Using the physics behind music, Jeremy discusses why the world is a better, more interesting place because everyone is different. He also explains powerful ways to work to find common ground among all the different people in an amazing and beautiful way. This article was originally given as a talk to launch a spiritual growth group series on Living in Harmony at the Virginia St. Church in St. Paul, MN. -Editor.
“I was shown that angels cannot live together in blessedness unless they are the kind that can speak and act together. Blessedness consists in unanimity and harmony, whereby many, even very many, consider themselves to be a one. For from many agreeing together, or a harmony of many, comes a oneness, which results in blessedness and happiness and, from a shared feeling of happiness, a doubled and tripled happiness. (Emanuel Swedenborg, Spiritual Experiences, 289)
Swedenborg makes clear in many places that living in harmony is an essential feature of heaven and eternal life1. It is also a fundamental feature of his philosophy that we can learn much about the spiritual world by examining the natural world. So I would like to explore what we can learn about spiritual harmony (which to me implies getting along with others, and also living in a state of integrity where your deeds match your words and beliefs) from looking at the physical nature of musical harmony. In fact, I would not be alone in saying that musical harmony is such a profoundly delightful experience that it bridges the gap between the natural and the spiritual. Everyone knows that a beautiful choir can be a sublime experience, and I’m here to explore the physics of why that is.
Before I begin, I’d like to point out that although there are countless species of animals that produce noise that could be considered musical in one sense or another, not a single one of them besides human beings do it in harmony. So, for instance, when a small group of people sing “Hello” in three-part harmony (or four-part, like these guys: https://www.youtube.com/watch?v=tf0BEx9ajgo), they are accomplishing a feat that no other singing animal can even come close to. Birds may sing beautifully, but they don’t do it together. Other animals make noise in concert with each other (such as coyotes howling), but even then, they don’t work out arrangements where one produces an A note, another a C#, and a third sings an E: a major triad. Yet not only are humans perfectly capable of that, but they’ve done it all over the globe for thousands of years. Why? The simplest answer is “It sounds good.” Now, when a chef tries to explain why certain types of food go together, s/he is venturing into a mystical, subjective realm where physics would provide little help. Luckily, when it comes to explain why certain musical notes go together, physics does answer the question.
Let’s begin with the concept of frequencies. If you sing the A below middle C, what you are doing, in physics terms, is making your vocal cords vibrate at 440 cycles per second, or 440 Hertz (abbreviated Hz). Calling that particular frequency “A” was an arbitrary decision, obviously, and without some help from an instrument or tuning fork, most of the population doesn’t even know what note they’ve sung2. Most people need help finding that A note, but once we’ve established that A, we can sing a simple rising scale: A, B, C, D, E, F, G and then H.
Uh, no. We don’t call the eighth note in the series H, we call it A again, although it’s clearly a different note. If we need to distinguish between the two A’s, we can say that they are an octave apart. That’s another way of saying that notes an octave apart are so similar that we can just call them by the same name3. Another thing you can say is that the two A notes are indisputably in harmony with each other. So if the A (or “do”) at the beginning of the ascending scale resonates at 440 Hertz, what is the frequency of the A an octave above it? The answer is exactly twice as high: 880 Hertz. If we went up another octave, that even higher A has a frequency of 1760 Hertz, and the octave above it, 3,520, then 7,040, then 14,080, and then we’ve gone out of the range of normal human hearing. All of those notes are “harmonious” with the original 440, and with each other. Another way of putting that is to say “Notes whose frequencies are in a 2-to-1 ratio are in harmony.”
What other notes are in “perfect” harmony with A? There are two. The most obvious is the fifth note of the scale, the E (or “sol”), and we call the interval between the A and the E a “fifth” interval (A-B-C-D-E, so E is the fifth note). No matter what note you begin with, the fifth interval above it is always in harmony with it. If the low A is 440 Hz, and the high A is 880 Hz, what could the frequency of that harmonious E be? The answer is 660 Hz. Another way of saying that is that a 3-to-2 ratio (660 Hz to 440 Hz) is in perfect harmony. And if we started at the E, and went up to the higher A, we say those notes form a “fourth” interval (E-F-G-A, so A becomes the fourth note up). 880 Hz (A) to 660 Hz (E) forms a perfect 4-to-3 ratio, and that is also in harmony. If you’re a singer and you want to find a part that goes with a note someone else is singing, a good way to do it is to go up 5 notes on the scale (including the one you start with), or go down 4 notes.
