[Harp-L] Ghost Notes and Equal Temperament

["John F. Potts" <hvyj@xxxxxxx>]

Jonathan Ross writes:

"A difference tone is produced whenever two or more intervals are
played simultaneously.  Any interval other than the octave on a 12-
tone equal temperament (12TET) instrument will produce difference
tones which have noticeable beats against the notes being played.
The layout of the harmonica and what two non-unison notes are played
will effect the degree of beating, but not whether beats exist and
thus a degree of dissonance."

This is unquestionably true.  BUT, it is my experience  that playing  
notes in NON ADJACENT HOLES generates significantly less beating than  
playing chords (or adjacent hole double stops) on an ET harp.  There  
appears to be some support for this in the summary calculations found  
on Pat Missin's web site.

Per Pat Missin:
"If you play a 12TET major triad, the difference tone generated by  
the root and the major third [ADJACENT HOLES] is more than 70 cents  
sharper than the pitch two octaves below the root of the chord; the  
difference tone generated by the major third and the fifth [ADJACENT  
HOLES] is more than 80 cents flatter than the pitch two octaves below  
the root of the chord; the difference tone generated by the root and  
the fifth [NON ADJACENT HOLES] isn't quite so bad, being only about 6  
cents flatter than the pitch of the note one octave below the root of  
the chord."

Moral of the story (per me);  If this is more or less true for notes  
all non adjacent holes, split intervals don't beat anywhere near as  
much as chords or adjacent double stops will on an ET harp.  I mean,  
can most people actually hear a difference of 6 cents in a live  
performance situation?

Jonathan Ross writes:

"I wouldn't be surprised if it is the omission of the third in the
chord itself that you are finding more pleasant, rather than the
addition of the difference tone.  This is particularly true of major
thirds in 12TET which tend to sound harsher than minor thirds (for
whatever reason)."

Probably sometimes, but not necessarily all the time, because i am  
not always blocking out the 3d.  For example, the 3 draw/6 draw split  
in second position plays the 3d and the 9th while blocking out the 5  
and 7b.  This may be an inversion, because i am omitting the root,  
but the 3d is there and does not beat or sound harsh.  Also, the  
ghost notes generated by split intervals always deepen, fatten and  
sweeten the quality of the tone, no mater which particular split  
interval is being played.  And this remains true even if one is  
playing octaves, although octaves certainly sound more powerful than   
"sweet."

I do not think any single factor involved in the split interval/ghost  
note technique can be viewed in isolation, because the ghost notes  
occur simultaneously with whatever is actually being played. So  
whatever is going on, it is just not one thing or the other.  It is a  
symbiosis.  And it works.

JP