The Rudolf Steiner Archive

Eighth Lecture

[ 1 ] My dear friends!

[ 2 ] The way we talk about sound and tone today in the standard physical description of them has actually only been the case since around the fifteenth century. It is precisely through such examples that we can best substantiate what I often express in general terms as a finding in the humanities: that people’s entire way of thinking and imagining before this turning point was simply different from how it was afterward, and this way of speaking—the way we now speak about sound and acoustic phenomena in standard physics—actually only gradually emerged.

[ 3 ] The first thing that caught our attention was the speed at which sound propagates. It is, after all, relatively easy—at least to a certain degree of approximation—to determine what can be understood as the propagation of sound. If you fire a cannon at a distance—a considerable distance—you can neglect what is known as the speed of light; you then see the flash of light in the distance and hear the sound just as you hear the thunder after seeing the flash, you then hear the bang, and, as I said, if you disregard the fact that there is a speed of light, you can describe the time that elapses between perceiving the flash of light and perceiving the sound as the time it took for the sound to travel the corresponding distance. And one can then calculate how fast sound travels through the air—say, in one second—thus obtaining something like the speed of sound.

[ 4 ] You see, that was one—I would say—of the earliest elements to attract attention in this field. People also—and it was Leonardo da Vinci in particular—began to take notice of what is known as resonance, or sympathetic vibration, which you are familiar with today: that if you pluck a string in a room or something similar, and there is a string tuned to the same pitch or a completely different object tuned to the same pitch, then that string or that other object vibrates in sympathy. Such phenomena were studied in particular by the Jesuits, and thus the Jesuit Mersenne made extraordinary contributions to the study of sound and tone in the seventeenth century. In particular, this Jesuit, Mersenne, made significant contributions to the studies of so-called pitch at that time.

[ 5 ] You can distinguish three aspects of a sound: First, a sound has a certain intensity; second, it has a certain pitch; and third, it has a certain timbre. Of these three, the most important—the most essential—is pitch. Now the question is to determine what corresponds to pitch from the perspective that has gradually been adopted specifically for the theory of music. I have already pointed out to you that it is very easy to determine that, when we perceive a sound, there is something vibrating underlying it—or, let’s say, accompanying it.

[ 6 ] It is very easy to observe this vibrational nature of air or other bodies through simple experiments—you need only think back to your school days—by striking something like a tuning fork and then—it is not necessary for us to carry out these experiments in detail—and then tracing the line here with the attached stylus. Thus, one can see from the image it creates here on the soot that the tuning fork is in regular motion. This regular motion is, of course, transmitted to the air, and we can say: Whenever we hear any sounding object, the air between it and us is in motion. We set the air in motion directly through the devices we call pipes, where we set the air in motion immediately.

[ 7 ] Now we have gradually come to understand what kind of movements these actually are. They are what are known as longitudinal vibrations, or vibrations along the length. It can also be observed that these are longitudinal vibrations in the air. If one takes a propagating sound—that is, one generates a sound here in a metal tube, connects this metal tube to a tube filled with air so that the movements of the metal tube are transmitted, and then fill this air-filled tube with a freely moving dust, you can observe from the movement of the dust particles that the sound is propagating and that an air compression is initially created. This air compression, in turn, rebounds when the body oscillates back. This creates an air rarefaction. The moment the metal strikes forward again, the original compression continues to propagate, and thus rarefactions and compressions alternate. One can therefore demonstrate directly through experimentation that these are indeed rarefactions and compressions. It is really not necessary for us to carry out such experiments, because such things, I would say, are self-evident. I don’t really want to present to you here everything that can be found in the books.

[ 8 ] Well, the important thing is, you see, that—especially in these branches of physics—an extraordinary amount was accomplished in the early modern period thanks to the social networks fostered by the Jesuits. However, there was always a tendency not to attempt to spiritually penetrate natural processes in any way—that is, to contemplate the spiritual aspect within natural processes—but rather to reserve the spiritual for religious life. The Jesuits always regarded it as dangerous to apply a spiritual approach—as we are accustomed to the term from Goethe—to natural phenomena. The Jesuits wanted to view nature in a purely materialistic way, certainly not to approach nature with the spirit, and in many respects it is precisely the Jesuits who were the first proponents of those materialistic views that are particularly dominant today. People do not realize—though history tells us otherwise—that this very way of thinking, which is applied in physics today, is, at its core, a product of this Catholic tendency.