Another note that is in harmony with that A is the third note in a major scale, the C# (or “mi”). So if the low A is 440, and the fifth note is 660, any wild, stabbing guesses what the frequency of the harmonious third note would be? Yes, it’s 550 Hz, which means it forms a 5-to-4 ratio with the A. And if you get three people to sing “Hello” with one singing the A, another the C#, and the third person singing the E, you’ve created a “major triad.” You have also created a neat mathematical 6-to-5-to-4 ratio.
If you wanted slightly more exotic sounds, you could sing the seventh interval, the G. That’s what the fourth gentleman in that video (https://www.youtube.com/watch?v=tf0BEx9ajgo – the short-haired blond guy on the left) did. We call that the 7th note, or “ti”, and in the key of A, it resonates at 770 Hz (7-to-4 ratio)—sort of (but we’ll get to that later). Most people consider that one not quite as harmonious as the other notes, so we call that an “imperfect” harmony, as opposed to the E or the C#.
Another not-quite-as-harmonious-but-still-fits note is the minor third instead of a major third, which in the key of A means singing C instead of C#. And that happens to create a 6-to-5 ratio. For some reason, most people perceive major scales to be “happy” and minor scales to be “sad,” which is another way of saying that (for whatever reason) a 5-to-4 ratio sounds more cheerful to us than a 6-to-5 ratio. You may notice that the higher the numbers, the less likely it is that people will find those two numbers to be harmonious: 3-to-2 is definitely harmonious, 6-to-5 or 7-to-4, not so much. Yet we can still say those notes are in harmony, just a little less perfectly.
So what notes are not in harmony with each other? Well, the low A and the D go together (forming a nice 4-to-3 ratio), and the low A and the C# go together (5-to-4), which means that A “gets along well” with both the D and the C#. Does that mean that the D and the C# get along with each other? Not at all: D and C# clash horribly. The ratio between D and C# would have to be expressed as something like 53 to 50, and we use words like “discordant” to describe that relationship.
Then there’s another interval that a lot of people find very disturbing, so disturbing that it has been called “The Devil’s Tritone”: A to D# (also known as an “augmented fourth” or “diminished fifth”). Going back to at least 1725, that particular interval picked up the name “diabolus in musica” (the devil in music) and was considered “dangerous” by composers such as Telemann. Although Telemann deliberately avoided it for that reason, fast forward a few hundred years and you find musicians who used that interval precisely because it feels satanic. Take, for example, the band Black Sabbath, whose first album (released on Friday the 13th) is full of lyrics about witches and the occult. Musically, the first song on the album (also titled “Black Sabbath”) consists almost entirely of the notes G and C#, which is an example of that “evil” interval (mathematically, a 45-to-32 ratio):
https://www.youtube.com/watch?v=h4m79oGDT_IBut even some people consider those notes reasonably harmonious with each other, and those chords and intervals are still common enough that they have names. Are there notes that are so dis-harmonious that even lovers of discordant music wouldn’t want to hear them? Sure. All you have to do is detune your instrument a little bit, so, for instance, when you play a low A and a high A together, one is at 440 Hz and the other one is at 871 Hz instead of 880. Nobody likes to listen to that, so even heavy metal bands tune their guitars before they play. Instead of a nice, simple 2-to-1 ratio, you have a ratio that can only be expressed in fractions with very large numbers in it.
The first person to notice that harmony is all about mathematical ratios was Pythagoras, and he concluded that “the gods generally prefer small numbers.”4 And although it’s nice to hear it attributed to the gods in a discussion of what musical harmony can teach us about spirituality, it’s still not a very satisfying answer. For that we have to turn to a different kind of note that you can produce on stringed instruments.
When you play “normal” notes on a guitar, you do so by pressing down against the fretboard with one hand while plucking the string with the other. The fret in that case acts as the end of the string, so the pitch of the note is a result of the length of the string. This raises the question of where the guitar-maker placed those frets in the first place, and the answer has everything to do with those ratios we were talking about. But for now let’s talk about a different kind of note you can produce on a guitar without using any frets. Not uncoincidentally for an essay like this, those notes are called “harmonics:” https://www.youtube.com/watch?v=mZ6HKrFFM_4
(You have to wait until 3:26 before he actually plays one).
