Music and Evolution: Hearing Math, Seeing Sound, and other Unanswered Questions

Music and Evolution: A Brief Overview

The evidence presented in the research on music and evolution, beginning with Darwin himself,^[1] focusses largely on music's purported ability to support "mate selection, parental care, coalition signaling, and group cohesion," ^[2] language development, ^[3] and other things. The prevailing evolutionary theories about music follow Darwin's lead—they are predominately sociological, cultural, and behavioral in nature.

Other researchers cite explanations that are more utilitarian:

How did music evolve? Here, we show that prevailing views on the evolution of music— that music is a byproduct of other evolved faculties, evolved for social bonding, or evolved to signal mate quality—are incomplete or wrong. We argue instead that music evolved as a credible signal in at least two contexts: coalitional interactions and infant care. ^[4]

Still, others provide more abstract explanations, claiming that music can "promote human well-being by facilitating human contact, human meaning, and human imagination of possibilities, tying it to our social instincts." ^[5]

While these behavioral adaptations may be relevant in the development of clans, tribes, and eventually larger social groups, I find these explanations to be unsatisfactory, and I am not alone in this assessment. Researchers in this field acknowledge that "human musicality poses a longstanding puzzle," ^[6] one which has not yet been solved. This is not surprising given the enormous timescale involved and the lack of primary evidence. With the rise of so many competing hypotheses since the dawn of Darwinism, it appears that researchers have resigned themselves to the fact that a definitive answer regarding music and evolution will not be forthcoming, as concluded by Mehr et al.:

It's unlikely that anyone will ever explain the full extent to which a particular behavior is accounted for by one or more adaptations because, given its complexity, human behavior cannot be exhaustively measured. ^[7]

There is also another perspective, one that is more glib and perhaps more revealing. Steven Pinker, one of the most successful evolutionary theorists and public intellectuals of our time, famously stated that music is "auditory cheesecake, an exquisite confection crafted to tickle the sensitive spots of ... our mental faculties."^[8] This is a remarkable characterization from such a prominent figure, one that stands in stark contrast with Friederich Nietzsche's statement that "without music, life would be a mistake."^[9] It is astonishing to see our incredibly sophisticated auditory system and the deep emotional responses that have so profoundly enriched our secular and spiritual lives in myriad ways over thousands of years, dismissed so casually, relegated to the status of evolutionary "cheesecake." As in the quote from Mehr et al. above, Pinker's comment seems to be an implicit admission that evolutionary theory cannot explain the phenomenon, and thus, the theory is not needed—we can just say that "evolutionary theory also produces 'empty calories,'" and leave it at that. Unfortunately, music is many things, but it is most certainly not "empty calories"—it is one of the human race's most astounding achievements. ^[10] From this perspective, Pinker's dismissive statement thus undermines and casts doubt on the very theory he wishes to advance.

The research into music and evolution is rich and fascinating, and, as mentioned earlier, does have explanatory power in the cohesion of social groups of varying sizes. However, Darwinian theory requires that individuals within those groups receive both a marked procreative or survival advantage, and the ability to pass the mutation on to their offspring. Given the many other characteristics (height, strength, hunting ability, eyesight, speed, cognitive ability, etc.) that could result in more offspring for a given individual, it is hard to imagine that an individual's ability to sing or to play a rudimentary flute or other instrument better would bestow a significant procreative advantage upon one of our distant hunter-gatherer ancestors. In addition, this musical skill would have to be genetically passed down to children. Research into music and genetics is currently underway, and shows that there may indeed be a genetic component:

Music, as a biological phenomenon, had to be shaped by genes which is best exemplified by extended pedigrees of musical families like the Bachs and certain disorders involving musicality. A multitude of so far collected data shows that music might be even a better denominator of genetic distances than language, i.e., high musical similarity predicts high genetic similarity. Thus, together with the recent progress in compound phenotype mapping of multigenic/multifactorial traits like musical aptitude could entail an even deeper exploration of the relationship between music and genetics. ^[11]

Anecdotal historical evidence exists in the musical lineages found in various families that is well-documented. For example, the many descendants of Johann Sebastian Bach, as referenced above, displayed considerable musical prowess for many generations after his death—however, this musical advantage appears to have disappeared a century after his death when we no longer find his descendants in prominent positions as performers or composers. Researchers in this field acknowledge that it is difficult to separate cultural and other influences from the genetic inheritance:

