Tuning The Duda

My acquaintance Rafał shared some pages from a book showing that the notes on the chanter of the Polish duda, a kind of bagpipe, are quite microtonal.

The tones are conventionally notated [D, F#, G, A, B, C, D, E] and they are separated by roughly [350, 85, 190, 190, 120, 140, 180] cents. We can see that these are only precise to 5 or 10 cents.

I tried to find frequency ratios to make sense of this. I looked for ratios that

1) Match the interval sizes, 

2) Are simple (have small numerators and denominators), 

3) Multiply together with adjacent ratios to be even simpler. 

Here's the scale that I came up with. The ratios only have factors of 2, 3, 5, and 7.

D to F# :: ~(350 cents) -> 60/49  (351 cents)

F# to G :: ~(85 cents) -> 21/20 (84 cents)

G to A :: ~(190 cents) -> 10/9 (182 cents)

A to B :: ~(190 cents) -> 28/25 (196 cents)

B to C :: ~(120 cents) -> 15/14 (119 cents)

C to D :: ~(140 cents) -> 49/45 (147 cents)

D to E :: ~(180 cents) -> 10/9 (182 cents)

Here are some nice compound intervals produced by this tuning:

Low D to G: 9/7

F# to A: 7/6

A to C: 6/5

B to high D: 7/6

G to C: 4/3

Low D to A: 3/2

A to High D: 7/5

If there were an intermediate tone "E" between the low D and F#, it would probably be 15/14 (119 cents) over the low D, leaving 8/7 (231 cents) to reach F#. The interval from E to G would then be 6/5, a just minor third.