[sdiy] saw vs ramp, audible?

[brianw]

On Dec 9, 2024, at 8:47 AM, Tom Wiltshire wrote:
> On 8 Dec 2024, at 22:43, Donald Tillman 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

One thing I learned when writing a software additive synth is that using the sin() function means that harmonics must be alternately flipped. Someone online pointed out to me that if I'd used cos() instead, then I would not have to alternate flipping each next harmonic.

Brian