Harmonics are very clear notes that ring for a long time. The way you produce them is by gently resting your finger at just the right points along the string and plucking gently. One place is right above the octave marker. In that case, if you press your finger down on that fret and play a regular note, and then lift your finger up so it’s only resting lightly on the string and play a harmonic note, they will be the same note. If you took a measuring tape and measured where that fret is, you’d notice that it’s exactly half way along the string. In other words, if you press against that fret, you’re making the string half its usual length, which makes the frequency twice what it normally is. But when you make the harmonic, you’re not changing the length of the string. So what are you doing?
If you ever played jump rope as a child, it will help you understand. Imagine two children holding the ends of a jump rope. The simplest way for them to do it is to swing that rope so that it forms a simple arc, and another child can jump into it. In the same way, when you pluck a string, it forms an arc: widest in the middle, coming to a point at both ends. The string is very tight, so it’s too narrow to see, but that’s what’s happening. Back to the jump rope: if you’re tricky, you can get the rope to swing in a double arc.
(Image taken from http://music.stackexchange.com/questions/5489/why-do-harmonics-happen)
The trick with a jump rope is to coax the rope into forming two arcs instead of one. On a guitar string, it’s easy to do: all you do is rest your finger along the halfway point and the arc is forced to split in half.
As the image illustrates, you can also split the arc into thirds if you find the right place to rest your finger. Where is that spot on the A string on a guitar? At the fret right above the E note—which happens to be a third of the way along the length of the string. The only difference is, that E will be an octave higher than the E you’d get if you pressed against the fret at the same spot. And if we said that E resonates at 660 Hz, and octaves always mean double the frequency, then that higher harmonic E comes in at 1320 Hz. And that E forms a perfect 3-to-2 ratio with the first harmonic at 880 Hz, so it makes perfect sense that you get that E note by splitting the note into thirds instead of halves.
Then you can find another harmonic note at the quarter point along the length of the string, and another a fifth of the way along, and another a sixth, etc. (It’s very hard to find the exact points after that, because fingertips are too round and fleshy to find those spots with the precision required). This raises the question: when you pluck an open A string on a guitar, and it produces a note at 440 Hz, is it also producing those other higher notes? In other words, is that note resonating at 440 Hz and at 880 and at 1320 and lots of even higher frequencies?
The answer is yes. How can a note vibrate at 3 or 4 or 5 frequencies at once? Well, actually most musical instruments do that abundantly, and we call that the “tone” or “timbre” of the note. If you want just a pure 440 Hz tone, you can do that electronically by producing a simple “sine wave” (or using a tuning fork). Here’s what a simple sine wave at 440 Hz sounds like:
https://www.youtube.com/watch?v=teb64y-D2sA
Note that it’s a very boring sound, and not many people would consider that a musical instrument worth listening to. Instead we like instruments like violins:
https://www.youtube.com/watch?v=a3whHx331uE
Or guitars or saxophones or pianos or any of the full range of instruments humans have created. Note that, even though they could all play that same 440 frequency, almost everybody can tell the difference between a violin and a saxophone and a pipe organ and a distorted electric guitar. Why? Because all of those instruments produce lots and lots of overtones: higher frequencies produced by the instrument, that start somewhere above the fundamental tone (440 Hz), and may extend all the way to the upper range of human hearing (20,000 Hz) and beyond.5
That is why electric guitars have a “tone” knob in addition to volume knobs. You can play the same note, and twirl the tone knob and get markedly different sounds out of it. In the same way, you can play music on any stereo and change how it sounds by turning up the treble, turning down the bass, etc. If you turn the treble knob all the way up and the bass knob all the way down, you get a thin, twangy sound; if you turn the treble down and bass up, you get a muffled, heavy sound even though the instrument on the recording can be playing the exact same note all the way through. The treble and bass knobs don’t change the frequency of the note on the recording—it doesn’t change an A into a B flat or F sharp. So what does it do, exactly?
What it does is change the relative volume of the overtones—turning the volume of the low frequencies up and reducing the volume of the high ones. And you wouldn’t be able to do that if the instruments weren’t making lots of high overtones in the first place. If you played that simple sine wave on a stereo, and adjusted the treble and bass knobs, it wouldn’t make any difference to the sound at all.