[ 9 ] Now, the main point is also to determine what underlies our perception of sounds of different pitches. How do the external vibrational phenomena associated with sound differ in relation to these different pitches? Such things can be demonstrated through experiments like the one we can show you. Right? We’ll set this disc with its various holes in rapid motion, and Mr. Stockmeyer will be so kind as to direct a stream of air toward this moving disc (which happens). You can easily tell how the pitch differed. What caused this difference? It was caused by the fact that we have the fewest number of holes on the inner side of the disc—only 40 holes. When Mr. Stockmeyer directed the air stream here, the air stream passed through whenever it encountered a hole, but it could not pass through the gaps, and so on. Due to the rapid movement, the next hole was constantly taking the place of the one before it, and as many pulses were generated as there were holes through which the airflow passed. As a result, we have 40 pulses here on the inside, and 80 pulses in the outermost circle. The pulses cause the waves, the vibrations. So, in the same amount of time—since the [entire structure] rotates at the same rate as the [outer] 80 holes and the 40 inner holes—we have, in that same time, 80 pulses and 80 air vibrations on one occasion, and 40 pulses and 40 air vibrations on the other. The pitch produced when we have 80 air vibrations is twice as high as that produced when we have 40 air vibrations. Through such and similar experiments, it can be demonstrated that pitch is related to the number of vibrations produced in the medium through which the sound propagates.

[ 10 ] Well, if you put together what I’ve just said, you can consider the following. Suppose that what constitutes an oscillation—that is, a compression and rarefaction—[is] such that we can define the wavelength as the characteristic of an oscillation. If \(n\) such waves of length \(l\) are generated in one second, then the entire wave motion advances by \(n \cdot l\); that is, the distance the entire wave motion travels in one second—which I’ll call \(v\)—is \(n \cdot l\).

[ 11 ] And here I ask you to recall what I have stated in my previous reflections. I have told you: One must carefully distinguish everything phoronomic from that which is not merely conceived through inner mental life, but which constitutes external realities, and I have said: External realities can never be merely the countable, the spatial, or movements. External realities, however, are always velocities. This is, of course, no different when we speak of sound or tone. External experience lies neither in \(l\) nor in \(n\); for \(l\) is merely spatial, \(n\) is merely a number; the real lies precisely in the velocity, and when I divide the velocity—which contains within itself the essence of what I designate here as tone or sound—into two abstractions, I naturally do not obtain any true realities in these abstractions, but rather I obtain that which he has abstracted, separated, and divided. Such divisions are the wavelengths, the spatial dimensions, and the number \(n\). If I wish to look at the reality of the tone, at the external reality, then I must look at the tone’s inner capacity to possess velocity. This is what leads to a qualitative consideration of sound, whereas the approach we are accustomed to in physics today is a quantitative consideration of sound—and this is particularly striking in the case of sound, music theory, and acoustics—where it almost always focuses on what is externally quantitative, spatially, temporally, and in terms of motion—and that can be quantified—to describe the qualitative aspect, which is expressed solely in a specific capacity for speed.

[ 12 ] Today, one no longer even realizes how, in essence, one strays into materialistic territory as early as the study of sound. One might say: The matter is actually so obvious that, apart from us, sound as such does not even exist; rather, it is the vibrations that exist apart from us. How could anything, one might say, be clearer than this: When a countercurrent has been established and it has then generated an air current that produces compressions and rarefactions, how could anything be clearer than the fact that compressions and rarefactions now exist here, and that when my ear hears them, there are compressions and rarefactions outside of me, and that then that unknown something within me—which, of course, the physicist need not address, since this is not physics—transforms the air vibrations, the vibrations of bodies, into purely subjective experiences, into what constitutes the qualitative aspect of sound. And you will find this expressed in the most diverse ways: that vibrations exist outside of us, while within us are the effects of these vibrations, which are, however, purely subjective. This has gradually become so ingrained in people that it has resulted in what you can find quoted from Robert Hamerling’s works in my *Riddles of Philosophy*, from which it can be seen that Robert Hamerling, in taking up the teachings of physics, states right at the beginning: What one experiences as a bang is, outside of us, nothing other than a vibration of the air; and anyone who, starting from this premise, cannot believe that what he actually experiences as a sensory perception exists only within him—and that externally it is merely vibrating air or vibrating ether—should not continue reading a book such as the one Robert Hamerling has written. Robert Hamerling even says that anyone who believes the image of the horse he perceives truly corresponds to an external reality understands nothing and should simply slam the book shut.

