Tone and timbre are functions of the amplitude of the sound waves that construct the note. That is to say, any note is combined of many vibrations of different pitches. Some of these vibrations are louder than others, and the different combinations of these sounds produce different sounds. A way to understand this easily is with the vowels we use when we speak. If you sing any note and change the vowel that you are singing, then you will hear the vibrations that construct the note changing the sound of the vowel. Listen closely, and you will hear a higher pitched vibration moving up and down within the note you are singing.

The vibrations that construct notes are highly organized. The root vibration is the strongest and most audible. All of the other vibrations are derived from that pitch. The next pitch, which is double the root vibration (2:1) sounds one octave higher. If you triple the root pitch (3:1), you will hear a note an octave and a fifth higher. This series continues with a pitch two octaves above (4:1), two octaves and a third (5:1), two octaves and a fifth (6:1), two octaves and a seventh (7:1), and three octaves (8:1). If you were to start on 'A,' the series would be A,A,E,A,C#,E,G,A.

Producing a good tone requires balancing the vibrations that construct the note that you are playing. If the root is the strongest vibration, and each subsequent vibration is musically balanced (meaning just a little softer) with the lower vibrations, then the note will sound full and warm.