Now, overtones are not exactly the same as harmonic notes, but there is a strong relationship between the two. Note, for example, that the Wikipedia page about “Overtones” (http://en.wikipedia.org/wiki/Overtone) devotes much of the space to discussing harmonics, and there is a chart representing the double-arc/triple-arc/quadruple-arc possibilities that I was talking about under the heading of harmonics. So, many of those overtones coincide with the harmonics. That means when you hit a plain old A note on a guitar, it’s not only producing a note that oscillates at 440 Hz, it’s also producing a note that oscillates at 880 and 1,320 and 1760 and 2,220, etc., etc., etc.
This may explain why those nice small ratios sound harmonic.
The way I’ve expressed it so far is: a low A (440) and a high A (880) are in perfect harmony because they form a 2-to-1 ratio. Another way of expressing it is: the reason they are in perfect harmony with each other is because they are both producing 1760 Hz—which, by the way, is well within the range of human hearing. The reason A (440) and E (660) are in harmony is because they both produce 1320. A (440) and C# (550) both produce overtones at 2,200. And the reason high ratios such as 45-to-32 (the devil’s tritone) or 53-to-50 (C# and D) don’t sound harmonious is because those frequencies don’t share any common ground until you get into extremely high ranges that no one can hear.
The More Accurate Version
But actually what I said does not accurately represent the way we make music these days. What I’ve been talking about is a system of ratios called “Just intonation” (http://en.wikipedia.org/wiki/Just_intonation), in which a C# really would be exactly 550 Hz. But musicians long ago discovered that this doesn’t really work very well. If you used this system, you could work out what all the notes on the A scale should be based on ratios alone. The second note (B) would form a 9-to-8 ratio with A, so it ought to be 495 Hz. The trouble comes when you try to switch key, and you eventually discover that a note like C# would need to be 550 Hz if you’re playing in A to get that 5-to-4 ratio, but it would have to be a higher frequency if you’re playing in F# in order to form a 3-to-2 ratio with that note, and a different frequency if you’re playing in D#, etc. People do like changing keys, either between songs or in the middle of a song. An instrument that can only play in one key is a very limited instrument.
So how do you make a piano that can play in any key? What you have to do is compromise on the frequency of the notes. Make the C# a little higher than it ought to be for one key, a little lower than it needs to be in a different key, and meet you in the middle. After many years of fine-tuning, we came up with a system in which A is, in fact, the only note that can be expressed as a whole number. Although E should be 660 Hz, it is in fact, 659.255 Hz. C# is much further off: 554.37 Hz instead of 550. And if G forms a seventh interval with A, it ought to be 770 Hz, but it’s nearly 14 cycles per second away from that: 783.991. Who calculated that to three decimal places? And if A and C# form a major third interval, that ought to be 1.25, but it is much closer to 1.26 (1.25993 to be exact).
What do we call this compromise version of musical frequencies? It has a name that I think teaches us something about the nature of music and the lessons it can provide about spiritual life. We call it the “equal temperament” system. Thanks to modern equipment, it is possible to make a synthesizer that doesn’t make these compromises, and all the notes are in precise ratios to each other. I’ve only heard one recording of such a piece (I believe it was by Terry Riley), and it sounded awful to my ears. I’m apparently not alone: David Byrne writes “When we hear music that is played in just intonation today, it sounds out of tune to us” (How Music Works, p 316).
If that sounds like it takes away from the mathematical purity of everything I was saying before, let me point out just how big a role compromise plays in music. Take, for example, vibrato. There are some musical styles that don’t incorporate or encourage vibrato, but most modern western styles do. One of the key components of training an opera singer, for example, is perfecting their vibrato. It’s essential for violinists as well. What is vibrato? It is the steady, rhythmic fluctuation in pitch of a note—and yes, pitch means the same thing as frequency. That means that when a trained soprano sings a high A, which ought to be 3,520 Hz, what she’s really doing is singing A, A flat, A, A sharp, A, A flat, A, A sharp. Why do we train singers to sing sharp-flat-sharp-flat-sharp-flat, instead of just training them to hit that 3,520 Hz on the nose?
There may be several aesthetic reasons, but one is practical in nature: it’s just impossible for her to hit 3,520 Hz dead on. Same with the violinist: the difference between an A and a A# might be millimeters apart, which means you are depending on a round, fleshy human finger being in exactly the right position along an unmarked piece of wood. The higher the frequency, the more impossible it is to be dead-on accurate. The frets on the low end of a bass guitar are spaced quite far apart, but on a higher pitched instrument like a ukulele, they’re very close together. I used to play a fretless bass guitar, and if my finger was off by a centimeter or two from the right position, no one would be bothered by that—but fretless lead guitars are unheard of because everyone would notice if they were off by a hair. In terms of the audience, then, when they hear a soprano singing sharp then flat then sharp then flat (in an intentional and controlled manner), they “hear” the correct note in the middle.