[ 13 ] Yes, but, my dear friends, such things must be followed through to their logical conclusions. Just imagine if I were to treat you—all of you sitting here—according to this physical way of thinking—a way of thinking, I say, not a method—which physicists have become accustomed to using when dealing with phenomena of sound and light; the following would result: All of you sitting here before me, I perceive only through my own impressions. These impressions are then entirely subjective, just like sensations of light and sound. Apart from me, none of you actually exist as I see you; rather, it is only the air vibrations between you and me that lead me to the vibrations that, in turn, exist within you, and I actually come to the conclusion that all of your inner spiritual essence—which, of course, is undeniable within you—does not actually exist; rather, for me, this inner spiritual essence of all of you sitting here would be merely the effect on my own psyche. Otherwise, there are merely something [like] accumulations of vibrations sitting there in the pews. It is the same kind of thinking as when you deny the inner nature of light and sound—the inner experience that you seem to perceive subjectively. It is exactly the same as when I have you here before me and regard what I have before me merely as something subjective within myself, while denying you the experience of this inner nature.

[ 14 ] What I am about to say seems so obvious and so trivial that, naturally, physicists and physiologists would never imagine themselves committing such trivial errors. But they do it all the same. This whole distinction between the subjective impression—that which is supposed to be subjective—and the objective process is nothing else. Of course, as soon as one proceeds honestly and says: As a physicist, I do not want to investigate sound at all; I do not want to address the qualitative aspect at all, but rather leave that aside and investigate only the external-spatial—one must not call them “objective”—the external-spatial processes, which, however, continue into me, I want to isolate them as abstractions from the totality and not engage with the qualitative aspects—then one is indeed being honest; but one must not claim that one is objective and the other subjective, nor that one is the effect of the other. For what you experience in your soul is not, when I experience it alongside you, the effect of your brain waves on me. It is so significant to recognize this that it is as significant as anything can be for the modern demands of our time and the demands of science placed upon humanity.

[ 15 ] In matters like these, one must not shy away from delving into the deeper connections. You see, it’s easy to say, for example: The vibrational aspect—the sole vibrational aspect—of sound and tone arises entirely from the fact that when I pluck a string in a room and another string, tuned to the same pitch, also resonates, this is based solely on the fact that vibrations are transmitted; vibrations are transmitted through the medium in which they propagate, a medium that runs parallel to the tone. But what one observes here cannot be understood unless one conceives of it as part of a much more general phenomenon. And this more general phenomenon is the following, which has indeed also been observed.

[ 16 ] Suppose you have a pendulum clock in a room that is running—one that you set in motion—and you have another pendulum clock in the same room—though it must be constructed in a certain way—that you do not set in motion; then, under favorable conditions, you will sometimes discover that, little by little, this second pendulum clock begins to run on its own. This is what one might call the “sympathy of phenomena.” This sympathy of phenomena can be investigated in a wide range of fields.

[ 17 ] It is, in fact, the last of these phenomena that still has something to do with the external world; the last of these phenomena is the one that could be studied much more than it usually is—because it actually occurs extremely frequently. You can experience this in countless instances: You are sitting at a table with someone, and they say something you had just thought a moment before. You thought it, and they voice it after you hadn’t said it. This is the sympathetic interplay of events and sequences of events attuned in a certain way, which manifests itself here in a very spiritual realm. And one must recognize a continuous sequence of facts between the simple resonance of a string—which, according to crude, non-spiritual conceptions, is still regarded as mere attunement to external material events—and that which occurs as parallel phenomena of a more spiritual nature, such as the shared experience of thoughts.

[ 18 ] Now, you see, one will not be able to gain clear insights into these things at all unless one is willing to engage with the way in which the human being is itself situated within what is called physical nature. Didn’t we, a few days ago, show the human eye here and analyze it a little? Today we will look at the human ear. As you know, the human eye has, toward the back, the vitreous body, which we could say still possesses vitality, and here [on the outside] is the fluid between the lens and the cornea; and as we move from the outside toward the inside, the eye becomes, so to speak, more and more alive. It is more physical in nature on the outside.

[ 19 ] Just as one can describe the eye, so, of course, one can now also describe the ear, and one can say, in a superficial sense: Just as light makes an impression on the eye by affecting it—or however one wishes to describe it—and the nerve then receives the stimulus, so sound vibrations exert an effect on the ear, enter the ear canal, and strike the eardrum, which closes off the ear canal. Attached to the eardrum from the rear are the ossicles—the malleus, incus, and stapes—so named according to their shapes. So, speaking in physical terms, what is produced there and manifests externally in the air as waves of compression and rarefaction is transmitted through this system of ossicles to what is located here in the inner ear. Here [at the end] in the inner ear is, first of all, what is known as the cochlea, [which] is filled with a fluid and into which the auditory nerve terminates. [Further] forward are the so-called three semicircular canals, which are characterized by the fact that their surfaces are perpendicular to one another in the three directions of space. One can imagine it this way: Sound enters here in the form of air waves. Its transmission is mediated by the ossicles and reaches the fluid. There it reaches the nerves and acts upon the perceiving brain. And so we have the eye as one sensory organ and the ear as the other. One can nicely consider these two things side by side and, as a further abstraction, arrive at a common physiological theory of sensory perception.

