Re: Beats

Hi Paul,

This morning when it was quiet, I noticed
a high pitched really pure toned steady pitched
and very quiet high a''' in my left ear. Also
some other lower notes are there too, all pure
tones at various pitches with some beating between
some of them too if you listen to it quietly.

It isn't bad enough to call it titinitus,
just a really quiet sound, but now I know
to look out for it I can hear the notes at
any time if I pay particular attention to them.

So I wondered if some of the beats could
be due to that.

So thought of a test for that, which is to
play the same audio file back at different
sample rates as I can do in Goldwave.
If it was due to beating with any external
source then the patterns would change in some
complex way and the pitches and numbers
of beats ditto.

However, that didn't happen. All the beats
were still there as described, at different frequencies
and with the beats slowed down as it went slower.
E.g. that very slow beat low beat in the first note and
the same pitch but a bit faster when the major
third comes in - those sort of patterns
are still recognisable as I change the pitch.

So I think they must be real, hard to see what
other kind of effect could do that.

They are also more obvious when it is transposed
down an octave. So here it is, the first clip,
transposed down an octave just by changing the sample
rate to 22050:

http://www.robertinventor.com/12_et_oddt2_to_12_seth_tr_-_oct.mp3

Do you hear beats in it now? E.g. in the first note already.
I hear really strong beats there at this pitch. Do you hear
the slow wah wah beat right at the bottom of that chord
of the partials for the first note, now at about one beat
a second instead of the two beats per second it is at
the higher pitch? Also the faster one higher up?
Some more slow ones too in that note if you listen
out for them.

Then there are loads of beats when the other notes come in.

The main note in my left ear is a pure tone btw, and pretty close
to concert pitch, almost good enough
to use as a tuning fork :-). I just had a go at
comparing it with a reference tone and it is certainly
very close. May be a couple of cents or so flat if anything.
Not as much as 10 cents flat certainly. I think
probably 2 cents or so.

When I used to practice the 'cello
I could sometimes remember the tuning
fork pitch from one day to the next
so that I could whistle the note
before I picked up the fork. This
is probably why.

I just tested it singing an 'a'
tuned to the note in my ear, then played it on
recorder and it was indeed an 'a'.

Maybe I should hire myself out as a
tuning fork :-).

Thanks,

Robert

Hi Paul,

Interesting what you say about combination tones
being non linear. Yes you can get them really
strongly with two recorders played loudly
with pure steady pitches, as a third !part"
sometimes unwelcome notes for the tune you are playing.

I've wondered if a composer could exploit combinaiton
tones to write a three part piece for two recorders
(expect it has been done).
However, that means you would have to play the music
very loudly too at the correct loudness level
to hear the third part as intended.

Yes, my soundcard is the SB Live! and
I've noticed before that it introduces
distortions at discontintuities.

Here is a screen shot of a saw tooth:

http://www.robertinventor.com/SBLive_saw_tooth.png

Can a high end soundcard reproduce even a discontinuity
accurately? After all it requires an infinite
fourier series to make a saw tooth so you would
think it is quite a challenge, and just
having e.g. a cut off of the frequencies at some level
(even maybe beyond human hearing range)
could mean it can't play a perfect
saw tooth.

I hadn't thought of the effect this could
have on other waveforms, but I suppose it
is a harmonic distortion and if it happens
at a discontinuity, maybe it can happen
elsewhere to lesser degree.

I listen over headphones and the ones I use are
reasonably good middle range ones (the Grado labs
headphones).

I wonder if there is any way to find out
whether particular beats that one hears
are due to harmonic distortion or
would be present anyway without it.

Thanks,

Robert

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:

> I wonder if there is any way to find out
> whether particular beats that one hears
> are due to harmonic distortion or
> would be present anyway without it.

Essentially, yes -- just lower the volume -- you'll be lowering the
percentage of harmonic distortion in both the sound system and in
your ears. You can get more refined by playing with various gain
stages in your system to improve the volume/distortion ratio.

HI Paul,

> > I wonder if there is any way to find out
> > whether particular beats that one hears
> > are due to harmonic distortion or
> > would be present anyway without it.