Or look at the example of unison singing. A minimalist choir might consist of one soprano, one alto, one tenor and one bass—but most people think that a larger choir sounds even better. So if you can get at least 2 or 3 sopranos, and a handful of altos, that sounds “richer” and “fuller.” Take it up to the level of the Mormon Tabernacle Choir (360 members), and it sounds amazing. And that’s not 360 people each singing different parts; it’s 90 sopranos, 90 altos, 90 tenors, and 90 basses—dozens and dozens of people singing the exact same part together.
How can you get all those people to sing at precisely the same pitch? Keep in mind, I’ve been talking about the low frequencies because they’re easier to discuss, but when a soprano sings an E flat above middle C, the frequency is 2,489.016. How is it possible that you can train people so well that they can all get their vocal cords to vibrate exactly 2,489.016 times per second?
The answer is: you don’t. Some will hit 2,482 Hz, others 2,503 Hz, and it still all works. In fact, the law of large numbers helps: the bigger the choir, the more likely it is that the sharp ones and the flat ones balance each other out, and collectively they do a marvelous job of approximating the right pitch. This is why pretty much any large choir will sound great6 .
And there are musical instruments that capitalize on slight variations as well. One that I’ve been playing since 1979 is a 12-string guitar. If you’re wondering, a 12-string guitar is tuned essentially the same way that a conventional 6-string guitar is, except that the strings are doubled. For the higher pitched notes, there’s two adjacent strings tuned to the same frequency; for the lower notes, the adjacent strings are an octave apart. Is it more difficult to play than a 6-string? Of course. So why do I play it? Because it sounds richer, fuller, nicer than a 6-string. On a microscopic level, where does that richness come from? From the fact that the two adjacent strings are almost exactly in tune with each other, but not quite (no matter how hard I try). It’s the imprecision that makes it sound good. Mandolins are the same way: four sets of doubled strings, and once again, the pleasing tone of a mandolin derives from the fact that those strings are never perfectly in tune with each other. One bagpipe alone can sound strident and harsh; a group of 20 bagpipes together can sound marvelous. Approximation sounds richer than precision.
This seems to contradict many of the lessons from the first half of this essay. If two singers whose notes form a nice 5:4 ratio are in harmony, but singers whose notes form a 53:50 ratio sound horrible together, how can two singers singing unison, one slightly flat and the other slightly sharp, possibly sound good together? Their ratio wouldn’t be a small ratio at all—it would be huge (a 201:200 ratio, perhaps). How can both principles—that precise ratios produce pleasing harmonies, and that approximation increases richness—be true?
I don’t know, but I think the take-away lesson is that when it comes to the full spectrum of frequencies that can possibly combine with another frequency, there are “zones” that sound great and zones that sound horrible, and they are spaced apart in interesting ways. Very close = nice and rich. A little bit further apart = unbearably horrible. Far enough away to form a 5-to-4 or 6-to-5 ratio = nice again. Far enough apart to make a 53-to-50 ratio = difficult, but tolerable to the right kind of listener. A little closer so that they form a 51-to-50 ratio = one just sounds out of tune with the other, which is unpleasant. A little closer still, perhaps 101-to-100 = now we’re back to satisfying richness again.
The Role of Discord
Does all this imply that good music should have no discord in it; that every note in every song should form a nice small mathematical ratio with every other note? Well, you’d better not inform Beethoven, or Mozart, or Jimi Hendrix, or pretty much any other composer, because they all deliberately introduce discord into their music. A little dis-harmony makes things interesting. Take, for instance, the second movement of Beethoven’s 7th symphony:
http://www.youtube.com/watch?v=mgHxmAsINDk
Note how many bars in that piece begin with a note that “slides into place” after a beat or two. When I say “slide into place,” what I mean is that the bar begins with a chord that is not one of those “perfect” harmonies. I don’t have the score, or sufficient knowledge of classical composition to be able to tell you all the details, but I can hear lots of “major 7th” chords in there. A major 7th in the key of A (which Beethoven’s 7th happens to be in) means a chord with an A (440 Hz) and a G# (830.61 Hz), which obviously don’t form a small ratio. And then that G# slides into an A (880 Hz) and everything sounds harmonious again. It’s a way of introducing tension into the music, and tension makes it much more interesting as long as it’s resolved. So one of the techniques that good composers perfect is how to create tension and resolution. Often it’s done in a way that the audience can predict—they can sense that it’s headed somewhere harmonious, but it’s not there yet, so the discord puts them on the edge of their seats for just a moment, anticipating that resolution.
