Re: [Harp-L] Re: Just Intonation and Difference Tones

["Dave Murray" <dlmurray@xxxxxxxxxxxxx>]

From: "jazmaan@xxxxxxxxxxxxxx" <dmf273@xxxxxxxxx>
> My original post which began this thread was asking about DIFFERENCE 
> TONES.  I said "correct me if
> I'm wrong" but doesn't a Just Intoned harp produce more pleasing 
> difference tones than an equal
> temp harp?

Any time you mix two frequencies in something that acts as a mixer you get 
the two original frequencies and two new frequencies, the sum and the 
difference. So if you use the link to the spreadsheet that I sent, you can 
see the frequencies in Hz for the notes with the different tunings.

I used 443 Hz A with 19 limit just the 2-3-4 draw on a C harp and got 
G=395.12 Hz, B=494.38 Hz, and D=592.70 Hz. So the differences are:

B4 - G4 (494.38 - 395.12) = G2 (99.26 Hz)
D5 - B4 (592.70 - 494.38) = G2 (98.32 Hz)

With ET  the 2-3-4 draw on a C harp are G=394.67 Hz, B=497.25 Hz, and 
D=591.33 Hz. So the differences are:

B4 - G4 (497.25 - 394.67) = G#2 (102.58 Hz)
D5 - B4 (591.33 - 497.25) = F##2 (94.08 Hz)

So the difference frequencies with the just tuning are close enough to the 
chord root (a couple octaves down) while the difference frequencies of the 
ET chords are a bit too sharp and/or flat to sound right. The difference 
frequency's sweetness/harshness is all about where it falls with respect to 
chord intervals.

Peace and music,
Dave