brain

In Part 1, we began to consider the questions below, and concluded that there is an evolutionary basis for the existence of music.  In Part 2, we found that there is no single, easy answer to the question of what makes music beautiful.  So are there multiple difficult answers?  Here we approach the question from another direction – what is it about ourselves that gives music the power to provide pleasure, or move us in other ways?

  1. Why does music even exist?  Is it an evolutionary adaptation, or an accident — an evolutionary parasite?
  2. What makes music “beautiful”?
  3. Why do we derive pleasure from music?  What is it about music that “moves” us?
  4. Why do individuals prefer one type of music over another?

Pinker’s Six Ingredients of Music Magic

Steven Pinker does not believe there is an evolutionary basis for music, so he is left to explain where it comes from and how it works:

I suspect that music is auditory cheesecake, an exquisite confection crafted to tickle the sensitive spots of at least six of our mental faculties.  A standard piece tickles them all at once, but we can see the ingredients in various kinds of not-quite-music that leaves one or more of them out.

Pinker’s ingredients can be summarized as follows:

  1. Language - Pinker compares music to “heightened speech.”  He notes that some singers like Bob Dylan and Lou Reed slip into “talking on pitch” instead of singing a melody, and points to Rap music as an intermediate form.
  2. Auditory Scene Analysis – This is the process of sorting out sounds in the environment and making associations among them.  “Perhaps melodies are pleasing to the ear for the same reason that symmetrical, regular, parallel, repetitive doodles are pleasing to the eye.  They exaggerate the experience of being in an environment that contains strong, clear, analyzable signals from interesting and potent objects.”
  3. Emotional Calls – Melodies may make evoke emotional responses because they have the “acoustic signatures” of whimpering, whining, moaning, growling, cooing, and other emotional outbursts.  We are referring back to language again, and Pinker points out that soul musicians mix growls and cries with their singing, and singers of torch songs use catches, cracks, hesitations, and other emotional tics.
  4. Habitat Selection – Just as we pay attention to visual cues that signal safe, unsafe, or changing environments, auditory signals such as thunder, birdsong, rushing water and footsteps can portend changing habitats.  Some program music and tone poems try to evoke environmental sounds
  5. Motor Control – Music may recreate the motivational and emotional components of movement, such as dancing, walking, running, and swinging.
  6. Something Else – Pinker suggests here that music may affect our emotions essentially by accident.  Among the possibilities he suggests: “perhaps a resonance in the brain between neurons firing in synchrony with a soundwave and a natural oscillation in the emotion circuits?”

In the end, Pinker admits that his analysis is speculative, but repeats his assertion that music is not an evolutionary adaptation.

As far as biological cause and effect are concerned, music is useless. It shows no signs for attaining a goal such as long life, grandchildren, or accurate perception and prediction of the world.  Compared with language, vision, social reasoning, and physical know-how, music could vanish from our species and the rest of our lifestyle would be virtually unchanged.

~ Steven Pinker, The Language Instinct

Levitan and the Music Instinct

Levitan believes there is an evolutionary basis for music, and he puts forward several arguments to support his case.  In addition to the idea that music plays a role in sexual selection as covered in Part 1, he offers two more possibilities:

  1. Social Bonding and Cohesion - collective music-making can promote feelings of group togetherness, and may have been a way to stay awake, ward off predators, and develop cooperation within the group.
  2. Cognitive Development – music may have prepared our pre-human ancestors for speech and other forms of communication.  Singing, instrumental, and rhythmic activities may have helped to refine motor skills, and develop the muscle control needed for vocal or signed speech.  And because music is a complex activity, it may help infants prepare for other mental work.

Taken by themselves, Pinker’s ingredients do not conflict with Levitan’s proposals.  The differences are in matters of context and primacy.  Where Pinker finds meaningless contemplation of auditory scenes, Levitan sees cognitive development and survival skills.  As a linguist, Pinker unsurprisingly believes that language came first, then music popped up by accident and came along for the evolutionary ride. Not everyone agrees.

