Ever noticed when a key person is missing from a meeting or some sort of social function how their absence is almost more palpable than their presence would have been? The fact that they’re not present may be foremost in everyone’s mind. Where is he? Why hasn’t she come?
The same sort of thing occurs in communication - at times, what’s not said, what’s left out, is just as important as what is said.
Well, music has absences, too, which leave us pondering and wondering. In fact, the music sound wave itself is missing a key player … or is it? Is it missing by design? Is it supposed to be missing so its presence is more felt when it shows up? These are questions I ask myself and the only thing I’m certain of is that it’s a mystery!
So what is this mysterious missing element?
Let’s look a little more closely at the harmonic series to find out!
The harmonic series is the set of overtones or harmonics that inherently accompany every music sound wave when a note is struck on a musical instrument - we’ve already briefly examined some of this in previous posts. These overtones are virtually the same for every instrument and every note. Meaning, they occur in the same order at the same intervals. For example, the first harmonic, which is the note that was struck, also called the fundamental, is followed by the same note, one octave higher. This is the 1st overtone, or 2nd harmonic. The next harmonic is a Perfect 5th higher, the one after that is another octave and so on. For example, in a C sound wave it would be: C C G C
But what else is in there? I’ve heard it said that these harmonics are endless, but, thankfully, our search will be limited to a 4-octave range of the fundamental!
Here are all the notes produced by the overtones in the sound wave when we hit C2 on the piano (the 2nd lowest C on the piano) as seen above:
C C G C E G B flat C D E F sharp G A B flat B C
Who'd have thought so much was going on in the sound wave! Here's what it sounds like, if we were to play all those notes in order!
Go ahead and play the harmonic series on your piano! Add a little improv to make it more fun!
Now, let's take another look at the notes listed above. Can spot what’s missing? Did you notice that we have all the notes of the C major scale … except one:
C (1st, 2nd, 4th, 8th and 16th harmonics)
D (9th harmonic)
E (5th and 10th harmonics)
G (3rd, 6th, and 12th harmonics)
A (13th harmonic)
B (15th harmonic)
All of the notes of the C major scale except F! We have an F sharp at the 11th harmonic, but no F natural. Amazing! Let's analyze "F" for a moment!
F is the 4th degree of the C major scale, and the journey from C to F covers the distance of, or interval of, a Perfect 4th, which is comprised of 5 half-steps
Travelling backwards, from C to F, it forms the interval of a Perfect 5th, and this is why it is also called the subdominant, because it's found below the C, unlike G, the dominant of C, which is both a Perfect 5th above and actually present in the sound wave. (Why they are called "perfect" is another study all in itself, but one reason is that their frequency ratios are more closely associated with the tonic and somehow more mathematically pleasing.)
Even though the 4th degree of the scale does not appear in the sound wave, the interval of a Perfect 4th is strongly present within the wave- for example, in the distance from G to C
Although the Perfect 4th above and the subdominant below the tonic are not in the sound wave, at least not at a frequency detectable to our ears, they impose themselves upon the sound wave when played
C is the dominant of the F major scale because it is a Perfect 5th from F. Every time an F is struck, it creates the following notes, in keeping with the harmonic series: F F C F A C etc, forging a strong bond between the F and C that imposes itself upon the C sound wave
It is this strong bond leading back and forth from F to C imposing itself upon the C sound wave that allows it to function as a cadence. A cadence is a harmonic pattern that produces a sense of conclusion and is often used at the end of a musical phrase and almost always at the end of a piece. The strongest of these cadences is the dominant to tonic, as that is inherent in the sound wave itself of the tonic, but one can see why the subdominant to tonic, called a plagal cadence, is also common, as it has strong ties to the tonic which impose upon the musical journey.
If you're lost by now, don't fret! It's a bit mind-boggling! Mysteries aren't easy to solve! As I ponder the glaringly absent 4th degree from the sound wave, I wonder if its presence is more appreciated or obvious when it is called upon and struck, since it resonates with the tonic and seals itself as an integral part of the journey the tonic sound wave is creating.
Equally fascinating to consider is what its impact might be were it present in the tonic sound wave, in this case, C. Would its own strong tonic (F)-dominant (C)-tonic (F) relationship interfere with, weaken or obscure the tonic (C)-dominant (G)-tonic (C) relationship already present in the C sound wave? Would it pull our ears in competing directions? Remember, the role of the dominant is to prepare your ear to return to the tonic. Or does this play out anyways on some level and add a depth to the whole scalar journey that we are not fully cognizant of?
One thing's for certain: the Creator of the sound wave - He knows exactly why He left it out! For me, I'm content to continue pondering the wonder of it all! Maybe that's the point!
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