Re: Beats (was Sad symmetric septimal minor tune)

HI Paul,

> > http://www.robertinventor.com/12_et_oddt2_to_12_seth.mp3
> >
> > You can hear many simultaneous beats there but they are
> > gentle (though fast) and it is quite smooth sounding.

> I find it hard to hear any beats in the individual timbres, and the
> notes of the chord are struck too far apart for me to hear whether
the chord itself is producing any beating or not.

Well, unless it is beating with my computer fan or
something, I've been fooled like that before,
but you would get that with a single
partial and they wouldn't only come in
when you stack them together, also I'd hear
them in the harmonic clips I posted aurely.
So I think these are real!

I'll try and describe them to you:

Listen for a low slow beating after the major third comes
in - that's the most prominent one in the clip.
It's pitched at middle c, and two or three beats
per second, really quite distinct when you hear
it but lower in pitch than you might expect.
You might perceive it as the c below middle c
but I think it is middle c itself if you listen
carefully to the pitch.

There's also a fairly prominent one at g',
a bit faster, maybe six or seven beats per second,
that starts at that point.

The ones with the single note at the start
are mostly very fast and gentle, maybe
a dozen or more a second, and several of them
are sounding simultaneously. I'm not sure what
the pitches are, quite high, in the
second or third octave above middle c,
as it is more like an impression of the
sort of effect I'm used to hearing when you
have several fast beats simultaneously, and
the feeling that with time, maybe with a longer clip,
or listening to it a number of times, and
listening quietly I could sort them all out.

But there is a slow one there at c above middle
c that is fairly distinct from the others
again in the first note.

There's an even slower one already at middle c
itself at that point, that's about a couple of
beats per second, at the same pitch
as the one you get when the major third comes in,
but even slower and much less pronounced.

> > Same one, not Setharised:
> >
> > http://www.robertinventor.com/12_et_oddt2_to_12_un_seth.mp3
> >
> > Some slow large amplitude beats there in the chord,
> > when the major third comes in, fairly smooth for the single note.

> Honestly, I can't hear the beats here. Which is no surprise -- a
> major third would only beat if the n*5th partial of the lower note
> > beats against the n*4th partial of the higher note. If you're using
> only partial #s 1, 2, 6, and 10, there's no opportunity for this to
> happen.

Listen carefully - the slow middle c for the major third is there again and more
pronounced than in the clip before. Other ones as well.

> > though
> > with really strong beats already in single notes, but these are
> > really musical ones so I like it, like bell beats.
> >
> > http://www.robertinventor.com/12_et_oddt2_to_12_Bessel_Seth.mp3

> Well, finally here's one where I hear beating when the major third
> comes in. Can you explain what this one is, how it's different from
> the one above, etc.? You say it's "Seth" (arized?) but somehow I
> think there must still be some just 5th partials in these
> timbres . . .

Yes it's metatimbres consisting of stacked Bessel functions so they will
all have the complete harmonic series I'd have thought.

Do you not hear the beating partial in the first note as well?
Slow, bell like, only about one beat or so a second and quite
pronounced. There is a higher simultaneous one too, a bit faster, maybe
two or three times a second, and not so pronounced - a sort of polyrhythm
effect as you often get with beats, I think it might be 2:3 or something.

It is a matter of listen carefully to individual pitches
in the notes and hear which of those are beating.
Listen to them as you would to separate instruments
in an orchestra - then it becomes really clear if
one is beating because that is all you are listening
to at that point - just like listening to a flute player
in an orchestra and hearing that he or she is playing
a note with tremulo at a particular point.

There is little or no volume variation in the
note as a whole, what there is would be
a complex pattern of superimposed beats,
not easily recognisable as beats at all,
just a kind of a roughness. Listen for
many simultaneous beats running with
different rhythms at once, like Bell partials.

Then on the rest of the e-mail - yes they are metatimbres,
using harmonic but very complex timbres superimposed.

Thanks,

Robert

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:
> HI Paul,
>
>
> > > http://www.robertinventor.com/12_et_oddt2_to_12_seth.mp3
> > >
> > > You can hear many simultaneous beats there but they are
> > > gentle (though fast) and it is quite smooth sounding.
>
> > I find it hard to hear any beats in the individual timbres, and
the
> > notes of the chord are struck too far apart for me to hear whether
> the chord itself is producing any beating or not.
>
> Well, unless it is beating with my computer fan or
> something, I've been fooled like that before,
> but you would get that with a single
> partial and they wouldn't only come in
> when you stack them together, also I'd hear
> them in the harmonic clips I posted aurely.
> So I think these are real!

One thing to keep in mind, Robert, is that combinational tones vary
*nonlinearly* in loudness with the amplitude of the signal. They can
be at negative dB values when I listen to them in the office, rise at
a low-integer multiple (such as 2 or 3 or 4) of the dB of the input,
and end up incredibly loud with two recorders playing ff in my ear.
So the very same audio clips may exhibit audibly different
combinational tones, and thus different patterns of beating --
particularly if the beating doesn't arise directly from very close
frequencies in the signal -- depending on the volume at which one
listens.

Another important factor is the audio equipment. Only very high-end
audio equipment can faithfully reproduce sound with no harmonic
distortion. Harmonic distortion produces combinational tones of all
orders.