Researchers generally agree that both genetic and environmental factors contribute to the broader realization of music ability, with the degree of music aptitude varying, not only from individual to individual, but across various components of music ability within the same individual. While environmental factors influencing music development and expertise have been well investigated in the psychological and music literature, the interrogation of possible genetic influences has not progressed at the same rate. Recent advances in genetic research offer fertile ground for exploring the genetic basis of music ability. ^[12]

It is, nonetheless, a promising avenue of study that may provide more definitive answers as our technology advances.

I have provided this brief overview not to argue for or against any aspects of evolutionary theory, but rather to provide some context and background for the discussion that follows. These evolutionary theories do not offer any compelling explanations as to fundamental questions of the origins of the how the brain processes sound in the peculiar ways that it does, instantaneously interpreting those sounds to create a profound emotional response. Consider the following:

Consonance and the Octave

In music, the concept of the "octave" is used to describe two pitches whose frequencies are entirely different, yet they are characterized as being somehow "equivalent." For example, A4 and A5 are one octave apart, and their frequencies are 440Hz and 880Hz, respectively. If these two pitches were played by plucking a string, the length of the string playing A4 is 40cm, and A5, with the same mass and tension, is 20cm.

The mathematical relationship between the frequencies of the pitches and the string length is obvious—A5 is twice the frequency and half of the string length of A4. We hear these two pitches as the second most consonant of all (with A4 and another A4 being the most consonant possible). Professional musicians and non-musicians characterize the two pitches in the same way, that is, "A5 is a higher version of A4—they are, somehow, two versions of the same pitch, found in different registers."

They are, however, two entirely different pitches. Yet, we characterize them as being extremely "consonant," which is curious. Furthermore, we consider this level of consonance so important that it warrants its own identifying term— this relationship between two pitches is called an octave. This reveals something truly extraordinary about how our "hardware" processes these two pitches.

We hear the two pitches, and instantly recognize that they are in a simple mathematical relationship with each other. We do not know the string lengths or the frequencies, nor do we have to—our brain "hears" that these are in a simple 1:2 relationship and the symmetry and simplicity are pleasing to us. We call it "consonant" because of their simple, symmetrical relationship, which is also reflected by the string lengths.

This same process occurs with each octave above A4 (Figure 1):

Figure 1: Pitch, Frequency, and String Length of A4-A7

Figure 2 is a diagram of the vibrating string that shows the pattern as each successive string length is halved, a process which continues upward past the point of human hearing:

Figure 2. Waveforms of Four Successive Octaves

The beautiful symmetry that we see here in both Figure 2 and Figure 3 is precisely what we hear when these pitches are played simultaneously. We are thus, literally, "hearing symmetry" in these ratios, and our characterization of that symmetry and the inherent orderliness which it exhibits, is pleasing to us. The lack of asymmetry or mathematical complexity in the waveforms of these pitches as they are simultaneously played elicits an emotional response that imparts a sense of stability, safety, and relative "peace." ^[13]

Figure 3. Waveforms of Four Successive Octaves Superimposed (i.e. "played simultaneously")



This curious aesthetic response that favors the symmetrical, and characterizes it as "pleasant," "free of conflict," or even "beautiful," is not limited to music, nor is it limited to humans. Research done by renowned entomologist Dr. Randy Thornhill shows that male Japanese scorpion flies with symmetrical forewings were clearly preferred by the females as mates, while those with asymmetrical forewings were rejected.^[14]Thornhill and Karl Grammer ^[15] also studied the concept of "beauty" in human attractiveness and found that:

...both men and women gave the most symmetrical faces the highest ratings... people judged to be facially attractive also have great overall body symmetry... There seems little question that for many creatures, from humans to scorpion flies, symmetry is a key ingredient in the mysterious mix we call beauty. ^[16]

