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Ayn Rand's Definition of Music

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Andrew Grathwohl
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Sound is my life. It is my study, my career, and my hobby. Though I am (relatively) new to exploring and studying Objectivism, and its associated sciences, sound is an area of self-proclaimed expertise for me. I recently finished reading Ayn Rand's brilliant The Romantic Manifesto but I have a few quibbles that I would like addressed.

Ayn Rand defines music as an art, which "employs the sounds produced by the periodic vibrations of a sonorous body, and evokes man’s sense-of-life emotions." She claimed that works employing techniques such as musique concrete, and other forms which employ non-traditional instrumentation, were not periodic, and therefore were not actually fit to be "music" as she defines it.

My problem with this is that an average human being would be quite hard pressed to find an example of periodic sonorous activity. If a clarinetist, or a violinist, were able to produce a truly periodic result from playing their instrument, it would be a miraculous physical achievement, and much study would need to go into both the performer's mind and the instrument's construction. 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. That being said, it is of particular interest that the only composers to probably ever achieve this are the very composers that Ms. Rand likely was addressing in her writings on music - Karlheinz Stockhausen, Edgar Varese, and others who utilized analog audio equipment as part of their concert-hall performances, are likely the only individuals to ever make music according to Ayn Rand's own standards.

The other problem with her definition of music is that it, by definition, labels all non-periodic traditional western instruments, like percussive instruments, as "noise" - not music. Instruments which are struck are of a particular sonic interest because they do not produce overtones which are harmonically-consistent with its fundamental striking frequency. These sounds, by definition, are aperiodic, which makes me wonder what Ayn Rand thought of music which featured percussion instrumentation. It should also be noted that any "noisy" sound could be made into a periodic waveform by means of either analog or digital manipulation. You will find almost all composers of the musique concrete persuasion are doing this.

Ayn Rand also made the claim that Western music was the best music ever made because its musical scales are the most capable in extending the possibilities of consonant spacings. She drew a connection between the cultures of societies and their respective musics. However, the North-Indian musical tradition, which has employed the use of raga for centuries (far before the first Romantic classical composers of the 19th century, and even before Bach), in fact has more consonant possibilities than Western scales, and also features heavy emphasis on improvisation. This doesn't gel with Ayn Rand's claims, as we all know what the Hindu cultural history consists of. She claimed that the Western individual has no ability to understand the musics of the "Oriental" persuasion, similar to how language barriers exist among different cultures. But we know from the countless numbers of people who enjoy both classical and raga music equally, and who, like myself, find just as much validity, pleasure, and - most importantly - musical possibilities - in them both, that the number of notes in a scale is not indicative of musical complexity. Musicologists have shown that where one type of possibility is limited in a particular musical form, another is greatly expanded. Rhythmic lines and counterpoints exist on a much greater conceptual scale in several cultural musics, including the Japanese, the Indian, and the Pakistani forms. And even those have varying degrees of sonic and harmonic complexity - ranging from five-note scales, all the way up to scales which feature different interval spacings in different octaves. The Qawaali tradition in Pakistan, for example, is a beautiful indicator of Romantic (big R, not little r) music, performed by savage peoples. Look into the recently-deceased Nusrat Fateh Ali Khan, who carried on a centuries-old family tradition in the Qawaali tradition. The rhythmic potential is vast, the performances are heart-felt, and the form and style is far from mathematically-dull (her claim was that music which did not feature mathematical-complexity would bore the listener, and only appeal to those whose philosophical premises were incorrect).

This is information that was available to anybody at the time when Ayn Rand wrote these things. Psychoacousticians, physicists, and musicologists alike, have been pursuing these topics, and it only takes an individual of great musical and sonic experience to understand the validity to my claims.

I want to side with Ayn Rand on these issues, but doing so would completely obliterate my reasonably strong knowledge of the physics of sound, the human perceptions of sound, and the musics of various cultures and time periods. Doing so would be nothing more than taking another person's words on faith, when I know well enough that they are not valid. What I wonder, after having said all of this, is if Ayn Rand addressed any of these issues at a later date than The Romantic Manifesto, or if there are any objections to my claims. Anybody?

