[sdiy] Additive Synthesis - phase shifts important??

[Florian E. Teply]

cheater cheater schrieb:
> Guys,
> 
> there are several misconceptions here that need to be cleared up:
> 
> 1. what is phase shift?
> there are several things that go under the general term phase shift
> that are *very* different.

Oh well...
That reminds me of my Prof. in Electronic Measurement course:
He impressed upon us, that the term "phase" has absolutely no meaning 
unless one is talking about sine waves of exactly the same frequency...
And, as far as my understanding goes, he's absolutely right about that. 
Still that term sometimes slips me in cases where -- as stated above -- 
this doesn't mean a thing anyways.
Most folks do understand what i'm talking about anyways (or won't, but 
independent of my use of "phase").

What i meant is something similar to (yet, as i read it, not the same 
as) version b).

What i meant probably needs a couple more words to tell properly, even 
though i had the impression that most folks that answered in this thread 
understood intuitively what i meant.

So, imagine some sine wave of frequency f. That sine wave is supposed to 
start at time t0 with its rising zero-crossing. Let's further use that 
time t0 as reference point.
So, let's add some more sine waves with frequencies being integral 
multiples of f (2f, 3f, and so on).
That makes the overall signal a sum of:
    A1 * sin( 2\pi f * (t-t0))
    A2 * sin(2\pi 2f * (t-t0))
    A3 * sin(2\pi 3f * (t-t0))
and so on.
Let's further introduce phase shifts on those multiples *with regard to 
t0*. That would make for the sum of:
    A1 * sin( 2\pi f *(t-t0))
    A2 * sin(2\pi 2f * (t-t0) + \phi2)
    A3 * sin(2\pi 3f * (t-t0) + \phi3) and so on with those phase shifts 
\phi being constant (but not necessarily the same).

I do understand that a variation of those \phi's between various sets of 
signals (being constant in any given set) will yield different 
waveforms, the intensity of those resulting waveforms as measured over 
frequency staying the same (as can be proven with fourier analysis).

I also guess (from the comment of Florian Anwander), that there will be 
a difference during attack phase of the envelope.

BUT: what's after the attack?
To me it looks like most on this list agree on that there won't be much 
of a difference to tell.

Greetings, Florian