[Trombone-l] Acoustics of brass instruments

[Richardson, Timothy Mr. DAC USAG Franconia DPW]

Warning***Geek Hat on**********

I think it is possible you've reversed the expansions for square and
triangle.  Think about superimposing sets of sine waves to get something
that looks like a square or triangle.  You're going to need lots more of the
lower harmonics to make it look like a square.  

Now that I think about it, you are right about a square wave sounding a
little "clarinetty."  Most of the shareware tone generators can do sine and
square, and some of the drone tuning CDs are square wave based, so you can
easily hear one.  I don't remember listening to a triangle wave since
engineering school so I no longer have a clue, guess I need to find one.  

However, I did that hairclipper experiment, remember?  Fundamental frequency
was 50 Hz, which the trombone did not amplify.  There was no octave.  But I
could clearly hear a strong octave plus fifth, which would correspond to 150
Hz, the 3rd harmonic.   So I have to think square wave is correct.

********Geek Hat removed*************

Musical story.  I live in a small farm village in central Germany.  The
walls are foot thick stone, I live on a corner with no houses really close;
also most locals pull down rolladens at night.  I have assumed that I could
practise with impunity and probably nobody even knew I played trombone.
However, this Saturday a band assembled outside my window at 5:00 AM, played
one tune, and departed.  I am wondering who I have p.o.'d.  



-----Original Message-----
From: Daniel Pliskin [mailto:daniel_pliskin at hotmail.com] 
Sent: Wednesday, June 07, 2006 05:12
To: TROMBONE-L at server5.samford.edu
Subject: Re: [Trombone-l] Acoustics of brass instruments


>We talked about the hairclipper
>buzz recently.  That timbre indicates the waveform is a square wave.  
>We know intellectually a square wave is made up of a fundamental plus 
>odd harmonics, with the 3X frequency at 1/3 amplitude, the 5X at 1/5th,
etc.


My impression of a square wave is more clarinet-like.

A hair clipper may well have only odd harmonics, but it sounds more like a
triangle wave, which also has only odd harmonics, but if I remember
correctly, the expansion is more like:

fundamental/1 +third/3 + fifth/5 +...

Where a square wave is something like:

Fundamental/1 + third/9 + fifth/25 +...

So the triangle wave has considerably more high harmonics.

Of course, there are all sorts of duty cycle alterations, which also
accentuate the higher harmonics.

Some day when I'm really, really, really bored, I'll mike a hair chippers
and check it out on an oscilloscope, for those inquiring minds out there.

DanP