On Mon, 19 Jan 2004 00:11:36 +0000, Laurence Payne
wrote:

On Sun, 18 Jan 2004 22:36:52 +0000, Chris Isbell
wrote:

Simple addition of two frequencies does NOT result in any new
frequencies. Only non-linearities causing one of the signals to be
multiplied by the other (aka 'mixing', 'modulating' or 'heterodyning')
will cause sum and difference frequencies to be created.

That poses the question, how can I tune instruments accurately using
beat frequencies?

If you want them to be "perfectly" (and I use that term precisely) in
tune, you tune for zero beats. This is quite easy for unisons and
octaves, takes a bit of practice for 5ths and 4ths.

[snip]

Sorry you asked? :-)

No, I could go on at great length about tuning and pitch. ;-)

The question I was trying to get at was that it the chain from the
instrument to my ear/brain is substantially linear, then why do I hear
beat frequencies? (If it is not linear, then why is linearity such a
concern for Hi-Fi systems?)

[Off topic: Many years ago when I was actively involved in playing
early woodwind instruments, the group I was playing with did some
interesting experiments in using 'just intonation' and changing the
tuning whenever the music modulated. Thus we were going for zero beats
- not that easy on a sopranino recorder.]


--
Chris Isbell
Southampton
UK

On Mon, 19 Jan 2004 09:32:32 +0000
Don Pearce wrote:

Try 400 and 401 Hz then - far more obvious.

You do not hear a tone at 1Hz in these circumstances - you hear beats.
These are very different. There is no tone, there is no need for any
non-linearity that might generate a tone. You are simply hearing
pressure peaks moving in and out of phase.

Its the same effect though. I agree 1 Hz isnt really a tone, but it is a
signal.

Or are you suggesting that the pressure peaks DONT move in and outr of
phase in the 400/450 case?

--
Spyros lair: http://www.mnementh.co.uk/ |||| Maintainer: arm26 linux

Do not meddle in the affairs of Dragons, for you are tasty and good with
ketchup.

On Mon, 19 Jan 2004 11:24:37 +0000, Ian Molton wrote:

On Mon, 19 Jan 2004 09:32:32 +0000
Don Pearce wrote:

Try 400 and 401 Hz then - far more obvious.

You do not hear a tone at 1Hz in these circumstances - you hear beats.
These are very different. There is no tone, there is no need for any
non-linearity that might generate a tone. You are simply hearing
pressure peaks moving in and out of phase.

Its the same effect though. I agree 1 Hz isnt really a tone, but it is a
signal.

No, it is not even a signal. There is a variation in level at 1Hz, but
absolutely no acoustic energy whatever at that frequency. Have a look
at the two tones on a spectrum analyser and try to find anything at
all going on at 1Hz - you won't find it.

Or are you suggesting that the pressure peaks DONT move in and outr of
phase in the 400/450 case?

Of course they do.
d

_____________________________

http://www.pearce.uk.com

On Mon, 19 Jan 2004 08:14:10 +0000, Ian Molton wrote:

On Mon, 19 Jan 2004 08:05:13 +0000 (UTC)
(Stewart Pinkerton) wrote:

Um, you think that he can hear a 1Hz tone more easily than a 50Hz
tone? From which planet are you connected to the Internet?

a 1 Hz beat frequency? you bet.

Unfortunately, you've no ideea what you're talking about. That 1Hz
beat frequency is an envelope effect modulating the amplitude of the
originals, and it doesn't exist in linear systems.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Mon, 19 Jan 2004 11:24:37 +0000, Ian Molton wrote:

On Mon, 19 Jan 2004 09:32:32 +0000
Don Pearce wrote:

Try 400 and 401 Hz then - far more obvious.

You do not hear a tone at 1Hz in these circumstances - you hear beats.
These are very different. There is no tone, there is no need for any
non-linearity that might generate a tone. You are simply hearing
pressure peaks moving in and out of phase.

Its the same effect though.

No, it absolutely is *not* the same effect.

I agree 1 Hz isnt really a tone, but it is a
signal.

Or are you suggesting that the pressure peaks DONT move in and outr of
phase in the 400/450 case?

This only occurs if you have two separate *sound* sources, it does
*not* occur in a linear system with a single speaker.

It works for piano tuning, but not for amplifiers..............
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Mon, 19 Jan 2004 08:05:13 +0000 (UTC),
(Stewart Pinkerton) wrote:

On Sun, 18 Jan 2004 18:05:14 +0000, Julian Fowler
wrote:

On Sat, 17 Jan 2004 11:51:36 +0000 (UTC),
(Stewart Pinkerton) wrote:


You can get at least 200 CDs onto a 120GB hard disk if you insist on
computer storage, and I don't know *anyone* who listens to more than
200 different discs in an average year.

RAOTFL ...

A quick estimate suggests that I probably listen to something like
2000 different discs in an average year.

I hope you get paid for that................

Nope (and why should I?). Can't imagine what it would be like to only
listen to 200 different discs in the course of a year ...

Julian

--
Julian Fowler
julian (at) bellevue-barn (dot) org (dot) uk

On Mon, 19 Jan 2004 08:05:13 +0000 (UTC),
(Stewart Pinkerton) wrote:

Try 400 and 401 Hz then - far more obvious.

Um, you think that he can hear a 1Hz tone more easily than a 50Hz
tone? From which planet are you connected to the Internet?

You can, and will, hear a 1Hz beat. Piano tuners do it every day.

On Mon, 19 Jan 2004 09:42:43 +0000, Chris Isbell
wrote:

No, I could go on at great length about tuning and pitch. ;-)

The question I was trying to get at was that it the chain from the
instrument to my ear/brain is substantially linear, then why do I hear
beat frequencies? (If it is not linear, then why is linearity such a
concern for Hi-Fi systems?)

How did we get sidetracked into this "linear" argument?

You hear beats because they are a simple physical result of mixing two
sounds of close pitch. That's it.

If you set up a series of pitches approximating to the overtones of a
low note, your brain will sometimes "hear" the low note. This isn't
mumbo-jumbo, it's an established technique in church organ
construction, and probably elsewhere. But it's nothing to do with
beats.

On Mon, 19 Jan 2004 11:37:26 +0000, Don Pearce
wrote:

Its the same effect though. I agree 1 Hz isnt really a tone, but it is a
signal.

No, it is not even a signal. There is a variation in level at 1Hz, but
absolutely no acoustic energy whatever at that frequency. Have a look
at the two tones on a spectrum analyser and try to find anything at
all going on at 1Hz - you won't find it.

You can hear it though, can't you. Are you troubled by being able to
hear a variation in level - sometimes called a tremolo (did I spell
that right?)

On Mon, 19 Jan 2004 18:31:45 +0000, Laurence Payne
wrote:

On Mon, 19 Jan 2004 11:37:26 +0000, Don Pearce
wrote:

Its the same effect though. I agree 1 Hz isnt really a tone, but it is a
signal.

No, it is not even a signal. There is a variation in level at 1Hz, but
absolutely no acoustic energy whatever at that frequency. Have a look
at the two tones on a spectrum analyser and try to find anything at
all going on at 1Hz - you won't find it.

You can hear it though, can't you. Are you troubled by being able to
hear a variation in level - sometimes called a tremolo (did I spell
that right?)

Yes a variation in level - but no tone, and very specifically, no
signal. It simply isn't there to be heard.

d

_____________________________

http://www.pearce.uk.com