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Periodic doesn't necessarily mean repeating which is what I believe you are implying. It just means it changes as a function of time. A sine wave visualized on an oscilloscope can be and usually is quite complex when it is an actual representation of real music.

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Periodic doesn't necessarily mean repeating which is what I believe you are implying. It just means it changes as a function of time. A sine wave visualized on an oscilloscope can be and usually is quite complex when it is an actual representation of real music.

In physics, periodic never means "repeating" - there's already a word for that. Periodic implies an event that recurs at equal intervals of time. Your definition is not valid in the field of physics.

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In physics, periodic never means "repeating" - there's already a word for that. Periodic implies an event that recurs at equal intervals of time. Your definition is not valid in the field of physics.

Same difference.

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Same difference.

Not at all. A periodic wave would never deviate from its starting frequency. As I've already brought up, no wave produced by a human being on a musical instrument fits that description. Frequency is a function of the number of occurrences of a repeating event over a unit of time. Thus, if frequency changes, then its periodicity has changed. In sound, the period of a wave can be found by dividing 1 by its frequency. It should be clear that if frequency changes, its period changes as well - making it aperiodic.

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Rand's definition of music sounds rather peculiar. However I just took it to mean music must have 'rhythm' (which is what periodic is alluding to).

I came up with my own definition of music a while ago. It was something like

'Sound-concepts organized linearly for entertainment.'

Sound-concepts because music is still music in its written form, or in the composers head, or the audience's memory etc

Organized so to discount the sounds of nature etc.

Linearly because 'time' is not a primary here - when written down music has order but not duration; and when performed actual duration can vary

Entertainment so as to discount obviously non-musical things like dial-tones

I suppose you could say this doesn't discount things like plays but I would argue that its not really 'sound-concepts' being organized, primarily, but linguistic units or actions

Additionally I think the traditional melody + harmony + rhythm definition theoretically applies but not in the snobbish way its usually brought up ('hiphop isn't music, there's no melody' etc). Think of a graph representing sound: x axis is melody; y axis is harmony; z axis is rhythm. Rhythm is the timing, melody is order of notes, and harmony is relationship of notes (intervals). Even if you just have a single ,ascending, recurring beep, it still has rhythm because there's a pattern in the timing, it still has melody because one beep is following another, and it still has harmony because there is an interval between each beep. Even a single beep and nothing else would have timing (start and end) and melody and harmony values that are set to 'zero' as it were.

Anyway i'm not saying it's easy to define. Rand's definition is interesting insofar as that she was a great mind and in the quest for an answer, she could probably give some insight, if not the final answer.

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Sound is my life. It is my study, my career, and my hobby. Though I am (relatively) new to exploring and studying Objectivism, and its associated sciences, sound is an area of self-proclaimed expertise for me. I recently finished reading Ayn Rand's brilliant The Romantic Manifesto but I have a few quibbles that I would like addressed.

Ayn Rand defines music as an art, which "employs the sounds produced by the periodic vibrations of a sonorous body, and evokes man’s sense-of-life emotions." She claimed that works employing techniques such as musique concrete, and other forms which employ non-traditional instrumentation, were not periodic, and therefore were not actually fit to be "music" as she defines it.

My problem with this is that an average human being would be quite hard pressed to find an example of periodic sonorous activity. If a clarinetist, or a violinist, were able to produce a truly periodic result from playing their instrument, it would be a miraculous physical achievement, and much study would need to go into both the performer's mind and the instrument's construction. 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. That being said, it is of particular interest that the only composers to probably ever achieve this are the very composers that Ms. Rand likely was addressing in her writings on music - Karlheinz Stockhausen, Edgar Varese, and others who utilized analog audio equipment as part of their concert-hall performances, are likely the only individuals to ever make music according to Ayn Rand's own standards.

Didn't Ayn Rand read Helmholtz?

Anyway, I find it hard to believe sounds from instruments are not periodic. They always sound the same. A violin sounds like a violin, because it has a particular timber and range of pitches. How can it sound the same and not generate the same wave form? And don't synthesizers store wave forms and replay them to mimic the sound of instruments? Or, am I misreading you here?

