#1: A Fresh Start: Experience Harmony

Our journey together will span a host of topics: harmonics (aka overtones, partials), pure tones (aka sine waves), traditional harmony (tonic, dominant, voice leading, etc.), psychology, and a small touch of math and physics. I will assume a minimal understanding of music notation, but much will be self-explanatory, even if you don’t read music well.

I’d love to start at the beginning, but the problem with that route is that would take a long while to get to somewhere practical. This would be fine if I were teaching a semester long course, but for a drop-by-as-you-please blog, I feel I need to start towards the end and work our way backwards.

So, let’s start with a fun tuning exercise. This will require you to hum or sing along, so be prepared!


We’re going to just experience harmony. (I sometimes get caught doing this exercise when I brush my teeth.) Below is a recording of my electric toothbrush. Play the loop (speakers or headphone, or if your toothbrush sounds similar, it’s even better to use that!), and start humming or otherwise vocalize against the drone.

Sonic Toothbrush drone on C4 (Middle C) — Higher voices use this one!
Sonic Toothbrush drone on C3 — Lower voices use this one!

Now try the following:

  1. Match the pitch you hear as closely as you can.
  2. Now slide up above the pitch just a little, then down below the pitch a little. Note how it feels when your pitch “rubs” against the drone’s pitch.
  3. Now slide either up or down (choose one, whichever is more comfortable for you) much further than before. Do you feel the spots where your pitch “blends” more than it “rubs”?
  4. Keep going and find as many of “blending” spots as you can. If you find several, notice how they are similar to the other “blending” spots, but also notice how they differ.
  5. Find as many “rubbing” spots as you can. Make note of how these are similar and/or different from other “rubbing” spots.
  6. Sing a tune against the drone. Include notes that “blend” against the drone, but also try to include notes that “rub” against the drone.

You’ve just experienced harmony! It is a real phenomenon that you can feel—your voice interacting with some other pitch.


You probably found multiple “spots” where your voice “blends” with the drone, these are the basis of our musical notes. Most likely, you found the following music intervals (I’m listing which are most prevalent, not which order you encountered them): unison, octave, perfect fifth, perfect fourth, major third, and perhaps more, if you’re particularly attuned (pun intended) or have musical training.

Here’s a quick diagram hopefully analogous to what you just experienced:

The places that “blend” with the drone are some of the most basic musical intervals, and are found in almost all musics around the world—these intervals are not “inventions” so much as “discoveries” of physical realities. Note that there’s nothing “wrong” with the places that “rub”, either—exactly what pitches are useful in what contexts are aesthetic choices made by a composer, and heavily influenced by culture. But that’s another blog post!

Next Steps

We will spend much time on this blog further exploring the “blend” and “rub” phenomena, and I strongly encourage you to keep exploring these phenomena on your own. Keep humming! If you play an instrument, hum along against that, or play your instrument against the drone. Experience!

> NEXT: #2: Harmonics: The Building Blocks of Pitch

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