The question posed by the Voyager project, namely whether humanity and an extraterrestrial culture could communicate via music, opens up some extremely interesting fundamental considerations, because a general characterization of music must be found for every conceivable type of listener. We cannot even assume that the potential listener has sensory organs similar to those of humans.
The German physicist and SETI (Search for Extraterrestrial Intelligence) expert Sebastian von Hoerner, who has a keen interest in this topic, presented his thoughts on this subject even before the Voyager project at a conference held in Ossiach, Austria, in 1973. Hoerner takes a look at the physiological conditions necessary for understanding and producing music. His thoughts also revolve around a few astonishing considerations on the question of the tone system, which arise quite independently of the specific nature of a living being.
Hoerner takes it for granted that an organism must have something that corresponds to our ears, i.e., that it is capable of perceiving sound waves in a differentiated manner. According to Hoerner, the ears obey five basic conditions:
First: Such an organ must have a built-in frequency analysis. Hoerner compares the human ear to the human eye. The eye is only capable of processing about one “octave” of light waves and, unlike the ear, does not have channel separation: it mixes yellow and red to produce orange. In this respect, the ear is much more subtle than the eye. It can detect sound events over nine octaves and easily perceive frequencies that are about a semitone apart. This means that the human ear has around forty separate channels for perceiving pitch. In principle, however, it can even perceive the finest differences in tone in up to 40,000 channels. Around 30,000 channels are sufficient to hear melodies. According to Hoerner, it can be assumed that such a refined ear provides an important survival advantage and is therefore likely to be present in extraterrestrial beings.
There are few objections to this assumption if we assume that good hearing primarily means being able to detect potential enemies at an early stage. Such a task is best accomplished by frequency analysis, which allows the sounds of the enemy to be clearly distinguished from other environmental noises. However, Hoerner makes an unproven assumption with regard to music, namely that the artistic or otherwise conscious organization of the auditory space takes the form of melodies and harmonies. The question of the frequency range that a living being can perceive also remains open. In principle, it is conceivable that an organism can clearly perceive frequencies above 20,000 hertz (as is the case with dogs, for example). The music of such a race of extraterrestrials would be completely inaudible to us.
Secondly: In order to understand our music, extraterrestrials would have to perceive frequencies on a logarithmic scale, as we do. Here, too, there is the possibility that extraterrestrial “music” could be organized in a way that is incomprehensible to us, namely on the basis of absolute frequency ratios.
Thirdly, there should be something like non-linear coupling. This ensures that we can distinguish between two tones and their overtone series, rather than mixing a new tone from the frequency difference.
Fourthly, it seems important to perceive the overtone mix of sounds in the form of timbre as an independent tone quality. According to Hoerner, from an evolutionary biology perspective, it makes sense for humans to immediately identify the roar of a lion as such without first having to count the overtones. Similarly, it makes sense to be able to distinguish whether one or more lions are approaching.
Fifth: With this condition, von Hoerner is skating on thin ice. He believes that a living being must also appreciate music as such in order to actually produce it. This has little to do with the structure of the ears. However, the idea is interesting: humans appreciate music because it gives them pleasure in some way and seems to be connected to their emotional life. On the other hand, we know from autism, for example, that people can completely lack this sense. Take the case of the famous, highly intelligent, autistic engineer Temple Grandin, recounted by neurologist Oliver Sacks in his book “The Anatomy of a Mind”. Temple, who has perfect pitch, explains that she does not understand music and that it does not trigger any emotions in her.
This leads to the conclusion that even if an extraterrestrial civilization is able to perceive our music adequately due to the nature of its hearing organs, this does not mean that it understands its “message” or that it even realizes that a message is present. Extraterrestrials could have more in common with autistic humans than with normal humans. It is also possible that we would not even perceive extraterrestrial music as such because it would mean nothing to us.
However, von Hoerner goes on to make some interesting observations about the universality of our tonal system: Is a system that divides the octave into twelve semitones a product of arbitrariness? Is it determined by the human ear’s ability to distinguish semitones well, or is it based on fundamental structural reasons? One might assume that there could be much finer subdivisions of the octave, such as fifth tones, seventh tones, or even two-hundredth tones, which a correspondingly finely tuned ear could perceive.
According to von Hoerner, there are two starting points for considering which scale systems are suitable for physical reasons: First, a “natural” unit must be divided into equal steps. The second prerequisite is that the tone steps of the system should have as many overtones in common as possible when they sound together, in order to be able to construct harmonic systems and generate a rich palette of timbres.
The interesting thing is that, theoretically speaking, these two conditions are incompatible. Mathematically speaking, our tempered twelve-tone scale means dividing the octave into fractions of √2. Since √2 is an irrational number, no simple divisors can be found to combine overtone spectra. As can be heard in our own tempered scale, approximately simple ratios of corresponding divisions behave in practice as if they were completely corresponding divisions. The tempered fifth is stimulated to resonate in the same way as the pure fifth. The definition of a chromatic scale can therefore be made tolerant:
Definition of a scale system: A division of the octave into equal parts, which also produces approximately harmonic divisions.