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A characteristic of any tone that can be recognized as such is that it is periodic, while non-periodic sound is perceived as noise with which we cannot associate a tone. For example the "concert A" is defined as an oscillation with frequency 440 Hz. That in practice such tones are not exactly periodic is in my view not essential. It is like saying that the Earth is a sphere, which is also only an approximation, but that is also true for a billiard ball. Further, periodic does not necessarily mean a sine wave, in general a tone will be a mixture of more or less audible sine waves with different frequencies, in which the lowest in general is the strongest and defines the tone. Even most percussion instruments produce periodic vibrations, only these are of short duration and often have different and strong overtones, so that the tonal quality is less obvious, but in most (not all) cases still a tone (defined by the periodic character of the sound) can be discerned.

That in music tones change continuously in frequency and volume doesn't change the fact that the building blocks are periodic - even if not exactly, still quite accurately as we can hear quite small deviations of frequency, which if they are unintended (as in a string vibrato, a kind of second-order periodicity) can be experienced as "out of tune".

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Periodic doesn't necessarily mean repeating which is what I believe you are implying. It just means it changes as a function of time. A sine wave visualized on an oscilloscope can be and usually is quite complex when it is an actual representation of real music.

Periodic is by definition repeating. And a sine wave is one of the simplest periodic functions. Most music instruments produce much more complex periodic functions, which can be seen as the sum of a series of sine waves (with Fourier analysis any periodic function can be described as an infinite series of sine functions), with a ground tone that defines the base frequency and a series of overtones, the values and the amplitudes of which determine the timbre of the instrument.

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Hint: A musical sound can be represented by a Fourier Series. This is a weightsum of periodic functions usually sin and cosine functions of various frequencies.

Bob Kolker

Quite true. You can sum component sign waves to recreate complex wave forms. I'm still curious as to what Andrew Grathwohl is saying.

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I'm still curious as to what Andrew Grathwohl is saying.

I am too. Rand did not write that striking a drum one time produces a sound that is aperiodic, therefore drums are forbidden from music. It sounds like he is focusing on the sounds that individual instruments make, but any sound at all that is repeated is periodic including a drum beat. Construing periodic as a perfectly pure single frequency is wrong because it is out of the context appropriate to the subject. People do not perceive frequency they perceive pitch. Physically frequency causes pitch but that is an abstract scientific understanding not necessary to form the concept of music. People don't perceive frequency in light either, they perceive color.

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My language was too loose I guess. I wasn't implying that all music is sine waves that would be sound from a tone generator. I meant "sine" wave in the loosest sense actually meaning a complex wave of both sine, cosine, and every other type. And all I meant by not "repeating" is actual music doesn't usually just repeat the same waveform over and over which once again would just be the output from a tone generator. I just think this is one time Miss Rand was also being loose in her language since she wasn't a physicist and it's obvious that the music she was referring wasn't the output from a tone generator.

And since frequency is inversely proportional to the period of a wave it is directly perceivable that as the the frequency changes the period must also.

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Didn't Ayn Rand read Helmholtz?

Anyway, I find it hard to believe sounds from instruments are not periodic. They always sound the same. A violin sounds like a violin, because it has a particular timber and range of pitches. How can it sound the same and not generate the same wave form? And don't synthesizers store wave forms and replay them to mimic the sound of instruments? Or, am I misreading you here?

Yes, Ayn Rand read, and cited, Helmholtz. Sounds from instruments are never periodic. They may always sound the same to you, but by nature, their sonorous output will never be periodic. It can sound "the same" to you because the ear is more sensitive to certain types of sound over others, and are unable to distinguish slight frequency and timbrel changes. The trained ear can certainly make this distinction better than the layperson's, but only by so much.

I'd be hard pressed to ever find a person who was able to record two identical sounds of any type from any source whatsoever and achieve the exact same waveform. But I imagine you're rather referring to the wave shape, which is not the same thing. Subtle timbrel changes happen all the time, because there is an elasticity to such musical outputs due to both performance and instrumental material restraints. In other words, the human being and the instrument are both incapable of maintaining the exact same sound quality each and every time.

