[sdiy] Fwd: saw vs ramp, audible?

[cheater cheater]

...in a perfectly linear system.

On Mon, Dec 9, 2024 at 8:36 PM Ian Fritz via Synth-diy
<synth-diy at synth-diy.org> wrote:
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> -------- Forwarded Message --------
> Subject: Re: [sdiy] saw vs ramp, audible?
> Date: Mon, 9 Dec 2024 12:25:45 -0700
> From: Ian Fritz <ijfritz at comcast.net>
> To: Tom Wiltshire <tom at electricdruid.net>
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> On 12/9/2024 9:47 AM, Tom Wiltshire wrote:
> >
> >
> >> On 8 Dec 2024, at 22:43, Donald Tillman <don at till.com> wrote:
> >>
> >> Note that a sawtooth ramping down has all the harmonics in phase with the fundamental.
> >>
> >> And a sawtooth ramping up has its harmonics alternating in phase (+1, -1/2, +1/3, -1/4,...) from the fundamental.
> >
> > That's an odd way to look at it, since it produces a waveform which is half-a-cycle out of phase. In my view, it's the half-cycle-out-of-phase that leads to the harmonics being alternately flipped, not the changed slope.
> >
> > If you want to flip the slope without changing the phase, you'd simply invert all the harmonics. E.g. the amounts are *all* negative, not every other one.
> >
> > Tom
> > _____
>
> Choose your coordinate system so the SAW is symmetrical both
> horizontally and vertically. Then it is zero at the origin and thus
> there are only Sin functions in its Fourier series expansion, Cos
> functions being non-zero at the origin.
>
> Now you should be able to see that inverting the SAW is the same as
> simply reversing the sign of each Sin component's argument. As you
> cannot hear the difference between Sin waves with opposite arguments,
> the two SAWs will sound the same, unless there are nonlinear process
> introduced in the audio pathway or in the ear.
>
> So Tom is, of course, absolutely correct.
>
> Ian
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>
>
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