[sdiy] Divide down question

[cheater cheater]

> Actually you don't need the latches. You're dead right with the rest of it;
> C1+ 1/2 C2 + 1/4 C3 + 1/8 C4 + etc gives you a steppy saw. Try it on graph
> paper, graphics calculator, or maths package (in ascending order of
> techno-overkill).

How about just ascii?

C4
1010101010101010

C3
1100110011001100

C2
1111000011110000

C1
1111111100000000

Instead of dividing, we can just multiply the other way around:


C4
1010101010101010

C3
2200220022002200

C2
4444000044440000

C1
8888888800000000

sum:

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Or alternatively if we put the C's in subsequent lines:

1010101010101010
1100110011001100
1111000011110000
1111111100000000

...and treat it as a matrix and transpose it...

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

As we can see it's all the numbers from 0 to 15. But the time actually
passes from bottom to top in that last list, therefore we get a
falling saw. :)

So what would happen if we used the latches?

C4
1000000000000000

C3
1100000000000000

C2
1111000000000000

C1
1111111100000000

...now let's multiply...

1000000000000000
2200000000000000
4444000000000000
8888888800000000

15, 14, 12, 12, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0

Or in crude ascii drawing: (1 is the waveform, 0 is 'background')

1000000000000000
0100000000000000
0000000000000000
0011000000000000
0000000000000000
0000000000000000
0000000000000000
0000111100000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000011111111

So indeed a fairly crappy result.

:^)

D.

On Tue, Aug 25, 2009 at 3:48 PM, Tom Wiltshire<tom at electricdruid.net> wrote:
>
> On 25 Aug 2009, at 15:09, cheater cheater wrote:
>
>> What about this:
>> start out with a normal square divide down, and then when you're e.g.
>> playing C1, then actually what is output is:
>> C1+ 1/2 C2 + 1/4 C3 + 1/8 C4
>>
>> Each of the higher tones would have to go through a latch. That latch
>> would only let through one pulse of C2, C3, etc, but it would be reset
>> on C1's rising slope. Maybe this could be a little bit difficult,
>> maybe not.
>
> Actually you don't need the latches. You're dead right with the rest of it;
> C1+ 1/2 C2 + 1/4 C3 + 1/8 C4 + etc gives you a steppy saw. Try it on graph
> paper, graphics calculator, or maths package (in ascending order of
> techno-overkill). Since it's a bright buzzy sound with even as well as odd
> harmonics, it actually sounds pretty much like a saw even with fairly few
> steps. A good substitute, anyway, even if not enough for perfectionists.
>
>> Actually, couldn't you do a big part of square-based divide down
>> topology in FPGA?
>
> Yes. Wasn't someone on this list doing a top-octave chip on an FPGA? That's
> the hard part! The rows of flip-flops would be a good "beginner's FGPA
> project" I'd have thought!
>
> T.
>
>
>