Path: utzoo!mnetor!uunet!nuchat!sugar!karl
From: karl@sugar.UUCP (Karl Lehenbauer)
Newsgroups: comp.sys.amiga
Subject: Re: Sonic Tomfoolery
Message-ID: <1527@sugar.UUCP>
Date: 6 Mar 88 15:38:54 GMT
References: <8802251858.AA21577@cory.Berkeley.EDU> <719@ur-cvsvax.UUCP> <4292@xanth.cs.odu.edu>
Organization: Sugar Land UNIX - Houston, TX
Lines: 32
Summary: phase relationship in two notes is readily detected if it's
	 changing

Multiple musical notes being played simultaneously are routinely out of phase 
with each other.  When this happens, you hear a fattening of the sound.
Consider one violinist playing a note compared to several violinists.  
They do not phase align their waveforms.  (More on this later)

Consider the Amiga.  You start one waveform playing on an audio channel, 
then the same waveform playing on another.  If the sounds are played at 
exactly the same frequency and enough time elapsed between starting them 
that the hardware wavetable pointers aren't the same, you have two notes 
out of phase.  You will hear two notes.

Now consider when you have two notes that phase shift.  In this case
the frequencies of the two notes are slightly different.  Thus, as the
notes play, they go into and out of phase with each other at the rate
of the difference in their frequecies.  In other words, their waveforms
slide into and out of alignment with each other at the rate of the
difference in their frequencies.  As this happens, it significantly
changes what you hear.  When, during the phase shifting, the waveforms 
have become very closely aligned, it sounds like one lound note.  As
they shift apart, the complexity of the sound generated goes up (although
the amplitude usually goes down) causing the sound to have a different 
quality (timbre).  Since they're lining up and moving apart, lining up
and moving apart, this change in sound occurs repeatedly, and rythmically.
This rythmic shifting and aligning caused by two notes playing at slightly 
different frequecies causes this "beating" sound mentioned in an earlier 
posting.  It is also the effect acheived by a wah pedal.  If the difference 
in frequency of the notes gets a little bigger it can sound downright 
discordant.  This is why musicians tune. :-)  If it gets a lot bigger,
it can produce harmony.
-- 
"Lack of skill dictates economy of style." - Joey Ramone
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