Two ears, two hands with fingers, one breathing channel. Prerequisites for human music, but how far do they reach?
If the world is shaped by the natural selection of replicators, music would logically seem to be memetically rather than genetically determined. It’s fairly obvious that any biological adaptation for music is minimal in comparison to the memetic fitness it brings us as meme-propagators. However the influence of the anatomy cannot be ignored and may be more important than intuition would suggest. Much of musicology predates the embracing of Universal Darwinism and so can be forgiven for not thinking about the art of music in terms of biology and memetics.
The easiest thing to look at is probably the audible range of frequencies humans can perceive. It’s easy to measure – if the pitch is too low or too high, it simply won’t be heard. There’s variation among people – in particular the upper audible range decreases with age and with damage caused by high-impact sounds on the hairs of the inner ear. But what does this audible range determine?
The highest frequencies we can hear as stable pitches tend to sound like beeps and whistles. They’re timbrally impoverished – understandably so since most of their harmonics lie outside the audible range. Harmonics are those parts of the fundamental frequency of a pitch which resonate in tandem, namely the simple natural number fractions of the wave: its two halves, three thirds, four quarters and so on. Traditional wisdom tells us that the first harmonic (that is to say the two halves of the fundamental frequency) sounds at the octave above the fundamental pitch and can be heard by the naked ear, that when we’re aware of it, the second harmonic at the perfect fifth above the first one can also be heard, but as the harmonic series progresses the pitches become less audible and affect the timbre of the perceived pitch in subtle ways that behave differently to simply being heard as pitches in their own right.
Obviously in the highest extremes of audible pitch this principle breaks down. The timbres become impoverished by the steady disappearance of first one then another harmonic from the audible spectrum. What of the lower reaches? More harmonics affect the timbre, obviously, but also more convergence of harmonics is encountered when more than one fundamental pitch is present.
When two fundamental pitches are present, each has its own harmonic series. The lower down the audible range of frequencies these pitches reside, the more of their harmonics are either directly audible or have significant effects on their timbre, and the more of their very highest harmonics have some small effect. Given the narrowness of the intervals in the higher reaches of the harmonic series, it seems obvious that any lowering of the fundamental pitch brings into the audible range large numbers of additional very quiet harmonics. When fundamental pitches combine, many of these are doubled up or are almost doubled up, leading to distortive ‘beats’.
Therefore the effects of the audible range and its limits on the sound we hear is not simply to determine which sounds can be heard at all, or to give a gradual flavour to timbre depending on pitch. The unexpected effects, all of which are hard-wired into human brains by the audible range of frequencies include:
Since lower frequency ranges support simpler, wider intervals, it is no surprise that much tonal music is based on simplified “bass notes” low in the range, stereotyped chordal material in the medium range and the most complex ‘melodic’ material riding on top!
The apparent “pull” of tonality derives in part from the fact that complexity tends to live further up the frequency range; for example the famous 9th, 11th and 13th chords of jazz – the higher reaches of these complex chords most routinely accumulate at the top end, and where this rule is broken the harmony sounds more complex.
The modern 12-note chromatic scale derives from a supposed ‘circle of fifths’. The reason for this is that, taking a fundamental pitch of, say, concert ‘A’, the interval of the “fifth” is determined by the ratio 3:1. The frequency three times that of the starting fundamental pitch is the pitch(-class) we call the one “a fifth above”. Extend the pattern by iterating the transformation and it yields the following series:
A, E, B, F#, C#, G#, D#, A#, E#, B#, F##, C##, G##
The “G##” pitch-class is not physically identical to the starting ‘A’, but it is so close that when the two frequencies are played together they ‘beat’ and sound like a timbral amendment not a two-pitch interval, and when played in succession they sound like very minor inflections of the ‘same’ note. Obviously the G## yielded by the iterated sequence of triplings is much higher in pitch, but due to the ‘octave rule’ it has the same flavour and can be treated as though it were halved and then halved again. In other words instead of a tripling, we can conceive of the process as multiplying the starting frequency by (say) 1.5, 1.125, 1.6875, 1.265625, 1.898438 and so on. By the time we reach the “G##”, it’s hardly surprising that it sounds a lot like an ‘A’ since the lowest multiplier to derive it above 1 is 1.0136, some 1.4% difference in real flavour.
