These notes are called the higher harmonics of the fundamental. Here is an example from nature. The Hermit Thrush Catharus guttatus, fairly common in eastern North America, typically sings phrases where one long note is followed by a sequence of more rapid ones. Examine the sonogram record of this particular phrase from this particular bird. Sonogram of Hermit Thrush song.
Time intervals are in seconds.
The first note of the Hermit Thrush's song with its higher harmonics written as separate notes on a musical staff. The bird sings 4 octaves higher than scored. The higher harmonics give a set of pitches that are naturally related to the fundamental. These pitches can then be heard by themselves. Sonogram of Song Sparrow song.