Rhythm is gonna get’cha

In Musicophilia: Tales of Music and the Brain, Oliver Sacks writes about the communal experience of music, suggesting that there is an actual “binding” of nervous systems, or to use a word favored by early mesmerists, a “neurogamy”.

The binding is accomplished by rhythm — not only heard but internalized, identically, in all who are present.  Rhythm turns listeners into participants, makes listening active and motoric, and synchronizes the brains and minds (and, since emotion is always intertwined with music, the “hearts”) of all who participate.

What came first – the words or the music?

Sacks later discusses the work of Merlin Donald, who believes that human evolution moved from the “episodic” life of apes to a “mimetic” culture that flourished for tens or hundreds of thousands of years before language and conceptual thinking evolved.  Sacks writes: “Donald proposes that mimesis — the power to represent emotions, external events, or stories using only gesture and posture, movement and sound, but not language — is still the bedrock of human culture today.”

Rhythm is an integrative-mimetic skill, related to both vocal and visumotor mimesis…Rhythmic ability is supramodal, that is, once a rhythm is established, it may be played out with any motor modality, including the hands, feet, mouth, or the whole body…

Rhythm is, in a sense, the quintessential mimetic skill…Rhythmic games are widespread among human children, and there are few, if any, human cultures that have not employed rhythm as an expressive device.

~ Merlin Donald – Origins of the Modern Mind

Music is more than just rhythm of course, and its emotional power can be more fully realized when melodies and harmonies are introduced.  Studies have shown intrinsic emotional qualities in music that are recognized across cultures.  Discovery Health reports on a study which found that that indigenous Mafa tribes from Cameroon could consistently identify emotions in Western music such as happiness, sadness, and fear.

Sex and Drugs and Rock and Roll

So far we’ve seen that music can make you more sexually desirable, and that rhythm can bind people together, but what about the pure pleasure part?  How can listening to an ordered succession of tones, alone — with a pair of headphones — produce chills, or musical “frisson“.

With drugs, as it turns out.  You may have suspected this all along (and so did many others, including Levitan), but a group of researchers from McGill University just proved it:

Our results provide, to the best of our knowledge, the first direct evidence that the intense pleasure experienced when listening to music is associated with dopamine activity in the mesolimbic reward system…One explanation for this phenomenon is that it is related to enhancement of emotions. The emotions induced by music are evoked, among other things, by temporal phenomena, such as expectations, delay, tension, resolution, prediction, surprise and anticipation

~ Nature.com – “Anatomically distinct dopamine release during anticipation and experience of peak emotion to music” – January 9, 2011

Using a combination of positron emmission photography (PET) scanning and autonomic nervous system (ANS) monitoring,  the authors studied a group of people who consistently experienced objectively verifiable chills during their peak emotional responses to music.   And where previous studies used experimenter-selected music, the subjects at McGill chose their own “highly pleasurable music.”

So in one sense, Pinker is correct: music does have self-reinforcing pleasure properties.  But unlike heroin, it is not associated with fatal overdoses, HIV/AIDS, or painful withdrawals.  And given all of music’s positive associations with cognitive development, social cohesion, and physical and mental health, it seems a little silly to categorize it as “useless”.  Would your world be virtually unchanged if music disappeared?

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Beauty and Bartok’s Shopping List

In Part 1, we began to consider the questions below, and concluded that there is an evolutionary basis for the existence of music.  In Part 2, we will focus on the second question: what makes music beautiful?

  1. Why does music even exist?  Is it an evolutionary adaptation, or an accident — an evolutionary parasite?
  2. What makes music “beautiful”?
  3. Why do we derive pleasure from music?  What is it about music that “moves” us?
  4. Why do individuals prefer one type of music over another?

At the end of Part 1, we introduced the Golden Mean, an irrational mathematical constant with an approximate value of 1.6180339887…  What does this have to do with music?  Well, according to Pearl, it makes drums sound better:

The Golden Ratio, also known as the Golden Section, Golden Mean, Golden Rectangle, and the Divine Proportion, has fascinated mathematicians since the time of the Pharaohs. It is a mathematical constant (1.61803) that is found repeatedly in nature and has been used by artisans for generations to create art and structure with pleasing proportions.

