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 two notes get farther apart in sound, the vibration gets faster. When they reach the exact tone, the vibration slows, and finally stops (we can't detect it anymore, or consonance). Anything else that makes the vibration faster is flat or sharp.
Listen to the difference in tone, such as dropping below the note (flat), or going above the note (sharp). Drop your tone a little, or raise it a little, and hear how you get away 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.
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. This is a quality of chords; the notes that make up the chord complement (sync with) each others' sound waves
Now that you can tell if you're sharp or flat, play two different notes on your own instrument, separately. Notice if one is sharp or flat in its own sound wave, compared to the other note. Does one note sound like it's complementing the other perfectly? Does it sound flat? Does it sound sharp?
Learning the proper distances between sounds, keeps chords and improvisational melodies in tune. Each will be a sound wave supporter.
You'll learn the boundaries of Major, minor, diminished, and Augmented intervals, and help yourself predict any key change in advance. Tones are no longer a jumble in your head. They actually work together to inspire, according to a reference point already in place, such as a root or key.
As in drawing, you can make a line, but the line's shape, angle, and length only make sense in the reference of another line. A tone's pitch, loudness, duration, quality, timbre, and octave has meaning within another tone. As you notice the subtle attributes of notes, you will feel more confident about creating art from more powerful, individual tools of sound.
The next page harmonizes with this one, to explain properties of sound waves.