Some famous pieces begin with discord, such as Mendelssohn’s wedding march, a song that people usually hear in a situation where no one wants to think about discord and tension. But it’s in there!
http://www.youtube.com/watch?v=8uSwpAvpbDU
Looking at the sheet music helps too, if you can read music (and perhaps even if you can’t). The top line of the score (the first 5 bars) are just building up a nice, harmonious major triad chord, but the audience kinda knows that nothing has “happened” yet. Then we hear the first big chord (in the video, at 0:21), which you can see at the beginning of the second line (I blew it up a little bigger on the right). In case you never noticed before, that’s a weird chord. What makes it “weird” is that it has an E in it (659.255 Hz) and a F# right next to it (739.998 Hz) in the lower octave, and the same thing an octave above (1318.51 Hz and 1479.976 H). Even if we simplify that to 660 Hz and 740 Hz, you can tell that’s not one of those note combinations that go well together (a 33-to-37 ratio). But nobody says “That’s a terrible way to start a song about people joining in wedded bliss” because the very next chord is a nice, perfectly harmonious B major chord and all is forgiven. And that brief disharmony is what makes the song instantly recognizable, and a much more interesting song than if it had been all perfect major chords throughout.
It reminds me of something Alfred Hitchcock, the “master of suspense,” said about how to put movie audiences on the edge of their seats. The way you do it, he explained, is to put characters in a room eating breakfast, and the audience knows that there’s a ticking bomb underneath one of their chairs. The characters in the scene might be having a most boring, mundane conversation imaginable, but the audience will be held in a state of tension until the scene is resolved. The resolution might take the form of the bomb going off (before or after the characters have left), or someone discovering and disposing of the bomb. But the one thing you can’t do, Hitchcock knew, is to just leave the bomb ticking forever. Some daring filmmakers have ended the movie with the bomb still ticking, so to speak, but the only reason they do that is to force the audience members to write their own ending7. The popularity of Hitchcock as a filmmaker, and suspense as a genre, shows that audiences can tolerate a lot of tension—but they’ll only put up with it for the “payoff” of the resolution.
8 Spiritual Lessons
One of the beauties of a philosophy that relies on metaphor, as Swedenborgianism does, is that there is a lot of room for different people to draw their own lessons. What you get out of all this may be entirely different from what I get. But I’ll take a minute and recap the lessons I draw:
- Harmony is about difference. The way to achieve a rich and satisfying and beautiful life is to get along with people who are different from you. It has been often speculated that if you were to ever meet yourself (or, say, an exact clone), the two “yous” wouldn’t get along. There is also a widely held belief that the people you have the most trouble getting along with are the ones who are just like you. I’ve heard these ideas repeated many times over the years, but I’ve never heard a detailed explanation of why that might be. Could it be that it’s because the other “you” is just enough out of tune with your frequency that you clash? You look at someone else and say, “I’m trying to be a different person than I am right now, and you look a lot like that person. But the way you’re trying to live your life is just far enough from the way I do it that it seems wrong.”
- As a corollary, I could say: “Exact sameness is boring.” I own a digital multi-track recording unit, most recently used to record a CD with my church band, Joyful Noise. I acted as engineer and producer for the CD, “Open Door.” Because the recording unit is digital, it’s possible to do things like cut and paste a track. But it wouldn’t improve the music any, because two identical tracks would sound just like a single track. When recording “Open Door,” I often asked the singers to sing their parts again, and kept both tracks. It sounded even better when they did that, because they did it slightly differently the second time.
- When you really “click” with another person, one possible reason is that, despite your differences (you are singing different notes), you are both producing the same high overtones. You may have to rise up to a higher frequency, but at some level, you’re singing the same note.
