Hold a single tone on a piano, or with:
Simultaneously play the same tone on your own instrument (if singing, match this tone as best you can). Listen to both tones, and see if you can detect differences. Then listen to the similarities. A new vibration occurs! Play or sing softer than the other tone, to better hear this phenomenon.
While the tone plays, vary your own tone, and attempt to make this new, third vibration slow, or stop. It doesn't take much!
We're attempting to match a sound vibration exactly. This will train the ear to know if we're sharp (higher in sound), or flat (lower in sound). As the same notes get farther apart in sound, the new vibration gets faster.
Conversely, when they reach the exact tone, the vibration slows, and finally stops (we can't detect it anymore, or consonance). Any shift in tone that makes this vibration faster is flat or sharp (out of tune).
Drop or raise your tone a little, and hear the difference from the original tone. The farther you get away, the more dissonant, or uncomfortable the two sounds become. Their sound waves start interfering, and the result is noise, or at least dissonance.
Furthermore, two notes played a half step apart won't sound good. Their sound waves interrupt, as they're not far apart enough to become distinct and complement one another.
Now that you can tell if you're sharp or flat, play two different notes on your own instrument, separately. Compare each notes' own sound wave for sharpness or flatness. Are they complementing each other perfectly?
Learning the proper distances between notes, keeps chords and melodies in tune. Each will be a sound wave supporter.
We hear the boundaries of Major, minor, diminished, and Augmented intervals, and predict any key change in advance. Tones are no longer a jumble in our head. They work together to inspire, according to a reference point, like a root, key, interval, or sound wave.
As in drawing, a line's shape, angle, and length only make sense within reference to another line. In the same way, a tone's pitch and octave has meaning within another tone. Hearing these subtle note attributes inspires us to create art from more powerful, individual tools of sound.
The next page harmonizes with this one, to explain properties of sound waves.