[sdiy] They aren't sawtooths, they're ramps

[cheater cheater]

Actually falling and rising exponential ramps are harmonically
different and if you add both together you get, I think (by trying to
picture in my imagination how the graph would look) some sort of
parabolic thing - imagine x^2 from -1 to 1 repeated over and over - of
course, mathematically, this is very wrong since it's e^x + e^-x, but
it's similar enough... actually, now that I look at that formula, it's
going to be exactly the hyperbolic cosine:

cosh(x) = 1/2(e^x + e^-x)

and you can get a hyperbolic sine this way:

sinh(x) = 1/2(e^x - e^-x)

which means that you need to flip the polarity of one of the waves.

And if you make a divider, then you can get tangens hyperbolicum also
known as tanh(x).

So I say that there *IS* a point in making a distinction in names. I'm
not so sure whether 'saw' and 'ramp' are the best names. I think that
'the expanding saw' is the best name that distincly describes y=e^x
and y=-e^x, and 'the receding saw' best describes y=e^-x and y=-e^-x,
by analogy with populations which expand exponentially and recede
anti-exponentially. I suggest using 'ramp' for linear versions: y=x
and y=-x. I don't think e^x looks like any ramp I've seen, the car
would get stuck. I further suggest calling y=x^k (for x = 0..1) the
accelerating saw and y = x^k (for x in -1..0) the decelerating saw
(that all for k > 1 of course)

D.

On Fri, Nov 6, 2009 at 21:40, Dave Manley <dlmanley at sonic.net> wrote:
> Donald Tillman wrote:
>
>>   > I think there's some 'prior art' that may conflict with your
>> definition.   > Didn't the original Moog modular oscillators and first gen
>> minimoogs use   > a unijunction transistor in the oscillator core?  I think
>> a buffered   > version of that is the sawtooth.
>>
>> Lots of older VCO's used unijunctions to reset the waveform.  That's
>> okay, they work like schmitt triggers.
>>
>
> My recall was faulty, in that the unijunction transistor is not used in the
> Mini, but is used in the 901B.  In the later it is used, as Don says, to
> reset the waveform.  Here's a link for those interested:
>
> http://www.hylander.com/images/schematics/901b.jpg
>
> -Dave
>
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy
>