Welcome back to "Continuous Hit Music" as we soldier on, exploring how music works. In the last installment, we took a look at the basic nature of sound. (If you haven't read it, don't sweat it; I'll be giving you the Cliff's Notes on everything you need to understand this article.) This time around, let's start to get into how sounds become music.
If you've ever seen The Wizard of Oz, you doubtlessly remember Judy Garland's soaring rendition of "Somewhere Over the Rainbow." You've also probably heard Israel "IZ" Kamakawiwo'ole's soulful rendition of the song; it was really popular a few years back, and has popped up in all sorts of commercials and film soundtracks since.
Comparing the two versions, it's pretty safe to say that Kamakawiwo'ole took some inspired liberties with the melody as the song progresses. That said, he seems extraordinarily faithful to Garland's version from the beginning of the first verse to the word "lullaby," when he starts adding notes.
His faithfulness in the first verse isn't complete, however. The two versions differ in the very first word, "Somewhere." Garland starts on a low pitch for the syllable "Some" and then changes to a much higher pitch for the syllable "where." Kamakawiwo'ole, on the other hand, simply stays on the same pitch for both syllables. Despite this break in pitch, however, it sounds like they're singing the same notes.
And, in fact, they are. If you were to find Kamakawiwo'ole's first two notes on a piano, you'd strike an "A" key twice. If you were to then find Garland's first two notes on a piano, you'd strike the same "A" key, followed by the next "A" key higher up on the keyboard. But how can they be the same note when they're two different pitches? How does this work?
In the last article, we discovered that sound is created by vibrations in air, and that most musical sounds are made up a number of frequencies -- a fundamental frequency, and additional "harmonic" frequencies. These harmonic frequencies are integer multiples of the fundamental. For instance, a sound with a fundamental frequency of 220 Hz would also have harmonics of 440 Hz, 660 Hz, 880 Hz, and beyond -- or 2*220, 3*220, 4*220, and so on. If we were to make this new 220 Hz sound, we'd hear it as pitched below both Judy and Israel's first "A" notes. But this new sound, too, would be an "A" note.
This may seem screwy, but it's entirely a matter of semantics: frequencies, pitches, and notes are not synonymous with each other. "Frequency" is strictly a scientific measure; you can determine exactly how many cycles per second a sound makes and measure them with precision. "Pitch" refers to how high or low we interpret a sound to be; while it is very dependent on the frequency of a sound, it is not objectively measurable. A "note" exists strictly within the context of music; we give the same name to sounds that share the same musical function. And fortunately for us, this function can be measured objectively.
In fact, let's measure Judy's opening "Somewhere." She moves from one A note to the next highest A note. If we were to measure the fundamental frequencies of both of these notes, we'd find that the lower A is at 440 Hz, while the higher A is at 880 Hz. The fundamental of the second note is simply two times the fundamental of first. To get to the next highest A after that, we'd multiply 880 Hz by 2 again to get 1760 Hz.
But why does this work? Let's try to look at it as simply as possibly. If you remember from the last article, a "pure" tone is a sine wave. Let's look at two sine waves, one with twice the frequency of the other:
Now, it's not terribly difficult to see that the two are related. But, specifically, look at all the points where the first frequency crosses the x-axis:
Notice that every time that the first frequency passes through the x-axis, the second frequency is completing a cycle. In other words, the first frequency will never finish a cycle without the second frequency concurrently finishing a cycle. Compare this to a frequency with 3x:
While these frequencies also cross the x-axis at all the same points, their cycles do not align exactly. In other words, they are closely related, but they could not be classified as the same note. Why is this? Music is, in many ways, the way in which frequencies relate and interact with each other. There are some notes that go very smoothly together, because their frequencies are closely related -- like x and 3x -- which bring about what musicians call "consonance." On the flip side, when frequencies clash against each other, it brings about what musicians call "dissonance." Dissonance isn't necessarily a bad thing; it's simply not consonance. It's the difference between tension and release, or conflict and resolution. No story would be interesting without some conflict. Visual arts wouldn't be interesting without any contrast. Music isn't any different.
With that in mind, what would be the ultimate example of consonance? Two identical frequencies; they would interact with any other frequency in exactly the same way. Next to being identical, though, what would be the best example of consonance? Two frequencies who, unfailingly, end their cycles in the same place. These frequencies would affect other frequencies in very similar ways due to their close relationship, and, as a result, serve extraordinarily similar musical purposes. Therefore, 440 Hz and 880 Hz can both be classified as a certain kind of note -- specifically, an "A".
With all that said, you may still be wondering, why is A specifically 440 or 880 Hz? The answer is simple: because we say so. It's pretty much arbitrary. Most places in the world use 440 Hz to tune to A, and then calculate all of the other notes from that frequency. (We'll do that in the next column, in fact.) Some places, however, use 442 Hz. Back in Mozart's day, they tuned A to something closer to 412 Hz. It doesn't really matter what frequency is used for an A, so long as all of the instruments use that frequency for an A. In other words, it doesn't matter that a note is a certain frequency, it matters how a note's frequencies relate other notes' frequencies.
If you want to hear other examples of two notes used opposite each other to get a feel for what they sound like, give a listen to Aimee Mann's "Wise Up" ("It's not..."), Mel Torme's "The Christmas Song" ("Chest-nuts..."), or Clap Your Hands Say Yeah's "Satan Said Dance" (the repeating beeps; these go from a higher A to a lower A). As always, feel free to send me any and all questions and comments you might have 'til next time, when we'll take a look at how we get all of the notes in Western music.