I’m fascinated by the relationship between mathematical ratios and what people perceive to be beautiful or pleasing. In music, simple ratios played as intervals like 2:1, 3:2, and 4:3 (an octave, fifth, and fourth, respectively) are generally considered to be pleasing (or boring, depending on your ear). Ratios that contain higher integers, like 5:4 (major third) and 9:5 (minor seventh) are consider more dissonant, complex, or “challenging,” depending on your personal taste and cultural background.
While it might seem that the way we perceive music has universal qualities, most evidence points the other way. Some people can’t actually perceive the patterns and beauty that most of us get from listening to music — instead they just hear noise (the condition is called congenital amusia). There are also cultural factors — Western ears are used to hearing equitempered scales, in which each note is tuned slightly away from a perfect ratio. This tweak allows a tuned instrument (such as a piano or other keyboard) to play music in multiple scales without retuning. Instruments that don’t have fixed tuning (string instruments, the human voice) can use “just scales” based on perfect ratios. Indian music uses a justly tuned diatonic scale. Most Western music, using chords and harmonies, would sound dissonant and jarring using such a scale. How does most traditional Indian music get around this problem? There are no harmonies — there is only rhythm and monophonic melody.
Most people would agree that music is emotionally evocative, but only people that are culturally similar get the same emotions from a given piece of music. If I listen to Javanese gamelan music, I can’t tell which pieces are “happy,” “sad,” or are meant to evoke other emotional states. I can still appreciate the music, but I don’t have a cultural context to help me understand the emotional narrative.
Why Do Ratios Matter?
Significant ratios show up in other art forms as well. The Golden Ratio frequently shows up in architecture. Why is the proportion of 1.618 to 1 so pleasing to the human eye? Perhaps it’s because we see it so much of it in nature, in the spiral of a nautilus or in the placement of leaves on a stem.
Nature uses simple algorithms to build things. The way I see it, the nature of reality is simple mathematical processes interacting in such a way to create infinite complexity and variety.
For example, the Fibonacci sequence is a simple progression of number. Starting with 0 and 1, the next number in the sequence is derived by adding the previous two numbers. So you get:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … etc.
The ratios of successive numbers in this sequence converge on Phi (the Golden Ratio).
1:1, 2:1, 3:2, 5:3, 8:5, 13:8 … etc.
If you were to play those ratios as musical intervals, they would become more dissonant as you went along (and as they got closer to Phi). An octave, followed by a fifth, followed by a major sixth, followed by a minor sixth. On a keyboard with standard tuning, you can’t get any closer to Phi than a minor sixth. If you use a computer to generate two tones with an exact ratio of Phi, you get what you could say is “the ultimate dissonant interval.” It’s not a pretty sound. On the other hand, it’s jarring and interesting and not at all boring.
Why do our eyes perceive Phi as beautiful spatially, but dissonant musically? I wish I knew.
My point is that we can start with a simple algorithm and quickly arrive at something that is complex and interesting. And I think that’s how reality itself works.
Vibration and Smell
What we perceive to be a musical note is actually air molecules vibrating at a particular frequency. The way we perceive colors from light is similarly dependent on vibrational frequency. Our sense of smell is different — it is dependent on the shape of particular molecules. Or is it?
They “lock and key” theory of smell has been around for a long time. The idea is that there is a nasal receptor that exactly matches each distinct molecule floating around in the air, and that when one of those molecules “latches in” to a matching receptor, nerves in the nose send a signal to the brain (red wine, orange juice, lavender, dog fart, etc.).
There are some problems with this theory. Do we really have enough room in our nose for a receptor for every single distinct molecule found on this planet? And what directed the evolution of those receptors? Did we only develop receptors for those molecules that we “needed” to smell, from an evolutionary point of view? Or do we also have the capacity to smell novel scents that we were never exposed to in our evolutionary history (like artificial chemicals)? Obviously, we’re able to smell artificial/evolutionarily novel scents. But why? As Bill O’Reilly might say, “You can’t explain that!”