[ 20 ] But if you take what I just said—about the interplay between the overall rhythm of the rising and falling cerebrospinal fluid and what is happening externally in the air—if you consider that, then the matter will no longer seem so simple to you. For you will recall that I said one must not assume that what one sees externally as a self-contained entity is a finished reality. For it need not be a finished reality. The rose that I pluck from the rosebush is not a reality, for it cannot exist on its own; it can only come into being through its connection to the rosebush. In truth, it is an abstraction when I think of it as a mere rose. I must proceed to the totality—at least to the entire rosebush. Similarly, when it comes to hearing, the ear is not a reality at all—the ear that is usually presented. For that which is transmitted from the outside through the ear to the inside must first, so to speak, enter into an interaction with that which unfolds as an inner rhythm and manifests itself in the rising and falling of the cerebrospinal fluid, so that we extend what is happening in the ear to what is happening within these rhythmic movements of the cerebrospinal fluid.

[ 21 ] But we’re not quite done yet. For that which unfolds as rhythm and, in a sense, draws the brain into its sphere of influence is, in human terms, essentially the foundation of that which manifests on a completely different side of our organism through the larynx and its neighboring organs during speech. You can just as easily attune your active speech—which, after all, is simply linked through its instruments to the breathing process, which also underlies this rhythmic process of the rising and falling cerebrospinal fluid — you can simply integrate your speech process, on the one hand, into everything that arises as rhythm within you during breathing, and integrate hearing, on the other hand, and you have a whole that manifests itself more intellectually on the one hand in hearing, and more volitionally on the other hand [in speech]. You have a single whole only when you bring together the volitional aspect that pulses through the larynx and the more intellectual-sensual aspect that passes through the ear. These belong together; one must recognize this as a simple fact. For isolating the ear on one side and the larynx on the other is merely an abstraction; one can never arrive at a wholeness by separating these things that belong together. Anyone who, as a physiological physicist or a physical physiologist, examines the ear and the larynx individually proceeds in their research process in exactly the same way as if, in order to better bring a human being to life, you were to cut them up instead of observing the elements in their living interaction.

[ 22 ] Once you’ve truly grasped what this is actually about, well, then you arrive at something else—namely, the following: If one observes everything that is still present here in the eye—if I have removed the vitreous body, and if I had also removed all or part of what extends here as the retina, if I could push that out as well—then something would remain: the ciliary muscle would remain, the lens would remain, the outer fluid [and the cornea] here would remain. And what would that be then? What kind of organ would it be? That, my dear friends, would be an organ that I could never, if I were to proceed realistically, compare to the ear, but which I would always have to compare to the larynx. This is not a metamorphosis of the ear; it is truly a metamorphosis of the larynx.

[ 23 ] Just as the laryngeal muscles—to give you only the broadest outline—grip the vocal cords and create a wider or narrower gap, so do the ciliary muscles here. They grip the lens, which is internally movable. I have isolated [in the eye] that which is, so to speak, the laryngeal counterpart of the etheric, just as our larynx is the laryngeal counterpart for air. And when I reinsert first the retina and then the vitreous body—and now, for certain animals, I would have to insert certain organs such as the fan, which exists only as an etheric form in humans, or the sword-shaped process; in certain lower animals, these are extended inward like blood vessels—if I take all of this, I may compare it solely to the ear. Such things as these spreading parts of the fan, I may compare to that which spreads out in the ear within the labyrinth and so on. And so, in the human organism, on one level I have the eye, which is internally a metamorphosed ear and is externally enclosed by a metamorphosed larynx. If we take the larynx and the ear together as a whole, then on another level we have a metamorphosed eye.

[ 24 ] I have hinted at something that leads down a very important path. For one simply cannot know anything at all about these things if one compares them in a completely wrong way—if one simply juxtaposes the eye and the ear—whereas, with regard to the ear, I may only compare what lies behind the lens in the eye, which is more vitalistic in its inner nature, while I must compare what protrudes outward and is more muscular in nature with the human larynx. This, of course, is what makes the doctrine of metamorphosis so difficult: one cannot approach metamorphoses in a crude manner, but must delve into the inner dynamics, the real, the actual.