- When you are having trouble getting along with someone, one strategy to try to overcome the difficulty is to actively try to seek out those high frequencies that you may share. They might be beyond the realm of your awareness, but they’re there. If you come from different ends of the political spectrum, you may think you share no values or goals—but if you look harder, you can probably find them. If you look at someone who has lived a completely different life than you have, it may be rational to assume that you share nothing in common with that person. You are a white middle class female who grew up in a religious context and have never been exposed to violence; the other person is a male homeless Colombian meth addict whose parents were killed at an early age and who never went to school. How can you possibly understand each other? By rising up a few levels of abstraction until you find a few shared universal emotional responses.
- Harmony is inherently relative. There is no such thing as a disharmonious note. Although it may not fit on the arbitrarily decided frequencies of the notes in the modern scale, any note is valid and legitimate by itself—and in fact, only 1 in 10,000 people will know if a note fits into those specific frequency slots or not. Harmony is about how notes fit together. That means, if you look at another human being and have a tendency to say “They are a bad person,” on a musical level it makes more sense to say “Our notes don’t fit together.” As a corollary:
- If you can’t change the note another person is singing, change your own. You can turn a “sad” minor chord into a “happy” major chord by altering the pitch of your own note.
- The action is in the high frequencies, and even the lowest notes produce high overtones (on anything but a sine-wave generator). In other words, “tone matters.” Sometimes it’s not what you are doing in life (the actions are the fundamental tones), it’s how you’re doing it (the overtones).
- A little conflict and tension makes the world interesting, as long as it doesn’t last forever. When it’s resolved, it feels even better than if there had been no tension at all.
Footnotes
1For examples, see Secrets of Heaven 687 and Marriage Love 273.
2For an extensive discussion of perfect pitch and the minority of the population who does possess that trait (estimated to be 1 in 10,000), see the charmingly titled chapter “Papa Blows His Nose in G: Absolute Pitch” from Oliver Sacks’ Musicophilia (2007).
3Another way to express the same concept is using the do-re-mi system you may remember from the “Sound of Music” song. A scale is represented by the names do, re, mi, fa, sol, la, ti, and do again. It shares the feature of calling the note at the top of the scale the same as the note at the bottom, but has the advantage that you can use it for a scale starting on any note, such as the F# scale. If you use the names of the actual (fixed) notes in order to represent the scale, you’d have to remember which of the notes has sharps on it (F#, G# A#, B, C#, D#, F, F#). In the do-re-mi system, you can just call the third note “mi” and don’t have to figure out if it’s an A or an A#. A choir can sing a whole song in perfect harmony using the do-re-mi system and still not even know what scale they just sang it in.
4From David Byrne’s 2012 book How Music Works, p 305.
5If you’re curious about how a guitar can produce those higher tones, think about this. One kind of guitar string is called a “round wound” string, and it’s what I have on my bass guitar. It consists of one “core” wire, and then another wire tightly coiled around the core one. That makes the string very “bumpy,” and if you drag a guitar pick along the length of that string, it will produce lots of screeching sounds that you won’t get on a “flatwound” string that consists only of one smooth core wire. But even if you don’t drag your pick along it, when you pluck a note on that round-wound string, the core wire produces the lowest note, but all those tiny ridges up and down the length of the string also produce tiny little sound waves of their own. With a violin, the bumpiness of the string interacts with the bumpiness of the bow, and all the texture along both of those surfaces creates a very complex sound. With a saxophone, the original sound is produced by the reed, which is a piece of split bamboo that under a microscope would look very bumpy and ridgy. Then that sound travels through the body of the saxophone, where it bounces off the walls and interacts with the brass, and generally has a long complex journey before it comes out of the mouth of the sax and into the air. In general, humans seem to like instruments that produce lots of complex overtones a lot more than we like simple instruments that sound more like sine waves.
6The bigger trick, when it comes to large choirs sounding good, is being rhythmically precise. If they start and end the notes at exactly the same time, and pronounce them all the same way, that will make a bigger difference in whether the choir sounds professional than whether they’re all singing exactly on key.
7The most notorious recent example was the finale of the HBO series “The Sopranos,” where audiences never knew if protagonist Tony Soprano had been killed or not. Given the level of audience outrage, this was a risky choice for the director to make.
Jeremy Rose
Jeremy is a senior lecturer in Communication Studies at the University of Minnesota, and the vice president of the board of the Virginia Street Swedenborgian Church in St. Paul. He is also a lifelong musician. His recent CDs include his own “Footprints on the Wall,” and a collection of songs by the church band Joyful Noise, entitled “Open Door.” On both of those recordings, he acted as composer, performer, and producer.