the higher the note, the faster the string vibrates. an a above middle c (the violinist’s a string) vibrates at 440hz (440 times per second). this is the “fundamental” or “first harmonic”. the second harmonic vibrates twice as fast (ratio 2:1): 880hz. this gives an a an octave higher. the third harmonic will give a ratio 3:2. this will be an e (an octave and a fifth above the fundamental). the higher the harmonic the quieter it is, but the ratio is always a whole number (not a fraction).