[Harp-L] Difference tones [was Re: can I blame the gear--please?]

["Tim Moyer" <wmharps@xxxxxxxxxxxxxxxxxxxx>]

Doug Schroer wrote:
> Joe's statement about: "two notes that are justly tuned make 
> another note that is lower in pitch and also in tune."  I haven't 
> checked this on Pat Missin's site yet, though I have read other 
> parts.  While I have noticed the fullness of chords on justly 
> tuned harps, I have not noticed anything I would have described as 
> a lower pitched tone.  I will acknowledge that a just tuned chord 
> is a full sound.  

It is a simple matter of physics that when two notes are played 
simultaneously a third note is generated at the frequency of the 
difference of the two pitches.  This is called a difference tone.  
One of the principles on which just intonation is based is 
generating resonant difference tones.  

For example, if I tune the 1 blow on an A harp to precisely 440 
hertz, then tune the 3 blow to a major 5th, with the E at 
the "equal" interval of 659.26 hertz, the differnce between the two 
frequencies is 219.26 hertz, which is a slightly flat A note and 
octave below the root.  However, if I raise the pitch of the E 
slightly to 660 hertz -- an adjustment of about 2 cents -- the 
difference tone is now produced at 220 hertz, a perfect octave below 
the root tone.  

It does take somewhat of a practiced ear to isolate the difference 
tone, but it's not too difficult to hear the "beats" generated by 
the dissonance between a difference tone that's slightly off from 
it's octave.  

-tim

Tim Moyer
Working Man's Harps
http://www.workingmansharps.com/