Stradivarius applied the Golden Ratio to define the location of the  ”f-holes” and proportions of his masterwork violins. The exterior dimensions of the Parthenon are said to form a perfect Golden Rectangle. The proportions found in Leonardo da Vinci’s “Last Supper” follow the Golden Ratio.

Intrigued by this, our engineers asked if the Golden Ratio was applicable to drums and more specifically to the location of the air vents. For every drum depth there is an upper and lower Golden Ratio location, and testing revealed that the upper location noticeably improves attack, which is perfect for snare drums, while the lower position improves low frequency response, ideal for toms and bass drums. Pearl’s revolutionary new Golden Ratio air vents are so unique they’re patent pending. Experience the sound of Golden Ratio air vents, centuries in the making, exclusively on Masterworks and Master’s Premium series drums.

~ Pearl Drums – Masterworks

Let’s say we’re convinced (after all the drums and the Stradivarius sound pretty darn good.)  Can the Golden Mean explain why we find music beautiful? And what does all of this have to do with the Fibonacci sequence anyway?

Let’s take up the latter question first.  If you did the extra credit work from Part 1 and watched the YouTube Short from Jane Weavis, or read the Theory Behind The Numbers from Cristóbal Vila, you already know the answer.

If we divide each value in the Fibonacci Series by the previous, the result tends to Phi. The higher the value, the greater the approximation (consider that Phi, like any irrational number, has infinite decimals).

~ Cristóbal Vila

Now that we’ve got that settled, what does it all mean?  Well it’s easy to see and measure these relationships when you’re dealing with physical objects such as bodies, buildings, and the human face.  And a fairly reasonable case can be made for the relationship between physical beauty and the golden mean.  (Although some argue that powers ascribed to the golden mean are often better explained by symmetry or other factors.)

Demonstrating the relationship between the golden mean and beauty in music is much more difficult.  First, despite the adage that “beauty is in the eye of the beholder,” there is general agreement, especially within cultures, on physical beauty.

Research shows that, despite the elusiveness of physical attractiveness, people overwhelmingly agree in their judgments about the physical attractiveness level of other persons, and can distinguish points along a physical attractiveness continuum that are consistent from one time period to another.

~ Gordon L. Patzer, The Power and Paradox of Physical Attractiveness

Conversely, there is much less agreement about what constitutes beautiful music.  And these differences exist not just across cultures, but among and within groups from the same culture.

Even if we ignore musical tastes, how do we measure the Fibonacci influence or “Golden Meanness” of a piece of music?  Rather tortuously, as it turns out.

Below is a brief survey of attempts to find the Fibonacci sequence and the Golden Mean in musical compositions, followed by some of the difficulties with each approach.

  • Some find Fibonacci numbers in the most commonly used used scales: Pentatonic (5), Major and Minor (8) and Chromatic (13).  The issue here is that major and minor scales actually contain seven tones, and the chromatic scale contains 12.  They only reach 8 and 13 if you include the octave, in which case, you need to drop the pentatonic scale.
  • Others claim that the interval relationships in various pieces of music are based on the Fibonacci numbers. If we include the octave, then the numbers 1, 2, 3, 5, 8 represent more than 62% of the available notes in a major scale.  These notes can also form all intervals within the major scale except for the most dissonant (minor 2nd, tritone, and major 7th.)  So it would be more astonishing to find pieces of music that did not use the Fibonacci numbers.  Also, some musicologists use scale tones to demonstrate the relationships, while others use semitones.
  • Both the Golden Mean and Fibonacci numbers are found in examining the structure of compositions, with the climax coming at the .618 mark, or the sections starting at bars with Fibonacci numbers.  Many of these calculations need some nudges to hit their marks, e.g., you need to leave out introductory measures, or ignore repeated sections. And in some cases, changes in time signatures or tempo move the temporal location of a section to a place that does not correspond to its bar count.