I am too. Rand did not write that striking a drum one time produces a sound that is aperiodic, therefore drums are forbidden from music. It sounds like he is focusing on the sounds that individual instruments make, but any sound at all that is repeated is periodic including a drum beat. Construing periodic as a perfectly pure single frequency is wrong because it is out of the context appropriate to the subject. People do not perceive frequency they perceive pitch. Physically frequency causes pitch but that is an abstract scientific understanding not necessary to form the concept of music. People don't perceive frequency in light either, they perceive color.

I wrote that bit under the assumption that people would nit-pick at the true definition of "periodic" - which I appear to have correctly predicted. I meant that even if one were to argue that a clarinet or a violin makes a periodic sound, there is no way that anybody with any knowledge on the subject could claim a drum, or some other percussive instrument, is periodic in nature. Percussive instruments are meant to be aperiodic in nature. A percussive instrument is composed of extremely aperiodic upper partials, along with its timbrel overtones not in any harmonic series, and its original striking frequency (which is also quite elastic, due to striking quality, strength, and precision).

You make a very incorrect claim that people perceive frequency as opposed to pitch. I am just as able to point out a sound's frequency as I am a sound's pitch. Having been trained in recording arts, I need to be able to do this in order to best prepare for live sound situations which call for very substantial equalization processing for a clear mix.

Actually, all sound CAN be deconstructed into a collection of sine waves of differing phases, frequencies, and amplitudes. But that's not what I said was the definition of "periodic" in the post, and it's aside the point - if Ayn Rand is going to claim that all music features periodic sonorous activity, then I imagine she had either evidence to prove this assertion true, the lack of knowledge to know any better, or did not think of the many ways in which her words could be misinterpreted.

What about her claims on non-Western music?

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I wrote that bit under the assumption that people would nit-pick at the true definition of "periodic" - which I appear to have correctly predicted. I meant that even if one were to argue that a clarinet or a violin makes a periodic sound, there is no way that anybody with any knowledge on the subject could claim a drum, or some other percussive instrument, is periodic in nature. Percussive instruments are meant to be aperiodic in nature. A percussive instrument is composed of extremely aperiodic upper partials, along with its timbrel overtones not in any harmonic series, and its original striking frequency (which is also quite elastic, due to striking quality, strength, and precision).

Yeah yeah, that's all fine except that percussive instruments are struck in a rhythm. Rythyms are periodic.

You make a very incorrect claim that people perceive frequency as opposed to pitch. I am just as able to point out a sound's frequency as I am a sound's pitch. Having been trained in recording arts, I need to be able to do this in order to best prepare for live sound situations which call for very substantial equalization processing for a clear mix.

Whatever it is that one is given directly upon hearing a sound, it is not a frequency. That is a later conceptual identification.

Actually, all sound CAN be deconstructed into a collection of sine waves of differing phases, frequencies, and amplitudes. But that's not what I said was the definition of "periodic" in the post, and it's aside the point - if Ayn Rand is going to claim that all music features periodic sonorous activity, then I imagine she had either evidence to prove this assertion true, the lack of knowledge to know any better, or did not think of the many ways in which her words could be misinterpreted.

What about her claims on non-Western music?

There is no general theory of music, and no Objectivist theory of music. She identified what music is by an appeal to essential traits, periodicity of the sounds and the effect on the listener. If I were going to argue with this definition, I would attack the 'effect on the listener' aspect as rather difficult to reduce to concretes in an objective way. Your attack on periodicity is the real nitpicking. Any sequence of sounds whatever that occur at regularly timed intervals meet this idea of periodicity and nothing more specific can be wrung out of it.

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Yeah yeah, that's all fine except that percussive instruments are struck in a rhythm. Rythyms are periodic.

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."

Whatever it is that one is given directly upon hearing a sound, it is not a frequency. That is a later conceptual identification.

It is not a pitch either. My point was that people learn how to quantify sounds in different ways, and some are far better at it than others.

