediately after attacking my own level of knowledge. This is backwards. Long attack and release times reduce spectral spread, short times necessarily broaden it.

You're right. That was a factual error on my part, caused by not reading over my post carefully enough.

It is no more impossible to hear a pure tone than to see a pure color, and even colors produced by lasers suffer from finite spectral spread.

Package-dealing. Human vision is a whole different sensory ballgame, with a much more refined sensitivity.

Musical scales are not just mathematically justified, they sound right. The mathematics of musical scales is an explanation, a story told in hindsight, not a cause of what is musical.

Traditional western scales (major, minor) use the equal temperament tuning system, which is completely based on the physics of frequency ratios. Why do they sound right? Because the interval spacings of the musical scale affect the bassilar membrane through ratios that the central auditory system perceives as pleasant. But that has nothing to do with the music people like. Nobody likes hearing sine waves, no matter what scale they're played under, no matter what tuning system is utilized. This is because, more often than not, and especially in popular music, timbre defines what people like and don't like. This is why popular songs often share many qualities, such as length, chord progression, structure, instrumentation, etc. The only justification for a scale "sounding good" is the bassilar membrane's logarithmic reaction to frequency and amplitude. As Ayn Rand herself has said, no objectively valid criterion of esthetic judgment is possible in the field of music, so the argument that something sounds objectively "right" is not a valid one to make.

Ayn Rand herself disproves your idea in "Art and Cognition":

Helmholtz has demonstrated that the essence of musical perception is mathematical: the consonance or dissonance of harmonies depends on the ratios of the frequencies of their tones. The brain can integrate a ratio of one to two, for instance, but not of eight to nine. - Ayn Rand

Ayn Rand's concept of music is invalid you say because periodicity does not actually exist and what does exist is not what she is referring to. Yet periodicity is an objective, specific, physical attribute and you want to replace it with "organized sound", a completely subjective 'eye of the beholder' type of standard. If "music is organized sound" extends so far as to cover "musique concrete" then there is no common denominator that distinguishes musical sound from any sound at all, except for the fact that it was recorded and placed into a composition which reduces to the explicitly subjective "music is whatever musicians do". You are advocating the disregard of a valid concept in favor of an anti-concept.

Periodicity absolutely does exist, and I never said otherwise. There is a difference between a thing being examinable only in certain fields of study and a thing being entirely unattainable in reality.

"Organized sound" would mean that frequency and timing were both manipulated by the composer. But disregard my attempts at definition for a moment and consider the way you've managed to pigeonhole an entire practice of musical composition, despite its potential for inherently musical qualities. You claim that any composer who composes with manipulated recorded sounds is not creating musical sound. Of the endless possibilities inherent in such practices, you make the ridiculous claim that this same process is incapable of making anything sound musical. Is it not possible to manipulate a sound's pitch to make it ascend a harmonic minor scale? Is it not possible to add algorithmically-determined harmonic information to a recorded sound to change its pitch properties over time, with those pitches being determined by an arpeggio function? Whatever your odd definition of music is, I'm certain that there exist a plethora of pieces composed in this manner which could be deemed "musical" in terms of both your own definition, as well as the psychological terms, which Ayn Rand discussed in "Art and Cognition."

Just because you don't like a certain kind of music does not make it unmusical. If you think musique concrete has no musical value, then you have absolutely no concept of the practice. How are all works composed with the musique concrete technique not music? I take it you'd have enough sense to not be a fan of naturalism, so surely you could defend this sentiment in the other arts. Is Rosencrantz and Guildenstern Are Dead not a play? Are the works of Jackson Pollock not pantings?

Fundamentally periodicity is required because it is the basis for constructing any scheme of musical scale, and there has to be some musical scale at work for an abstract sequence of tones that don't particularly sound like anything else to evoke an emotional response. The definition Rand gives skips over this 'middle term' of the musical scale and isolates a fundamental, which I admit I did not follow at first but I'm on board with it now that I recall the relationship between tones and scales.

You're confusing process with result. It is standard practice for any composer to understand and manipulate the frameworks that he/she is using to compose, but outside of musical composition, the presence of a scale in a piece of music, or the type of scale used, is only inherently necessary to consider for composers who write works of music containing standard musical scales. Scales are not concepts that are necessary to understand for musical listening or enjoyment. In fact, there is no need for a piece of music to have a scale of any sort for it to be enjoyed, even if you consider the fact that musical scales help you reach a broader audience by using musical qualities that your audience has grown up hearing their entire lives. This is evident by examining the emotional responses that atonal and non-Western pieces elicit from listeners. Periodicity is not required for performing a musical composition because, if it were, then very little music would ever be played, since fluctuations in frequency occur all the time in musical performance, which can be the result of either intentional modulations or unintentional fluctuations due to technique and materials. Periodicity is involved in anatomically perceiving music, due to the human ear's auditory nerve fiber tunings and the Greenwood function inherent in the bassilar membrane's place-frequency map. However, once we deal with the psychoacoustic processing of sound, it's anybody's guess at this point. Even Ayn Rand herself stated that the jury is not out on that one, as referenced above.

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Do you have a defintion of music that you could offer in alternative to what you disagree with concerning Ayn Rand's statement? Most specifically, if real-world instruments are "aperiodic", do you think there is a defining or essential characteristic to aperiodic sounds that makes it possible to separate them into two categories: musical and non-musical?

My position is that any "auditory object" can be used to create music as long as it can be heard by a human ear and understandable to a human mind as pitch specific. So, you can create sounds from a violin, synth, or drums that are pitch specific enough to be musical in nature.

I do not have a definition of music that I am comfortable with. I started this thread because my studies of sound, audio, and music, completely refute Ayn Rand's definition.

I agree with your position. The problem is defining what is musical. A guy named Thomas Clifton wrote a book called "Music as Heard" in the 1980s, and he claimed the following definition of music:

an ordered arrangement of sounds and silences whose meaning is presentative rather than denotative. . . . This definition distinguishes music, as an end in itself, from compositional technique, and from sounds as purely physical objects." - Thomas Clifton

This one works best, in my opinion. But frankly I have not put too much thought into coming up with a better definition.

Also, I listened to your MP3s on your myspace page linked in your signature. Are all the sounds in those MP3s representative of what you regard as musical sounds? Can you provide an example of a sound that is not potentially musical in nature?

That last piece was written on commission, and I openly state that it is not of value to me. So with regard to that piece, no, I don't regard it as fully musical. I slipped a melody into the piece, but that's it. The first two are movements of a string suite, and I take that work very seriously.

Any sound can be MADE musical by means of electronic modification, so no, I cannot provide you with a sound that is not potentially musical.

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