[ 25 ] But look, my dear friends, if that is the case, it forces us not to simply draw a parallel between what happens with sound phenomena and light phenomena without further consideration. If one starts from the false premise that the eye is a sense organ and the ear is a sense organ, then one will view what arises from this relationship in a completely mistaken way. When I see, it is something entirely different from when I hear. When I see, the same thing happens in the eye as when I hear and speak at the same time. On a higher level, an activity—which I can only compare to speaking—accompanies the eye’s essentially receptive, absorbing activity. In general, progress in this field can only be made if one strives to grasp the realities as they are. For when one becomes aware that here in the eye two things are united that are otherwise, in the case of hearing—of sound—assigned to seemingly entirely different physical organs, then one realizes that in seeing—in the eye—there is something akin to a kind of communication with oneself. The eye always proceeds in the same way as you do when you hear something but are only allowed to repeat it in order to understand it. The activity of the eye is truly like listening; but at that point you would not yet have the correct understanding—even if the other person says, “He is writing,” you are not yet clear on it. “He is writing,” you repeat. Only then is the whole process complete. This is how it is with the eye and light phenomena. What enters our consciousness through the unique interrelationships—namely, that we possess the vital part of the eye—only becomes a full visual experience when we reproduce it in that [non-vital] part of the eye which corresponds to the larynx and is located at the front [of the eye]. We are, in a sense, having an ethereal conversation with ourselves as we see. It is a soliloquy carried out by the eye. Therefore, one cannot at all compare what is the result of a soliloquy—which already contains the human being’s own activity—with what is merely a moment, a part, of mere hearing.

[ 26 ] I believe, my dear friends, that you will gain an extraordinary amount from this reflection if you work through it thoroughly on your own. For you will see from it how greatly the materialistic, physical view of the world strays into the utterly unreal by comparing things that simply cannot be directly compared with one another—such as the ear and the eye—and it is precisely through this purely external approach, which does not take into account the real totalities, that one actually strays from a spiritual contemplation of nature. Just consider how thoroughly Goethe’s Theory of Colors, in its conclusion—in the sensory-moral section—logically [ideally] develops the spiritual from the physical. And you can never achieve this if you take today’s physical theory of colors as your foundation.

[ 27 ] Now, however, the same reservation arises that we have regarding sound and tone, because in those cases it is, so to speak, obvious that, as they say, only vibrations are taking place externally. But you must ask yourself the question—and I ask you to decide for yourselves whether this question, by being properly posed, is not already answered in a certain way—whether the following might not also be the case. You see, if you have a balloon here and this balloon is filled with air, then even if you have a hole in the balloon and can open this hole with a valve, as soon as the air inside has the same pressure as the air outside, nothing will happen even if you open the hole. But if this balloon is evacuated of air, then something will happen: the outside air will rush in here, filling the vacuum. In this case, would you say, for example, that the air that is later inside was produced solely by what took place inside? No, you would naturally say: The air entered from the outside, but the empty space, so to speak—purely from a visual perspective—sucked in the outside air.

[ 28 ] By rotating the [perforated] disc [of the siren] here and then blowing through it, we simply create conditions that result in something [for our auditory perception] that we must describe as a suction. What later appears as sound—when I set the siren in motion and cause the air to vibrate—what appears as sound there—well, that exists only beyond the space; it is not yet inside the space. The [physical] conditions for it to enter the space are not present as long as I do not create these conditions, just as the conditions for this external air [in the balloon] to penetrate here are not present as long as I do not create them. What the external air vibrations [for hearing] are, I can only compare here [in the balloon] to a vacuum, and what then becomes audible, I can only compare to something that penetrates from the space-less into the vacuum as a result of the conditions being created. But in its inner essence, what these air vibrations are has nothing to do with sound, other than that where these air vibrations occur, a suction process arises to draw the sound in. Of course, what is drawn in as sound is modified by the nature of the air vibrations. But that would also be modified here in the vacuum if I were to [in this vacuum inside the balloon] were to create channels and the air were to expand [only] along certain paths; then the lines along which the air expands would be present in their image. Thus, the sound processes are externally represented in what exists as [specific] vibrational processes.

[ 29 ] Yes, you see, my dear friends, what is presented here as the foundation of true physics cannot be conceived of as easily as through a few mathematical concepts one might have about vibrational processes. It places greater demands on the qualitative aspects of human thought. But unless these demands are sufficiently met, the only physical worldview one will produce is one that relates to reality—that physical worldview that is idolized today—in the same way that a papier-mâché figure in a circus relates to a living human being. Think about that again, and we’ll continue next Friday at a quarter to eleven.