Music is just sound, and notes are just the air vibrating a certain number of times per second. The vibration is sensed by the hair in your ears and your brain interprets it as sound. A pretty amazing thing if you stop to consider it.
In a way that is very similar to the concept of beauty, some music is very pleasant, some is decidedly not. There is no good reason for some music or combinations of notes (chords) to be pleasant while others are not. There is seemingly no reason for us to recognize some notes as “beautiful music” and other notes as brow-furrowing noise. At no point in our past could music have assisted us in finding food or other resources. Just like the beautiful face tells us nothing about the owner’s abilities or fitness.
To standardize our definition of “music”, Western civilization has arbitrarily decided to use a 8 note scale (do, re,mi,fa,so,la,ti,do) and calls it an “octave”. There are also 5 “minor” notes (the black keys on the piano) within this scale for a total of 13 as shown here. These numbers (5,8,13) will become important in a minute. Keep in mind that these notes were not predetermined in any way. The “A” on a piano is 220 hertz (”ok, that seems like a nice round number”) while middle “C” is 261.6 hz, “D” is 293.7 hz (”hmmm..”) Hertz is vibrations per second.
I’m tempted to launch into a long, mathematical discussion of which certain notes sound best together, but I suspect you don’t care. Let’s simply conclude that combinations of notes as arbitrarily created by this 5/8/13 note scale are pleasing, and some (”thirds” and “fifths”) are used more frequently than others. But for more entertaining take on the subject, make sure you to check out this video of Bobby McFerrin (the “Don’t Worry Be Happy” guy) hacking directly into your brain and proving my point. If you check it out, don’t overlook the word Pentatonic in the title. Pent, as in Pentagon. The Pentatonic scale is comprised of the 5 black keys on the piano, seemingly installed in our brains prior to birth. Maybe this teaser from the accompanying article will get you to check it out:
But then Bobby jumps somewhere unexpected. He goes further up the stage, to a position of higher pitch that he hasn’t defined, and the audience follows along perfectly.
So here’s the takeaway: everything I’ve said up to this point is based on the numbers 3,5,8, and 13.
We’ve established that there are two wonderful parts of life that have seemingly no reason to be wonderful. We all love our favorite music and are attracted to good-looking people for no obvious reason. Neither of these tendencies get us anything other than their own rewards. But I believe they have a common, mysterious similarity – the Fibonacci sequence and related concept, the Golden Ratio.
Creating the Fibonacci sequence is fairly straightforward. Start with 0,1, and add the last two numbers of the sequence together to get the next number.
0,1,1 (add 1 to 1 to get the next number, 2):
0,1,1,2 (add 2 to 1 to get 3):
0,1,1,2,3 (and so on):
0,1,1,2,3,5,8,13,21,34,55,88 (get it?)
(Remember our numbers from above? 3,5,8,13!)
A related number, the Golden Ratio, can be approximated from any two sequential numbers in the sequence; as the numbers in the fraction get bigger, the ratio is “headed” towards the same “magic” number, approximately 1.61803 … (the number is a decimal with no end).
3/2 = 1.5
8/5 = 1.6
55/34 = 1.61747 (the bigger the numbers, the closer you get to the real number)
The Golden Ratio (also known as Phi, which has nothing to do with Pi, that circle thing you learned about in high school) is an “irrational” number, meaning it cannot be fully expressed as any fraction. You’ll notice our fractions above get us closer and closer to Phi as the numbers within the fraction get bigger but there is no fraction that defines Phi exactly. As examples of other irrationals, Pi (3.14159…) and e (2.71828…) are also irrational but have nothing to do with what we’re talking about here.
The Golden Ratio is actually the most irrational of all irrational numbers (there’s a girlfriend joke in there somewhere that I will skip), meaning that there is no number that is harder to approximate with a fraction. Take Pi for instance, 22/7 = 3.1429… is fairly close to 3.1416… (off by 13 parts per 30,000) but the closest you can get with numbers that low for Phi is 21/13 = 1.6154… as compared to 1.6180…, which is off by 26 parts per 16,000, which is 4 times as “far away”.