The question now is how many overtones must be included in the overtone spectrum. The crux of the matter is that the overtone and all the ratios belonging to it must also represent an interval existing in the tone system. If we require that only the octave (overtone 2) be represented, then only the ratios 1:2, 1:4, 1:8, and so on must be represented. If we require that the fifth be present in the overtone spectrum, then the ratio 2:3 is added.
A table of all ratios that must be represented by a number of overtones looks as follows (it only contains ratios that cannot be reduced to others):
P = prime number up to which all overtones are represented, M = number of ratios that are represented.
One might also ask how “approximate” can be expressed quantitatively in the definition of the tone scale system. How large can the deviation from the theoretical ideal value be?
Von Hoerner uses a generalization of the cent system for this purpose. In musicology, the unit cent is used to subdivide intervals for fine measurements. In our twelve-tone system, a semitone corresponds to 100 cents, and an octave therefore consists of 1200 cents.
The generalization: for any subdivision of the octave, a tone step should measure 100 cents. An octave then comprises N times 100 cents. Furthermore, a deviation from a tone step can be a maximum of 50 cents before it is closer to the next tone step. With some theoretical considerations, von Hoerner concludes that it makes sense to limit the deviation from a tone to a maximum of about 20 cents so that the individual tone steps remain easily distinguishable and enough of the generated overtone ratios fall within a desirable proximity to a tone of the tone scale.
In other words, the deviation should be chosen so that the harmonics produced by lower tones fall as close as possible to higher tones of the tone scale, thus producing a rich resonance spectrum.
After running a computer program to see what happens when all pairs of octave subdivisions and numbers of overtones are selected, von Hoerner makes two interesting observations. First, the finer the octave subdivision, the fewer overtones fall close to tones in the scale. This means, for example, that a system with two-hundredths tones would not only place extreme demands on the frequency analysis capabilities of the auditory organ. The music produced would also consist of tones that would not stimulate each other and thus would not have a proper overtone spectrum.
In fact, the relationship between octave subdivision and overtone richness actually only exists in three cases: a five-tone system with three overtones taken into account, a twelve-tone system (our tone system) with five overtones taken into account, and a thirty-one-tone system with seven overtones taken into account.
Von Hoerner goes beyond the derivation of “good” scale systems and attempts to prove that the major/minor system also has universal characteristics. Broadly speaking, he uses the same strategy as Riemann to prove his point, but without referring to “undertones”: The major chord is derived from the first six overtones, i.e. from the multiplication of the fundamental frequency by 2, 3, 4, 5, and 6. The resulting elements (contracted to an octave—which Hoerner does not mention, however) produce the familiar major chord. The minor chord is produced by the analogous procedure, using division instead of multiplication. Because pitch has only two directions, this results in exactly two chord forms that fulfill the condition that their tones are also found in the overtone spectrum. In the case of the five-tone scale, the two methods make no difference, meaning that it has only one tone gender. The thirty-one-tone scale therefore also has two tone genders. The seventh overtone is included in the calculation, the overtones 8, 9, and 10 result in octaves of existing tones, and the eleventh overtone is omitted.
Hoerner’s speculations are highly interesting, but not immune to objections: The most important implicit assumption he makes is that the merging of overtones is a desirable effect. On the one hand, this may be because it is pleasant for a living being, whatever one understands by “pleasant.” On the other hand, the overtone hierarchy allows hierarchical structures to be established.
To make the first assumption about extraterrestrial beings would mean attributing to them an emotional inner life comparable to ours. This is anything but trivial. It only becomes plausible if one assumes that evolution on other planets is roughly the same as on Earth, i.e., that the history of evolution is universal. One could argue that under similar conditions, such as the oxygen cycle and so on, similar structures—sexual reproduction and food chains—have developed. However, it is entirely conceivable that a living being that does not reproduce sexually and does not know hunting and being hunted has an emotional structure that is completely different from ours, if it has one at all. Love and danger are the most fundamental emotional experiences of human beings. It is the food chain that makes Schubert’s “Trout Quintet” an emotional experience.
The second prerequisite is also not trivial: complex musical structures can also be conceived without the hierarchical model of overtones. Group-theoretical structures could be possible, for example, if the overtones that would actually be the most interesting, namely the prime numbers 7 and 11, were not simply excluded from the construction of the scale. One could also imagine that a hearing organ has volume band analyzers and could establish a “volume scale” analogous to the pitch scale, whatever the biological motivation for this might be.
Von Hoerner shows himself to be a skeptic in the best sense of the word and does not rule out systems other than the physically “most natural” ones with a five-, twelve-, or thirty-one-tone scale and at most two tone classes as a basis. He merely believes that it seems as if “some of our fundamental musical principles are universal enough to be expected to a large extent in other places.” The implicit assumptions should have shown that expectations in this regard probably need to be scaled back even further.