> Essentially, yes -- just lower the volume -- you'll be lowering the
> percentage of harmonic distortion in both the sound system and in
> your ears. You can get more refined by playing with various gain
> stages in your system to improve the volume/distortion ratio.

Rightio, I've done that.
The saw tooth now looks
fine, just slightly rounded
at the top.

In the audio clip,
the beats are all still there,
all the main ones that I
described, and beating at the
same rates as before. Some
of the others are not present
any more.

The overall ipression
is that it is much smoother than it
was when louder.

The most prominent beating partial
when it is quieter is in the
major third and it is a fast
beat at maybe eighr or ten
beats per second pitched at
an octave below the major third.
There's also a very fast beat on the
e itself, so fast as to just
be an impression of roughness, maybe
twenty or so beats per second, very
rough guess.

Also the slow beat in the
first note at c, maybe one
per second and the same pitch again
a bit faster when the major third comes in
- more subtle but you can hear it still.
I think it is actually an octave
below the c of the chord.

When the last note comes in then
it is almost beatless when
played quietly like this, but there
is one fast beating partial
maybe a dozen or so beats per
second still present - it's
a g. You can also hear the slow
beating c partial still from the
previous note, not so obvious
but it is still there, same speed.
The fast low beating e has more or less
faded away by then, though maybe another
oscillation or two could just be
traced into the next note if you follow it.

(those are all very rough guestimates
at the beat rates).

I wonder if anyone else can hear
these particular beat patterns?

This is the clip again:

http://www.robertinventor.com/12_et_oddt2_to_12_seth_tr_-_oct.mp3

which plays a 12-et c e g chord, with the notes consisting of
sine waves stacked in a harmonic series of the partials
1 2 6 10 and the partials quantised to the pitches of 12-et.

Thanks,

Robert

Thanks for your reply, Robert. I'll listen when I have a chance.

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:
> HI Paul,
>
> > > I wonder if there is any way to find out
> > > whether particular beats that one hears
> > > are due to harmonic distortion or
> > > would be present anyway without it.
>
> > Essentially, yes -- just lower the volume -- you'll be lowering
the
> > percentage of harmonic distortion in both the sound system and in
> > your ears. You can get more refined by playing with various gain
> > stages in your system to improve the volume/distortion ratio.
>
>
> Rightio, I've done that.
> The saw tooth now looks
> fine, just slightly rounded
> at the top.
>
> In the audio clip,
> the beats are all still there,
> all the main ones that I
> described, and beating at the
> same rates as before. Some
> of the others are not present
> any more.
>
> The overall ipression
> is that it is much smoother than it
> was when louder.
>
> The most prominent beating partial
> when it is quieter is in the
> major third and it is a fast
> beat at maybe eighr or ten
> beats per second pitched at
> an octave below the major third.
> There's also a very fast beat on the
> e itself, so fast as to just
> be an impression of roughness, maybe
> twenty or so beats per second, very
> rough guess.
>
> Also the slow beat in the
> first note at c, maybe one
> per second and the same pitch again
> a bit faster when the major third comes in
> - more subtle but you can hear it still.
> I think it is actually an octave
> below the c of the chord.
>
> When the last note comes in then
> it is almost beatless when
> played quietly like this, but there
> is one fast beating partial
> maybe a dozen or so beats per
> second still present - it's
> a g. You can also hear the slow
> beating c partial still from the
> previous note, not so obvious
> but it is still there, same speed.
> The fast low beating e has more or less
> faded away by then, though maybe another
> oscillation or two could just be
> traced into the next note if you follow it.
>
> (those are all very rough guestimates
> at the beat rates).
>
> I wonder if anyone else can hear
> these particular beat patterns?
>
> This is the clip again:
>
> http://www.robertinventor.com/12_et_oddt2_to_12_seth_tr_-_oct.mp3
>
> which plays a 12-et c e g chord, with the notes consisting of
> sine waves stacked in a harmonic series of the partials
> 1 2 6 10 and the partials quantised to the pitches of 12-et.
>
> Thanks,
>
> Robert