So where am I headed with all this (Jesus, are you still reading?! You are a trooper.)
Phi is nature’s favorite number. Consider petals on a flower. If you were designing a flower, you would want the petals to be placed in a way that they would get the most sun that they could. So how do you define where the petals get placed? Let’s take the opposite approach, how don’t you want to place the petals? What you would NOT do is place the petals at regular intervals that overlap, like every 1/2 of the way around the flower. You’d end up with 2 stacks of petals with only two of the petals actually getting any sun. That’s a pretty stupid looking flower.
So your next try might be some weird fraction like 3/11, putting a petal every 3/11ths of the way around the flower, but that would leave you with 11 stacks of petals, a big improvement but still a pretty weird looking flower. You’d realize that fractions are your enemy and would try to find a number that is the farthest away from any fraction that you could find to avoid overlapping. As described earlier, that number is Phi! Nature places each new growth approximately 222.5 degrees from the last one (1 / Phi X 360) and almost all flowers have a number of petals that equals a Fibonacci number (3,5,8,13, etc.)
In nature, the Golden Ratio is everywhere. Pinecones and sunflowers use this ratio to create their spirals. Most shells use the ratio. We’ve already discussed flowers. Ants and bees use this number in the formation of their hives. Branches in trees and leaves on a stem also follow this arrangement closely. This idea is why a 4-leaf clover is so unique, it doesn’t follow the rules!
So now that I’ve impressed you with my seemingly meaningless knowledge of Phi, I’m going to continue by telling you that humans seem to have a natural attraction to this ratio. Credit cards, paper, windows, etc. all have a tendency to match the Golden Ratio, meaning their sides are close to a ratio of 1 to 1.618. Coincidence? Why aren’t more things square, wouldn’t that be the most efficient use of space in many cases? Whenever we have a choice, we naturally gravitate toward the magic ratio. Phi’s place in art, dating all the way back to the Greeks is well known. Da Vinci was basically obsessed with it. Plato called Phi “The key to the physics of the cosmos”.
For years, TVs had a standard aspect ratio of 4/3 (1.333), now the (improved!) standard for movies and TV is 16/9 (1.78). That’s no smoking gun, as they overshot somewhat, but I will bet you the next standard moves closer to 1.618/1. Any takers? I also wonder if this ratio was “forced” by the necessity of choosing nice round numbers instead of 13/8; 16/9 was actually chosen almost 20 years ago as the new cinema standard and I’ll bet it’s pretty difficult to move away from this well-established standard, due to the physical construction of TVs, film, cameras, etc.
Phi can be also be found in our bodies way more that one would think. The ratio of hands to arms, head to torso, etc, etc. can all be shown to conform to multiples of Phi. One might argue you could measure any number of different things to find the ratio you wanted but if we made a list it would be hard to argue with the sheer number of these occurences.
This has been taken one step further by Dr. Stephen Marquardt, who has used Phi to develop a map of the “perfect human face” by for use in his plastic surgery practice. You can play with his “map” here. He believes that celebrity faces have these ratios and that when “normal” faces get changed via computer imaging to conform to the Phi ratios, people regard the new image as more attractive than the old. There is also semi-conclusive evidence that well-rounded athletes like decathlon competitors have body measurements that are closer to the Phi-based ratios than “normal” people.
So, is this natural tendency to recognize and appreciate Phi responsible for our “taste” in people? Is it the same with music and the reason we have developed our 5/8/13 musical scale? Is it why we enjoy “thirds” (standard harmony) and “fifths” (rock’s “power chord”) more than other chords? More directly, do we have a deep, indescribable, inborn attraction to this ratio? Would I go too far to ask if it tugs at our very souls?
Try this one on for size … could ALL of life’s wonderful intangible qualities like music, art, beauty, even love, boil down to the basic act of recognizing a simple, humble number, the fundamental building block of nature, as identified by our ancient, subconscious, reptilian brain?
Thanks for this.
And for your Freepmail.
C