Enough.  There’s more, but you get the idea.  Given a sufficiently complex piece of music, you can conjure almost any mathematical relationship between its intervals, rhythms, and structure.

Even the simplest pieces of music can yield results.  Think of “Happy Birthday” in F Major.  Eight measures long, and the climax comes with the high C at measure five (the third “Birth…”.)  Eight divided by five equals 1.6.  Hmmm.  (Of course if we count the pickup as bar 1, we get 9/6, or 1.5.  Or if we count beats, we get 25/14, or 1.78.  But close enough, right?)

The composers most often trotted out to support the Golden/Fibonacci theories are Bartok and Debussy.  And the piece of music mentioned most frequently is Bartok’s “Music for Strings, Percussion and Celesta.”  Erno Lendvai write extensively on the topic in his book, Bela Bartok: An Analysis of His Music.  But not everyone agrees with his conclusions.

Some musicologists do not accept Lendvai’s analyses.  Lendvai himself admits that that Bartok said nothing or very little about his own compositions, stating: “Let my music speak for itself; I lay no claim to any explanation of my works.”  The fact that Bartok did not leave any sketches to indicate that he derived rhythms or scales numerically makes any analysis suggestive at best.  Also, Lendvai actually dodges the question of whether Bartok used the Golden Ratio consciously.  Hungarian musicologist Laszlo Somfai totally discounts the notion Bartok used the Golden Ratio, in his 1996 book Béla Bartók: Composition, Concepts, and Autograph Sources.  On the basis of a thorough analysis (which took three decades) of some 3,600 pages, Somfai concludes that Bartok composed without any preconceived musical theories.  Other musicologists, including Ruth Tarlow and Paul Griffiths, also refer to Lendvai’s study as “dubious.”

~ Mario Livio: The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number

Having introduced dubiousness into the conversation, consider this unsubstantiated comment from a forum discussing Bartok and the Golden Ratio.

For a long time, there was no evidence at all to suggest that Bartok actually did all this on purpose, that he ever calculated anything. No papers, nothing.

Then, somebody found something. It was a paper in Bartok’s documents that was just covered with numbers from the Fibonacci series. Different calculations and so forth.

It raised a huge controversy; kind of like the rosetta stone, as one of the professors here described it, of Bartok study.

Well, you know what it was? A shopping list. Bartok had just been adding and subtracting prices, and figuring out taxes, and it’s just a coincidence that these prices happened to be fibbonaci (sic) numbers!

~ Sam, #353863

Suppose evidence of Bartok’s use of the Golden Mean was found, would his compositions be heard or appreciated any differently because of it?  Even though “Music for Strings, Percussion and Celesta” is one of my favorite pieces of music, not everyone would describe it as “beautiful.”  My daughter actually seemed a bit frightened by it during her first listen.

We may never find a completely satisfactory answer to the question of what makes music beautiful.  Victor Hugo said, “Music expresses that which cannot be put into words and cannot remain silent.”  Robert Jordain concludes his book Music, the Brain, and Ecstasy, with some thoughts on beauty and music.

The experience of unsullied order persisting simultaneously at every perceptual level may be taken as a working definition of the word “beauty.”  When events in everyday experience come together perfectly, we’re apt to exclaim “Beautiful!” and to register the pleasure of anticipations perfectly met.

Many people say that it is beauty alone that draws them to music.  But great music brings us even more.  By providing the brain with an artificial environment, and forcing it through that environment in controlled ways, music imparts the means of experiencing relations far deeper than those we encounter in our everyday lives.  When music is written with genius, every event is carefully selected to to build the substructure for for exceptionally deep relations.  No resource is wasted, no distractions are allowed.  Thus, however briefly, we attain a greater grasp of the world (or at least a small part of it), as if rising from the ground to look down upon the confining maze of ordinary existence.

