Additional notes that are being played besides picked ones

Question

I was experimenting with sound analysis lately and from what I see when I plot spectral data of an audio file is that apart from notes that were actually plucked there are some other notes with quite high local amplitude.
For example I have a sample where D major chord is played with some nasty distortion. After looking onto the spectral plot I can observe a note D, F# and A as expected. But as I go higher some other notes have higher amplitude than threshold, one of those is E.
So, the question is: is it a normal thing that when I play D major the note E could be observed on a spectral plot but not heard or that's just error during recording ?
Additional info:

• that is not a DC component
• audio is in high quality, therefore there are almost no background noise
• the note E has some harmonics further in spectrum

Answer 1

Most natural instruments will produce a tone which contains frequencies that are near-multiples of the tone; for some instruments such as the clarinet most such frequencies will be near odd multiples (3x, 5x, 7x, etc.) while other instruments will produce a mixture of even and odd multiples.

For any two frequencies x and y which are present in a signal, harmonic distortion may add additional frequencies Nx+My for any two integers M and N (generally the larger M and N, the less of that frequency will generally be present). For most kinds of chord using equal temperament, this produces a very nasty sound because a major third has a frequency ratio of about 5.04:4, meaning that a distorted version of the chord will contain significant content at frequencies like 4(5.04)-4(4), i.e. 4.16, or 6(4)-4(5.04), i.e. 3.84, thus yielding a blurry mess. Power chords have frequencies concentrated in 2x/3x/4x ratios and multiples thereof, meaning most of the harmonic content will be concentrated at multiples of a frequency an octave below the bottom note.

Depending upon the nature of the distortion, it might be possible to do spectral analysis by applying Foorier transforms only to the portions of the source waveforms which don't appear to be distorted, computing how the exclusion of other parts of the waveform would affect the results, and then reversing those effects, but the reliability of that approach would depend upon the nature of the distortion involved and the original frequency content.

Answer 2

The other notes are not being PLAYED. But the sound of an instrument depends on several things - largely the characteristics of the initial attack of the note, but also the less complex waveform of the sustained note. (You might be surprised at the effect of splicing the attack of one instrument onto the sustain of another, and which makes most difference. A whole system of "hybrid synthesis" with a sampled attack and synthesised sustain exploits this.) Sometimes an upper harmonic of a note can feature strongly in a spectral analysis. Your ear, having locked into the pitch of the note's attack may not hear it as strongly as the microphone and computer does. This is what's happening here I think.