An alternate theory of smell, based on the vibrational frequency of various molecules, can explain how we can smell such a wide variety of scents. The biophysicist Luca Turin has been building support for the vibration theory of olfaction. An experiment he published as recently as January of this year demonstrated that fruit flies can distinguish the deuterated form of a compound (in which hydrogen is replaced with deuterium) from the non-deuterated form. The two isotopes tested have an identical shape and structure — but a different vibrational frequency.
Other researchers have proposed that the mechanism behind the vibration theory of olfaction involves electron tunneling and quantum mechanics. Basically, an electron tunnels to a different energy state (and triggers the nasal receptor) when the vibration frequency of the molecule matches the energy difference between two states. Should you trust a sentence that starts with “basically” and is about quantum mechanics? Absolutely not — and I don’t pretend to completely understand the process. What I do understand is that there’s a strong possibility that smell, like sound and light, may one day be described and quantified mathematically. We may find that there are basic “notes” of smell that can be combined into chords or sequenced into melodies, just as the three primary light colors (red, blue, and green) combine into the thousands of distinct hues and tones the human eye can perceive.
Does this sound farfetched? Consider this unpublished excerpt (cut due to length) from Chandler Burr’s The Emperor of Scent:
Turin remembered that in late 1994 at an exhibition in London he had run into the perfumer Guy Robert and told him about his vibrational theory and this idea that there should be primary vibrations, primary smells. Robert mused for a moment- Turin watched him intently- and then remarked that once, years ago, he had walked into a hot, darkened room in southern France. Inside was a basket containing bananas and lemons, ripening in the ambient heat. When he opened the door, said Robert, the two smells hit him at once and he got… jasmine.
Jasmine? Hm! Banana + Lemon = Jasmine? Add two smells, get a third. To Turin, it sounded like Robert, with his relentlessly refined olfactory sense, had split the smell “jasmine” into its primaries.
He left for Paris, where he hung out in cafes and wandered the streets with Francoise. She lived near the Bastille, next door to a neighborhood shop that sold a terrific dirty rum from Martinique, a killer rum that gave industrial strength hangovers. He went right out and got some. That evening he was fixing a little rum. He sliced fresh mint leaves on it and brought it to his mouth. And he froze, transfixed, because he was smelling black currant. Mint + rum = an olfactory hologram of Black Currant, hovering in the air. He thought: I’m smelling black currant in its primary components.
He went back to London. He got a very cheap rum and a glass and some mint leaves and went over to Jane Brock’s lab. She was working. She looked up. He put his stuff down on her various papers on tissue histology and neural connection, and she calmly watched (she’d been through this enough times) as he poured the rum into the glass, then cut up the mint and put it in. He held the glass up to her nose. She leaned over and inhaled.
She sat back, waited an instant, and said “Black currant.”
He hadn’t uttered a word.
There are many challenges to the vibrational theory of olfaction, but more scientists are considering that Turin’s ideas about smell are not as farfetched as they initially seemed.
Back To The Zeitgeist
We’re all different, and we all have different perceptions and opinions regarding what is beautiful, pleasing, or entertaining. Within any given culture at any given time, certain trends dominate (down to individual colors, smells, and chords, not to mention fashions, genres, and styles). As a music producer and label owner, I’ve learned (the hard way) that my own tastes don’t necessarily line up with the mainstream. I’ve also never had any luck “chasing the zeitgeist” — trying to predict where tastes are going. My greatest successes have been from trying to create (or sign to Loöq) something that excited me personally, and then getting lucky when whatever product resulted overlapped with the direction of changing tastes. That’s probably the way that I’ll continue to operate, but that doesn’t stop me from being fascinated with the deconstruction of aesthetics. You like that? Why, exactly, do you like it? For the consumer/appreciator of art or music, examining this question too intently can detract from pleasure. But artists who want their work to have emotional impact need to consider the question, right down to how different vibrational frequencies impact the senses and the brain.