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

["Dave Murray" <dlmurray@xxxxxxxxxxxxx>]

> Sorry if i'm being repetitive, but..........
>   What is the difference in the sound that is produced between 7  limit JI 
> and 19 limit JI? 

There is a spreadsheet at http://trinity.psnw.com/~dlmurray/data/Tuning.xls that lets you look at the beat frequency of the intervals for the chords with various tunings. The lower the beat frequency, the less harsh the chord. The examples tab gives you some numbers to plug in for different tunings. 

For a C harp, assuming that the G and C (2nd pos I/IV) chords are the ones that you care about (use a proportional font like courier new to line up the following):

I  1-3   3-5   5-7
G  7.83  1.34  14.3  ET
G  0.21  0.03  39.6  7L
G  0.94  0.03  14.38 19L

C  5.23  0.89  6.72  ET
C  0.14  0.02  0.18  7L
C  0.14  0.02  0.97  19L

You can see that the 1-3 interval is improved (a lot) over ET with both just tunings. The 3-5 interval is also improved, though it doesn't need it as much. The 5-7 interval is where the difference in 7 & 19 limit shows up. For the G there is no improvement with 19L and the 7L gets more harsh. For the C the 7L shows a bit more improvement. The -29 cent shift for the F is a high price to pay with the 7 limit just. I can see why the 19 limit seems to be preferred.  This all assumes that my math is correct, I could be completely full of beans, but it seems to jive with the Pat Missin explanations. :0)

Thanks to the Viet Cong I can't tell the difference in the chords on a Special 20 and a Lee Oskar anyway so it's all academic to me.

Peace and music,
Dave