The notes from a musical instrument can vary in three ways – pitch, loudness and quality or tone.
The pitch of a note depends only on the frequency of the note. Higher pitched notes have higher frequencies so there are more vibrations per second. This means also theat they have shorter wavelengths and are typically produced on smaller instruments.
The loudness of a note depends only on the amplitude. Louder notes have bigger amplitudes and require more energy.
The quality or tone of a note depends on a range of factors. Very important is the instrument that produces it. A violin and a piano playing the same note – having the same pitch and amplitude – produce notes that sound different because the notes differ in quality. The soundwaves produced on each instrument differ in shape and this makes them sound different. This is because each note is actually a combination of many sounds with different frequencies and amplitudes. Each constituent of a note, called a harmonic, change the shape of the sound wave associated with the note. Because each instrument produces a different set of harmonics, each note produced on different instruments sounds different. All the notes shown below have the same frequency and amplitude but different waveforms, so different tone or quality.
Modern electronic synthesisers allow us to select the frequencies to mix together. \We can select the frequencies to mimic other musical instruments or create entirely new sounds.