The term "multiphonics" describes the technique of playing two or more pitches simultaneously on an instrument that is designed to produce only one tone at a time, or with the voice. Jazz saxophonist John Coltrane was one of the more well-known pioneers of this technique for saxophone and fingering systems for producing multiphonics have been developed for most wind instruments - oboe, flute, trumpet, etc.
Obviously, the harmonica differs from most wind instruments in that it is capable of playing multiple pitches simultaneously by virtue of having multiple reeds. However, the diatonic harmonica is also capable of something that may be loosely termed multiphonics, allowing additional note combinations that are not possible by more common playing techniques.
As you are probably aware, each hole in the typical Richter harmonica (single reed diatonic, or "blues harp") has a pair of reeds - one activated by blowing, the other by drawing. You may also know that when you play a bend, the two reeds interact to produce a pitch somewhere in between the natural pitch of each reed and when you play an overblow, the sound you hear is actually coming from the draw reed, sounding somewhat higher than that reed's usual pitch. (For more detailed information about the physics behind all this stuff, you may want to read this paper in .pdf format..)
I remember some years ago, trying in my ignorance to bend 6 blow on an A harp (nobody had explained to me that you can't get a typical blues-style bend on this note, as only the higher note in each hole can be bent). I was hoping to lower the E down to an Eb. That didn't happen, but I got something else instead - a really wild raucous noise that sounded great in a down and dirty blues. It was some time later that I found out that what I was hearing was the natural pitch of the 6 blow reed (in the case of my A harp, the note E), plus the overblow note coming from the 6 draw reed sounding about a semitone sharp (in this case, the note G). I used to use this sound quite a bit in my playing, until I learned about what overblows were and started working on getting nice clean pure notes from my overblows.
However, there are times when it can be quite useful to sound the natural blow note and the overblow at the same time, as this can often allow you to play note combinations that are otherwise unobtainable.
For example, if you play the blow note and the overblow in hole 1 of a C harp (which can often be somewhat easier than producing a clean overblow from this hole!), you get the notes C and Eb:
This can be used to suggest a Cm chord, a F7 chord, an Ab major chord, etc. Obviously using the same technique in hole 4 gives you the same notes an octave higher.
If you play the blow note and the overblow in hole 2 of a C harp, you get the notes E and G#:
This can be used to suggest an E major chord, a C# minor chord, etc.
If you play the blow note and the overblow in hole 6 of a C harp, you get the notes G and Bb:
This can be used to suggest a Gm chord, a C7 chord, a G7#9 chord, etc. Applying this technique to alternate tunings can give you many other possibilities
Again, these sounds can be somewhat rough and often tend to come out rather flat, so you may need to exercise some discretion in their use.
Similar sounds can also be produced whilst drawing, sounding a draw bend at the same time as the unbent draw note. Here is the lowest draw bend in hole 3 sounded along with the unbent 3 draw.
In this example it is played on a C harp, so the notes are G#/Ab and B, which could be used to suggest an E chord, or an Abm. The same technique can be used as a tonal or textural effect rather than as a harmonic device, adding a raucous edge to a note. Playing the 2 draw bend at the same time as the unbent 2 draw adds a dissonant attack which can be accentuated by amplification:
This can also be done on 1 draw and 4 draw and as the bent note is only a semitone lower than the unbent note this makes the effect even more dissonant, however I find it considerably harder to do than on holes 2 and 3.
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