Our inherent aesthetic sense of beauty thus reveals itself as a mathematical calculation that is conducted automatically, without our direction; our visual and aural faculties are hardwired to recognize the symmetry and simple proportional relationships inherent in objects and in sound.^[17] These phenomena are remarkable—an auditory faculty that recognizes a geometric sequence! This is not a computer performing this analysis; it is done by a living entity that can itself not only recognize the mathematical relationships at play, but also utilize those same relationships in myriad and profound ways, in both the arts and sciences. In regards to the latter, it is worth noting that the frequencies of consecutive octaves are an elemental geometric sequence—based on the power of two—described algebraically as y=2^{x ,} or 2⁰, 2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷...or 1, 2, 4, 8, 16, 32, 64, 128, etc. This is found at the core of computer science, where y=2^x is a foundational formula, known as the "binary sequence." This formula is used to convert binary numbers to decimal numbers, which is fundamental to modern computer systems.

This is hardly a new observation—philosophers and scientists like Aristotle, Pythagoras, Ptolemy, Galileo, and many others have been aware of these curious relationships for millennia. The famous philosopher and mathematician, Gottfried Leibniz (1646-1716), stated it quite poetically when he said that "Music is a secret exercise in the arithmetic of the soul, unaware of its act of counting."^[18]

Music, Math, and Narrative: The Evolutionary Songbird Sings

In my teaching, I begin each class with a presentation entitled "How Does Music Work?" First, we delve into the function of music in the students' lives— What do you use music for? What does music do to you? How is music used in our culture? and other similar questions. This firmly establishes the importance of music in our own individual lives and in our culture, as it permeates entertainment, sports, religion, and other activities. Students relay that music can lift our spirits, it can make us sad, it can make us dance, it can make us more outgoing, it can help us to grieve, worship, study, exercise, contemplate, etc. The eponymous question arises—how does music do this?

I then play a short example on the piano, with one student watching me to ensure that I do not play a C.^[19] After the example is played, the class is asked to "sing the note that 'should' follow." Of course, that note is C and they all sing it, even though it was not played. So, a group of 20-25 students, mostly non-musicians, heard some sound waves, and when those ended, they instantaneously and automatically directed their vocal cords to sing the same pitch. How did they do that? Where did that note come from?

It comes from yet another remarkable characteristic of our auditory and nervous systems—the ability to hear complex relationships between pitches, and then "fill in" a pitch that would "resolve" the complex numbers by supplying the nearest pitch in a "simple relationship"—i.e. a two, four, or some multiple of two. The example played created complex waveform relationships, and the simple waveform solution to those was to move to C, whose frequency is the nearest downward and stepwise member of the geometric sequence y=2^x.

Max Meyer showed this in a rather elegant manner in his study of melody from 1901 in which participants were played melodies consisting of only two pitches. Some of the pitches chosen were adjacent members of the harmonic series ^[20] (Figure 4), others were not.

Figure 4. The Harmonic Series on 'C' to the 16th Partial

When he used adjacent members on the harmonic series, because of the peculiar relationship of the pitch's numerical position and its string length, the ratio of their wavelengths to each other is the same as their positions in the series. Thus, the string length ratio of the second overtone to the third overtone is 2:3, and the third and fourth is 3:4 and so on. Whenever one of the pitches in the melody was a "pure power of two," the listeners chose that pitch as the one that "should" be played in order to end the melody in a "satisfying" manner, as described by Meyer:

...after hearing 2 [C2] and then 3 [G above C2], he wishes to go back to 2, i.e., to hear 2 once more. On the other hand, when we hear first 3 and then 2, we do not wish to hear 3 once more. If 3 and 2 are repeated several times in order to prolong the melody consisting of these tones, we are satisfied in the case where the melody ends with 2, dissatisfied in the case where the melody ends with 3. Save in a few instances, where a peculiar psychological effect is aimed at, no melody that contains 2 can end with any tone but 2. In the case of the tones 3 [G] and 4 [C above it] , the melody must end with 4, not with 3; in the case of 4 and 5, with 4; 5 and 8, with 8; 7 and 8, with 8; 4 and 9, with 4; 1 and 16, with 16; i.e., the general law is: When one of two related tones is a pure power of 2, we wish to have this tone at the end of our succession of related tones, our melody. ^[21]

This response is one of the most important tools in a composer's toolkit. It allows composers to set up long- and short-term expectations in the listener, and then those expectations can either be fulfilled or foiled, and it is from this that a narrative in sound is created. It is also what allows for the establishment of key areas and the movement into other key areas within the same piece. Without this ability, music would not have functioned as the vehicle of expression for so many highly differentiated geniuses over so many centuries.^[22]

It is important to recognize how deeply embedded, culturally and psychologically, the idea of music being in a "key" is. It is something that we accept as so self-evident that we barely give it any thought at all. We treat this with a marked nonchalance, but a characteristic of music that offers such profound artistic utility is is not something that should be cast to the side as a commonplace—our ability to perceive "key" is remarkable.

