Let’s talk about music. Let’s talk about how musical notes can create singular links.
When you play a note on a piano or any instrument, you are actually hearing several notes wrapped together. Let’s say you play what piano players call the A2 note on a standard-size keyboard. This note is below middle-C, two octaves above the lowest note. The loudest pitch you hear is called the note’s fundamental. In the case of A2, the fundamental vibrates at 110 Hertz, or 110 times per second.
In addition to the fundamental, you also hear other harmonic notes, or overtones, that work together and complement the fundamental. These overtones vibrate at higher frequencies. However, their volumes are lower than the fundamental, so their contribution to the overall sound is more subtle. The first overtone of A2 is A3, which is an octave above the fundamental, and it vibrates 220 times per second. The second overtone is E3, a perfect fifth above A3, vibrating 330 times per second. Then there’s A4, which vibrates 440 times per second and is the reference note for “standard 440 tuning” or “concert tuning.” The next overtone is C-sharp, two octaves plus a major-third above the fundamental, and it vibrates 550 times per second.
All these notes ring simultaneously when you play that single A note on the piano, and together they create a rich, blended sound. Whichever note you play on the piano, the fundamental will be accompanied by several overtones.
What happens when you play multiple notes simultaneously? Let’s say you add an E3 to the A2. The new fundamental you hear is roughly 165 Hertz. This combination of A2 + E3 will sound harmonious to most listeners because the two notes have natural affinities with one another. The E note is a perfect-fifth of the A scale, whether major or minor, and it is also the third overtone of the A note.
If your eyes are glazing over because of these technical details, just know that the main point of this topic is how notes interact with each other to create different effects.
When you play the two notes E3 + A2, the relationship of vibrating frequencies (165 Hertz to 110 Hertz) is close to a ratio of three-to-two, an important building block of Western music. Since at least the Middle Ages, our ears have been culturally accustomed to recognizing that ratio when we hear it.
This is true whenever you pair a root note and its perfect-fifth. The same harmonious relationship exists between C and G, between F and C, etc. They are like close friends or identical twins or maybe like lovers. They fit with one another. They feed one another. They join together naturally like carefully machined gears of a watch. When you hear them, you hear accordance, symmetry, cooperation.
What other pleasing relationships can you find? A2 fits harmoniously with a D2, which vibrates roughly 72 times per second. Again, their fundamental vibrations approximate a ratio of three-to-two (110 Hertz to 73 Hertz). The A is a perfect-fifth above the D, and it is also the third overtone of the D. The first overtone of D2 is D3, which is a perfect-fourth relative to the A. They have a pitch ratio of about four-to-three (147 Hertz to 110 Hertz), which is also culturally pleasing, and another staple of Western cultural tradition.
The relationships of root notes to their perfect-fourths and perfect-fifths are ubiquitous in Western popular music. They form the foundation of most of the sounds coming out of your playlist, from ABBA to ZZ-Top.
Put it this way, if you set out to play all the pop tunes that only use A, D, and E, you would have to clear your entire calendar for days and days and days. You could start playing Friday evening after you got home from work, and you would still be playing Monday morning with no end in sight. Going through the pop-music catalogue alphabetically, by Monday morning you probably still would be a long way from “Hang on Sloopy,” and you might only have reached the second verse of “Crimson and Clover,” even if you have been playing the tunes at a fast tempo. The root-fourth-fifth relationship is everywhere.
Here’s where things get interesting.
Since root-fourth-fifth relationships are everywhere, and your ears are accustomed to hearing them, you can compose evocative music by intentionally deviating from those relationships. Good composers and songwriters create different emotions through different combinations of notes. They string together chord progressions that lead their listeners through a sonic journey, inducing different emotions, building tension and resolving tension. Even though Lennon and McCartney, for instance, were not schooled musicians in the traditional sense, they were hyper-aware that different chord progressions created different feelings in their listeners. The same is true of nearly every songrwiter.
Bringing it back to the fundamentals of the A note, if you were to add a C-sharp, you would create a major chord. The two notes sound natural together, and you may recall that one of the overtones of A is C-sharp. Western listeners are used to hearing this combination.
Likewise, if you added a C to the A instead, you would create a minor chord. These also sound natural together, since they share E in their overtones and Western listeners are also very familiar with this combination.
What have you done so far? Let’s recap. YOu started with the A, and you have been pairing it with descending notes, from E to D to C-sharp to C. What happens when you choose one note lower, adding a B to your A? This would definitely add some tension to your chord, since they are close enough together to create some dissonance. The overtones don’t coincide very well, but they could potentially work together. The B appears in the A-major and A-minor scales, and the A can act as a dominant seventh in some B scales. If combined, these notes would work best to create temporary tension in a passing chord on the way to resolving with a more harmonious chord. In other words, this combination could work selectively as an intentional effect.
If you drop down another semitone to add a B-flat to your A, however, now you’re getting into serious dissonance territory. Since the two notes are right next to each other, all their harmonics compete and clash and oscillate over and under each other. To Western listerners, this combination sounds like a mistake. It sounds mutated. It sounds shrill, shocking, like nails on a chalk board, more like noise than a chord.
And that is exactly the point of this topic. The farther away you go from convention, the more you create the opportunity for something completely new. The A and B-flat are almost never heard together, which is why bringing them together intentionally could conceivably have a powerful effect on the listener.
The combination is unnerving. No question about it. In fact, oscillating between the two notes was exactly what composer John Williams did when he scored the iconic, tense soundtrack for the shark thriller Jaws… “do-DA-do-DA-do-DA-do-DA-do-DA-do-DA-do!” His work is a beautiful, powerful, simple two-note example of a singular link.