There is no general theory of music, and no Objectivist theory of music. She identified what music is by an appeal to essential traits, periodicity of the sounds and the effect on the listener. If I were going to argue with this definition, I would attack the 'effect on the listener' aspect as rather difficult to reduce to concretes in an objective way. Your attack on periodicity is the real nitpicking. Any sequence of sounds whatever that occur at regularly timed intervals meet this idea of periodicity and nothing more specific can be wrung out of it.

Was this a response to my questioning of her near hatred for non-Western music, or a continuation on the topic of music's definition? Because I am not necessarily concerned with her definition as such - we all likely knew what she meant. My problem is that Ayn Rand would have never used the word "periodic" if she actually knew what it meant in the context of sound, and would have rather used the typical definition of organized sound. My thinking is that she tried to rationalize with the music that she hated and could not understand, and thus came up with this definition (which is, in plain English, wrong) as an attempt to exclude certain types of music. There is no true reason to use the word "periodic" in this context if she knows what she's talking about.

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Remember esthetics is a branch of philosophy. All of the philosophic concepts in this category must be self evident and ubiquitously available to perception. Andrews point seems to cross over into the special science aspects of sound.

So we are allowed to be imprecise as long as it relates to aesthetics in a philosophic context?

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We all knew it was going to happen. There's no use denying it! From the moment of the thread's conception, it was known that this post would come. And now here it is:

Main Entry: pe·ri·od·ic

Pronunciation: \ˌpir-ē-ˈä-dik\

Function: adjective

Date: 1642

1 a : occurring or recurring at regular intervals b : occurring repeatedly from time to time

2 a : consisting of or containing a series of repeated stages, processes, or digits : cyclic <periodic decimals> <a periodic vibration> b : being a function any value of which recurs at regular intervals

3 : expressed in or characterized by periodic sentences

Yes, that's right. I just threw a dictionary definition up. This is not an attempt at snark or sarcasm toward any poster in this thread. It is simply a definition for clarification of a term.

Periodic means something very specific and important in the context of musical theory. Ayn Rand was not and did not claim to be a musical theorist, nor a psychologist, or any other kind of scientist.

Periodic also has a general definition which can be used outside the context of the science of musical theory with the above definition. Saying that "if she knew anything about physics, if she knew anything about musical theory, this is what she'd mean." is dropping the context. She did not know anything about physics, or about musical theory, at least that is what you should assume about her when reading one of her philosophical treatises. Her philosophical studies into the branch of aesthetics are not an example of Ayn Rand cavalierly using a basic knowledge of music theory to critique music, she is not using any knowledge of any special science.

The usage of 'periodic' is meant in its most general form as a concept, probably denoting that anywhere within the music there is some sort of repeat and interval. This is certainly true of all the music I listen to, and I listen to a wide variety of music from many cultures. You cannot reduce her definition to the smallest possible component of the song and say 'it doesn't repeat within this tiny context, so she either didn't like this kind of music, or she didn't know what she was talking about.' She meant that in general for a song to be 'musical' it has to repeat at some interval. This is simply a definition of music, much in the same way there is a definition of poetry which sets it apart from prose.

EDIT: As far as her attitude toward oriental musics, I believe her derision was directed specifically at the traditional musics of the area, probably specifically the music of China, Japan, and other Eastern Asian cultures. Until the influence of the West on this music it was largely antiperiodic and non-melodious. I find myself commonly wondering how one can stand to listen to it for long periods of times. However, since the introduction of many instruments to that region they have released tons of music which combines the strange traditional tunes with Western instruments and rhythms, making what I regard to be very nice music.

Edited by Jackethan
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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."

Why would you ever approach anything Ayn Rand wrote as invocations of Platonic Forms that are precise and perfect? Why would you do that to anyone?

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There seems to be a misunderstanding about Rand's use of "periodic" in her discussion of music. She does not mean that certain musical elements (motives, themes) are repeated in a composition, she's talking about periodic vibrations, i.e. sounds that have a definite pitch. A few quotes:

The sounds produced by nonperiodic vibrations are noise.

The proof lies in the fact that music is the product of periodic vibrations - and, therefore, the introduction of nonperiodic vibrations (such as the sounds of street traffic or of machine gears or of coughs and sneezes), i.e. of noise, into an allegedly musical composition eleminates it automatically from the realm of art and of consideration.