~ Robert Jordain, Music, The Brain, And Ecstasy: How Music Captures Our Imagination

Yeah, what he said.  Come back for Part Three, where we look more closely at what exactly it is about music and its ordered relations that so move us.  None of this means you can’t consciously use the Golden Mean or Fibonacci numbers as a compositional tool (see the video for Lateralus below) — just that they aren’t necessary or sufficient to create beauty in music.

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Music: The Heart of Human Nature, or Auditory Cheescake?

Among the big questions, one of the biggest is: “Why is there something rather than nothing?”  Think about music for a moment, and several questions naturally follow:

  1. Why does music even exist?  Is it an evolutionary adaptation, or an accident — an evolutionary parasite?
  2. What makes music “beautiful”?
  3. Why do we derive pleasure from music?  What is it about music that “moves” us?
  4. Why do individuals prefer one type of music over another?

Searching for answers to these questions will lead us through the field of evolutionary pyschology, fields of sunflowers and dragonflies, and Tool’s Lateralus.  Let’s go!

Music and the Meaning of Life: Darwin vs. Pinker

In This Is Your Brain on Music: The Science of a Human Obsession, Daniel Levitan outlines the evolutionary argument for the existence of music.  In order for genes to be successful, two conditions must be met: 1) an organism must be able to successfully mate, passing on its genes; and 2) the offspring must be able to survive in order to do the same.  From his theory of natural selection, Darwin came up with the notion of sexual selection.

I conclude that musical notes and rhythm were first acquired by by the male or female progenitors of mankind for the sake of charming the opposite sex.  Thus musical tones became firmly associated with some of the strongest passions and animal is capable of feeling, and are consequently used instinctively…

~ Charles Darwin – The Descent of Man

In “The Meaning of Life” — chapter 8 of How the Mind Works, the usually sensible Steven Pinker proposes that music is essentially a byproduct of evolution: “auditory cheescake” that serves no real purpose.

What benefit could there be to the diverting time and energy to the making of plinking noises, or to feeling sad when no one has died?  As far as biological cause and effect are concerned, music is useless…[it] appears to be a pure pleasure technology, a cocktail of recreational drugs that we ingest through the ear to stimulate a mass of pleasure circuits at once.

~ Steven Pinker – How the Mind Works

Levitin counters: “The number of sexual partners for rock stars can be hundreds of times what a normal male has, and for the top rock stars, such as Mick Jagger, physical appearance doesn’t seem to be an issue.”

Advantage: Darwin.

Music and Beauty:  The Fibonacci Sequence and the Golden Mean

You would hope that there are deeper meanings and pleasures in music beyond increasing the count of sexual conquests.  (Otherwise, how to explain bassoonists and banjo players?)  Many of us find pleasure in music for its own sake — whether playing or listening, together or alone.  Studies have shown health benefits from playing music as well as from music listening and music  therapy.  But is there something intrinsic to music that provides meaning, or makes it “beautiful”?  Time to trot out Fibonacci.

Nature by Numbers

First, let’s do the math.  Take zero and add one: 0 +1 = 1.  Now extend the sequence by adding the previous two numbers (e.g., 1 +1 =2; 1 +2 = 3; 2 +3 = 5) and you get the Fibonacci sequence:

 0  1  1  2  3  5  8  13  21  34  55  89  144  233  377  610  987  1597... 

Easy enough.  The Golden Mean is a little trickier.  Take a line, divide it into two sections so that the ratio of the total line to the longer section is the same as the ratio of the longer section to the shorter section.  And voilà: you are golden.  That is, you have arrived at the Golden Mean (or Golden Ratio), an irrational mathematical constant approximately equal to 1.6180339887…

How is the Golden Mean related to the Fibonacci sequence?  More important, how is any of this related to music?  We will explore those questions in Part 2.  Until then, enjoy the Fibonacci sequence and Golden Mean in action from Cristóbal Vila below.  If you just can’t wait for more, check out the excellent exposition on Vila’s eterea studios site, and a well-done YouTube short from Jane Weavis.

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