This is the foundation of the twelve-note chromatic scale used by most of the world’s music since the invasion of western classical and popular music. It has been postulated that harmonic systems with fewer pitch-classes arising naturally tend to draw from the above series in left-to-right order, with the first five, for example, spelling the most common type of pentatonic scale, and the first seven (eg. F, C, G, D, A, E, B) spelling the most common types of western mode (including obviously the ‘major scale’).
If we assume that the twelve-note chromatic scale is the naturally-occurring logical baseline for musical diversity of flavour (artificial systems of 13 divisions to the octave, etc. notwithstanding), then an interesting consequence occurs statistically from the definition of the system.
It is naturally predisposed to consonance.
The simplest intervals possible by combining two fundamental pitches are as follows:
By my reckoning, of the eleven possible simple intervals, seven are perceived as consonant. If we rule out anything above the tritone on the grounds that in simultaneous presentation as aggregates they are functionally redundant, the figure is
four out of seven.
Either way an interval arrived at within the chromatic scale by pure chance has a better-than-average chance, even in its barest context, of consonant perception.
My conclusion then is that the evolution of the tonal attitude was inevitable: bass-notes at wider intervals in the lower range, chordal and melodic complexity progressing in line with the harmonic series and the natural probability of consonant intervals combine to conspire towards consonant-sounding music.
This is counter-intuitive. The natural perception is that tonal music must be carefully sculpted and that nature left to its own devices would produce dischordant cacophony. In fact it is dissonant structures in sound which take the most directing from human intervention and serious attempts at randomising pitch-events, so long as the layering of complexity is within certain limits, produces music which the ear automatically perceives as consonant. Indeed John Cage and Christian Wolff noted the tendency for even the most abstracted sonic events to end up being perceived melodically.
What of the two hands? I would suggest the following as evidence of the consequences of our bimanual anatomy:
i) One hand, other hand
ii) One hand, same hand
These can produce all the patterns of periodic metre and may explain why more artificial metres (eg. patterns of five) sub-divide into twos and threes
These are only suggestions and are the most obvious examples but it seems clear that the shape of the hands affects instrument design, and memetically the experience of playing an instrument will affect how one writes for it. The product of a lifetime’s cultural memes will be influenced by the material learnt at every stage, much of which is designed for comfort in human hands for the purposes of playing. Even the wild excesses of virtuosi can be said to exploit the comfort principle in reverse – showing that they do not need comfort in order to remain competent; perhaps a display of deliberate handicap, Zahavi-style.
Finally I mentioned the single stream of human breath. This gives a sense of monophony for melodic units and, because of the need to breathe, a sense of phrasing; it’s nothing new to speak metaphorically about “breathing” when writing instrumental melodies, even for electronic instruments. The oscillation of inhalation and exhalation in breathing is mirrored in the memetic selection of bowed instruments, the early bellowed organs and even the sustain pedal in the piano.
All of these factors suggest a musicobiology or an evolutionary aesthetics, with the principal driving force (or at least a major player) being the replicating unit of the gene rather than the meme. As with many other areas of human endeavour the most interesting end-products may be the result of an overwhelming volume of influence from the replicating unit of the meme but at the lowest level the defining force is the gene.
The exception is the highly abstract music of modernism, which, to a greater or lesser extent, subverts the principles inherited directly from our anatomy, often substituting other anatomical baselines such as compositional systems or models from the world such as the spectra of sound-waves. If tonality is the natural option for composition and modernism an artificial interloper, a Darwinian explanation is the struggle of the selfish memes to escape the leash of the selfish genes. Attempts at a meme-focused compositional approach can benefit from knowing the basis of the gene-focused heritage and as such, evolutionary aesthetics is an area worthy of further research.