I'll run through how I do it and you'll hopefully be able to get something useful out of it.
Scroll down to the last link if this math stuff is making you drowsy!
First, lets assume you want a 16x32 grid since (16*32) with 1.5 inch units gives a 24x48 inch size.
This doesn't work for two reasons. 16*32 is not coprime, they both have 2, 4, 8 and 16 in common. The sum of those 16*32=512 is not one less than a primenumber either, which is the other criteria for the grid. I don't know any more elegant way of doing it than to hit the calculator with various suggestions and see if the sum is prime minus one. 16*33 is not, 16*35 is not, but 16*37 gives 592 which is one less than the prime number 593. 16 is also coprime to 37 since there is nothing in common for those numbers except 1 and itself.
This will give you a 24*55.5 inch total build size. If it doesn't work for you, search for another grid that works better!
Time to input the numbers into
Oliver Primes calculator. First, go to
this page, enter the prime number into the "primitive root modulo N" field and write down the result. In this case, it's 3. So we already have the most important parameters for the calculator:
Prime number P: 593
Primitive root of P: 3
# columns: 37
# rows: 16
That's the important part. The frequency stuff is just for convenience, making those numbers easier to use in the real world. The calculator is in meters. A hundred of meter is centimeter, with 1 inch being 2.54 cm and 1 cm being 1/2.54 inch. The speed of sound is set to 343 meters per second, or 1125 feet per second. It doesn't matter what the value reads, it's just a reference.
The build uses 1.5" inch widths, so the high frequency have to be set accordingly if you want the calc to display well width and final size in the correct measures. It doesn't change anything, practically speaking, but it looks better in the calculator. The corresponding high frequency cutoff is speed of sound divided by size of object divided by two. The size is 1.5(inch)*2.54=3.81(cm). The speed of sound is 343 meters, divided by 0.0381 meters (3.81cm) divided by two. In numbers: (343/0.0381)/2=4501.31233595800 Hz. <- that's the high frequency cutoff that'll give you 1.5 inch divisions.
The low frequency cutoff is the depth of your build. A nice looking example is to use the prime number divided by four as the starting point. This is 148.25. Again, the relevant frequency is found by using speed of sound divided by depth divided by two. If depth is 14.825cm's, equation is: (343/0.14825)/2=1156.82967959527824620 Hz. The reason do this is obvious when looking at the intermediate results in the calculator:
Calculate a Two-Dimensional Primitive Root Diffuser (Skyline) As can be seen, each step have it's own unique number and it's all integer numbers or nice looking rationals. You don't need to use that number, but it's a neat way to check that you've got everything right. If there's something wrong in prime number, coprimes etc, it'll be very clear as the numbers will look messy.
You want 7 inch depth, so it's 2.54cm times seven, 17.78 cm's depth. That's (343/0.1778)/2=964.5669291338582 Hz. The quantization should be set as fine as you can be bothered. BBC states a reason for using only 5 different depths. I didn't get it and neither did my PRD diffuser hero around here
, GE. If you want to be safe, use more quantization steps if you can be bothered to have more different depths. Quantizing with 2.54cm gives inches, half that gives half inches etc.
All in all, with 7" depth and quarter inch quantization:
Calculate a Two-Dimensional Primitive Root Diffuser (Skyline)
Is this better?