Nonetheless, the idea that music is in a "key" is assumed and often explicitly acknowledged prominently in the titles of many pieces—for example, we find it in the title of J.S. Bach's "Prelude and Fugue in C minor," W.A. Mozart's "Piano Sonata in B-flat major," Johannes Brahms' "Symphony No. 1 in C Minor," Duke Ellington's "Prelude in D," and countless others.^[23]

Encyclopedia Brittanica defines "key" as follows:

Key, in music, a system of functionally related chords deriving from the major and minor scales, with a central note, called the tonic (or keynote). The central chord is the tonic triad, which is built on the tonic note. ...The concept of key is fundamental to the system of tonality (the organization of notes, chords, and keys around a centrally important tone), the basis of most Western art music from about 1700 to the 20th century and beyond.^[24]

The definition contains interesting terminology—apparently there is a tonic, which is a "central note" and this is "fundamental" to tonality.

"Tonality" is then defined as follows:

Tonality, in music, principle of organizing musical compositions around a central note, the tonic. Generally, any Western or non-Western music periodically returning to a central, or focal, tone exhibits tonality. ^[25]

These definitions, somewhat circular as they are, are helpful in defining the terms for those who have already experienced them, but they do not get to the heart of the matter from a phenomenological perspective. From this perspective, we can define them as follows:

Tonality is the auditory phenomenon that results from the use of particular sets of pitches to create a perceived hierarchy in those pitches where one of those pitches is recognized as the most prominent, which is called the "tonic." This hierarchy is created by carefully managing complex waveforms (i.e. 1:17) which the human auditory system recognizes as such. The same auditory system automatically supplies the listener with a "resolution" of the complex waveforms that is normally the closest downward simple relationship that uses the power of two (i.e. 1:16). Tonality thus builds powerful expectations in listeners; these expectations create musical "plot" and are exquisitely exploited by composers in myriad ways to create long-and short-term musical "narrative."

Key identifies the tonic, which in turn determines which set of pitches (and chords made from those pitches) are to be used to create the tonal hierarchy. The sets of pitches that create the most powerful expectations in the human auditory system are known as the major and minor scales.

Tonality is thereby revealed as the foundational psychoacoustic response that makes the concept of key possible in the first place.

Thus, when we are told by a composer, like Ellington, that his prelude is in D major, embedded in that statement is the following:

This piece is constructed with the note 'D' as the tonic. To create the effect of 'D' as the prominent pitch, it will primarily use the D major scale. This scale is chosen because the dissonances (complex waveforms) that exist between its members lead to 'D' being perceived by the auditory system to be the consonant (simple waveform) resolution to those dissonances. This creates expectations in the listener for what the next note/chord should be—the listener's auditory system automatically and instantaneously supplies these. Those expectations will be fulfilled and foiled during the piece, surprising and consoling the listener as a musical narrative is created. The piece will end on 'D' which marks the end of the narrative, providing a final resolution to all of the dissonances in the piece.

From an evolutionary standpoint, questions regarding the origins of these peculiar abilities arise:

• What caused our auditory system to evolve to hear mathematical relationships in sound? Was this ability incrementally accrued? Did we hear other intervals as equivalent first, and then somehow miraculously evolved to hear the very same geometric sequence that is the foundation of our modern-day computers?
• What caused our auditory system to evolve to learn how to automatically "solve" those complex, non-symmetrical relationships, by projecting a nearby pitch that creates a simpler, more symmetrical relationship between the waveforms?
• What evolutionary pressures created such a profound emotional response to this aural "dance" between the simple and the complex, one so powerful that it has resulted in a body of creative work spanning thousands of years?

