I imagine two threads: one is a software-based approach using Python with NumPy and SciPy. The other is a hardware approach using C/C++ on Arduino. Since I am more comfortable with the software, I am tackling the hardest part first. And I am starting with an Arduino-controlled analog synthesizer.
I'll present the design later. But before I get to the actual synthesizer, I want to start with something I "invented" that might be useful: a cheap and easy way to connect a 3.5 mm audio jack to a solderless breadboard.
There's a $5 solution here: http://store.curiousinventor.com/plug-in-bread-board-stereo-1-8-quot-audio-jack.html
Or you can get the jack for $1.50: https://www.sparkfun.com/products/8032
And a PCB breakout board for $0.95: https://www.sparkfun.com/products/10588
And solder them together. But if you already have the jack and some break away-female headers, you can make your own solution. Here's how:
1) Make sure the holes at the top of the female headers are big enough for the pins on the jack. It looks like they come in at least two sizes:
The ones on the left are too small. The ones on the right are good.
2) Break off two headers with 5 pins each (or you can make one of them smaller). UPDATE: after more experimenting, I recommend headers with longer pins than the ones below (stackable headers). The short pins do not make a good electrical contact with the breadboard, and they do not make a solid mechanical connection.
A few suggestions for breaking so-called break-away headers: (a) you can't break between two adjacent holes; you have to sacrifice a hole in between; (b) before cutting, use pliers to remove the metal pin from the hole you are sacrificing; (c) you can use wire cutters to make the cut, but you should wear eye protection -- the pieces go flying! (d) you can use wire cutters and sandpaper to clean up the cut edge.
3) Put the headers into a breadboard and then stack the jack on top. Four pins go into the back header; one pin goes into the front (so the front really only needs to have 1-2 pins). Use super glue to hold the whole thing together.
Here's the other side (with the rough edges I didn't bother to sand).
So there it is. Just a little bit cheaper than using a PCB breakout board, and no soldering.
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