It's clear that she distinguishes here periodic vibrations, which we hear as a musical tone with a definite pitch and non-periodic vibrations, sounds which don't have a clear pitch and which she calls noise. This is a physical and not a musical distinction, i.e. it doesn't concern the structure of the music (like: does it have repeating notes, motifs, rhythms), only its elementary building blocks themselves.

Edited by Tensorman
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There seems to be a misunderstanding about Rand's use of "periodic" in her discussion of music. She does not mean that certain musical elements (motives, themes) are repeated in a composition, she's talking about periodic vibrations, i.e. sounds that have a definite pitch. A few quotes:

It's clear that she distinguishes here periodic vibrations, which we hear as a musical tone with a definite pitch and non-periodic vibrations, sounds which don't have a clear pitch and which she calls noise. This is a physical and not a musical distinction, i.e. it doesn't concern the structure of the music (like: does it have repeating notes, motifs, rhythms), only its elementary building blocks themselves.

Thank you for this. I should have been more attentive and supplied those quotes myself. I wrote the OP with those passages fresh in my mind, but failed to provide these passages in the post itself.

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There seems to be a misunderstanding about Rand's use of "periodic" in her discussion of music. She does not mean that certain musical elements (motives, themes) are repeated in a composition, she's talking about periodic vibrations, i.e. sounds that have a definite pitch. A few quotes:

There is already a pre-existing concept called music, the question is how to define it. Periodic is a good stab at identifying what is essential about the sound of music that distinguishes it from other sounds. But a particular musical tone in isolation from any structure has no power to evoke any emotional response whatever, so it is not a complete identification. It is rationalistic to put the definition in front of the concept and claim Ayn Rand thought the presence of percussion disqualifies a piece from being considered music.

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There is already a pre-existing concept called music, the question is how to define it. Periodic is a good stab at identifying what is essential about the sound of music that distinguishes it from other sounds. But a particular musical tone in isolation from any structure has no power to evoke any emotional response whatever, so it is not a complete identification. It is rationalistic to put the definition in front of the concept and claim Ayn Rand thought the presence of percussion disqualifies a piece from being considered music.

Well, in her own words, Ayn Rand disqualified percussion instruments from being musical vessels. Percussion instruments are just as aperiodic as a sneeze, and even more aperiodic than machine gears, and she specifically rules those sounds out from being musical.

The fact is that people have constructed beautiful works of music out of periodically-processed/rendered recordings of machine gears and other "non-musical" recordings. (The composers that immediately comes to mind are Tim Hecker, an electroacoustic composer, and Burial, a London-based electronic musician.) Music's definition should be no more than: an art form whose medium is "organized sound," as defined by composer Edgar Varese. What Ayn Rand tried to do was disregard certain sounds used in modern (at the time) musical compositions which she clearly didn't like. However, saying that is akin to saying Jackson Pollock's works were not paintings. Just because they're naturalist trash, ill-constructed, and make use of completely irrational and ugly forms, doesn't negate the fact that they're paintings nonetheless.

Why would you ever approach anything Ayn Rand wrote as invocations of Platonic Forms that are precise and perfect? Why would you do that to anyone?

I was answering your claim that rhythm featured periodicity, which is simply false. Those two words are not related to one another in any meaningful way, in any context. My words had nothing to do with neither Ayn Rand's works, nor their "preciseness."

Edited by Andrew Grathwohl
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Well, in her own words, Ayn Rand disqualified percussion instruments from being musical vessels. Percussion instruments are just as aperiodic as a sneeze, and even more aperiodic than machine gears, and she specifically rules those sounds out from being musical.

Well.. for starters lets remember that the piano is categorised as a percussion instrument (unless its changed since I was in orchestra).

Ms. Rand was a brilliant thinker but her judgement of music was based on incomplete understanding.

Regarding "oriental" music scales and such. They can certainly ring as discordant to someone unfamiliar with their structure. In many ways it is like speaking another language and I can see someone becoming frustrated with music one doesn't know how to listen to just as one could get frustrated being in a room full of people speaking a language one doesn't know a word of.

Just watch this and tell me it ain't a fine work of art:

;)

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