There are many ways in which we could imagine more acute hearing to be an advantage that would increase an individual's ability to survive and reproduce.^[26] However, it is entirely unclear what reproductive advantage these three abilities would bestow on an ancient predecessor. It seems unlikely that an individual who could hear two pitches and perceive them as equivalent, or being in octave relationship as opposed to one who could not, would be more attractive as a mate or have enhanced survival capabilities. Similarly, it is also unclear why the ability to predict the next pitch, using a very sophisticated and automated calculation, would give an individual a reproductive or survival advantage. Finally, in terms of the emotional response, evolutionary theorists have argued that music played an evolutionary role in infant care, which it may have, but it is difficult to imagine such a complex, nuanced, and robust auditory system evolving from behaviors surrounding infant care.

This brings us back to Pinker's "cheesecake" comment—are all of these abilities simply an accident that did not provide any significant evolutionary advantage? Why do we hear a geometric sequence, y=2^x, when we perceive octaves as equivalent pitches? Why do we automatically supply simple resolutions to complex waveform patterns? And finally, why do these resolutions translate to such a rich emotional response in human beings?

Evolutionary theory has strong explanatory powers within certain frameworks—for example, the sociological and behavioral hypotheses that dominate the field of music and evolution are generally compelling, although some stretch credulity ^[27] to the breaking point. The problem is that they begin with our auditory faculties already in place—they do not answer the fundamental questions of origin raised above.

Music enriches our lives immeasurably. As evolutionary theorists have claimed, it certainly gives us a means of nurturing social cohesion and establishing differentiated cultural and personal identities, among other things. However, music is capable of much more than that—through this abstract medium, we can express the ineffable and encounter the infinite. It is precisely as Nietzsche said—without it, our lives would be deprived of one of the most profound means of expression ever created, so much so that one cannot imagine life without music being on par with life with music.

Given music's exalted position in our culture, the evidentiary bar, in my opinion, is very high. Evolutionary theory regarding music needs to provide plausible and convincing answers to the questions posed regarding the origins of both our "hardware" and our "software"—without these answers, the theory attempts to build an ever-growing conjectural framework without a proper foundation grounded in root causes.

Special thanks to: Anneli Ryan for the graphic design assistance, and to Dr. Benjamin Whitcomb, Dr. Jerry Scripps, and Dr. Ed Aboufadel for their kind assistance and disciplinary feedback.

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Endnotes

^[1] In his book, "The Descent of Man," Darwin mentions "music/musicality" almost 150 times.

^[2] Savage, Patrick E et al., "Music as a Coevolved System for Social Bonding," The Behavioral and Brain S ciences vol. 44 e59 (2020), doi:10.1017/S0140525X20000333.

^[3] Andrea Ravignani, "Darwin, Sexual Selection, and the Origins of Music," Trends in Ecology & Evolution, Volume 33, Issue 10 (2018), 716-719, doi:10.1016/j.tree.2018.07.006.

^[4] Samuel A. Mehr et al., "Origins of Music in Credible Signaling," The Behavioral and Brain Sciences vol. 44 e60 (2020), doi:10.1017/S0140525X20000345.

^[5] Raglan J. Schulkin, "The Evolution of Music and Human Social Capability," Front Neurosci (2014), 8:292, doi:10.3389/fnins.2014.00292.

^[6] Bowling, Daniel L et al. "Progress without exclusion in the search for an evolutionary basis of music," The Behavioral and Brain Sciences vol. 44 e97. 30 (2021), doi:10.1017/S0140525X20001466.

^[7] Mehr, Samuel A et al., "Origins of music in credible signaling," The Behavioral and Brain S ciencesVol. 44 e60 (Aug. 2020), doi:10.1017/S0140525X20000345

^[8] Steven Pinker, How the Mind Works, (New York: Norton, 1997), 534.

^[9] Friederich Nietzsche, Twilight of the Idols. trans. Richard Polt (Indianapolis: Hackett, 1997), 10.

^[10] Music was deemed by NASA to be such an important part of what makes us human, that they included 25 pieces of music—on the "Golden Record" that was sent into the cosmos on the Voyager spaceship. The recording, a 12-inch gold-plated copper disk, featured classical music from J.S. Bach, Ludwig van Beethoven, W.A. Mozart, Igor Stravinsky, along with folk music from around the world, and even Chuck Berry's "Johnny B. Goode." (While containing multiple pieces by only one composer, J.S. Bach, it curiously contains only one jazz piece—"Melancholy Blues" by Louis Armstrong and His Hot Seven.)

^[11] Krzysztof Szyfter and Michał P. Witt, "How far Musicality and Perfect Pitch are derived from Genetic Factors?," Journal of Applied Genetics vol. 61,3 (2020): 407-414, doi:10.1007/s13353-020-00563-7

^[12] Yi Ting Tan et al., "The Genetic Basis of Music Ability." Frontiers in Psychology vol. 5, 658. (June 2014), doi:10.3389/fpsyg.2014.00658

^[13] From the earliest discussions about music, going back to Ancient Greece, the special properties of the octave were noted. When the first European theorists began to write about music, they characterized the octave as a "perfect" interval because it was free of any conflict. They classified other intervals, like the seventh and the second as "imperfect" because of the dissonances—irregular/non-symmetrical wave patterns—that they created. The "perfect" intervals were associated with God, while the imperfect intervals were associated with Man. We have continued to use this terminology ever since.

^[14] Randy Thornhill and Steven W. Gangestad, "Human Facial Beauty," Human Nature, vol. 4, no. 3 (1993): 237—269, doi: 10.1007/bf02692201.

^[15] Karl Grammer and Randy Thornhill, "Human (Homo sapiens) Facial Attractiveness and Sexual Selection: The Role of Symmetry and Averageness, " Journal of Comparative Psychology, 108(3): 233- -242, doi: 10.1037/0735-7036.108.3.233.

^[16] Randy Thornhill, "The Allure of Symmetry," Natural History, vol. 102, no. 9 (Sept. 1993): 30

^[17] An example I use in class illustrates this from a "hands on" perspective: I ask students to fold a piece of paper in half, then into quarters (by folding in half again). This continues until the width of the paper makes it impossible to keep folding. Nonetheless, they see how it would be possible, theoretically, to continue to halve (or double) indefinitely. They are then asked to fold it into five, seven, or eleven equal parts, which they cannot do. This exercise illustrates the power of "two" and the symmetry it contains which allows us to conceptualize and organize matter and abstract concepts alike.

^[18] His use of the word "soul" is worth noting, for it implies that he considered this to be deeper than a materialist view would allow.

^[19] A video of the musical example of that portion of the presentation is found below.

^[20] All naturally occurring sounds are governed by the harmonic series. The fundamental pitch (C1) contains all of the pitches above it as "partials" or "overtones," but the proportion and duration of each of the harmonics varies depending on the source of the sound. (The harmonic series accounts for why a trombone sounds so different from a flute.) The mathematical elements of the series are noteworthy:

• Each of the partial's numerical position in the series coincides with its string length in comparison to the fundamental. For example, overtone #5 (E) sounds on a string that is 1/5 the length of the fundamental (C).
• The position of all the Cs, as noted earlier, are the geometric sequence, y=2^x

^[21] Max Meyer, "Contributions to a Psychological Theory of Music," University of Missouri Studies (1901): 8-9.

^[22] Classical and Jazz music have mined this element of musical narrative to an incredibly sophisticated degree, but popular music uses it to great effect as well.

^[23] Even when key is not mentioned in the title, it is still a defining feature of most classical, jazz, folk, and popular music. For example, the first question musicians ask when learning a new piece, or improvising over a jazz piece, is "What key is it in?"

^[24] Britannica definition of "Key," accessed on January 27, 2022.

^[25] Brittanica definition of "Tonality," accessed on January 27, 2022.

^[26] David A. Puts et al., "Masculine voices signal men's threat potential in forager and industrial societies." Proceedings. Biological Sciences vol. 279,1728 (2012): 601-9, doi:10.1098/rspb.2011.0829

^[27] Benjamin D. Charlton, "Menstrual Cycle Phase alters Women's Sexual Preferences for Composers of more Complex Music," Proceedings of the Royal Society B: Biological Sciences 281.1784 (2014): 20140403.

Selected Bibliography

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