Yahoo Tuning Groups Ultimate Backup tuning beating v. roughness (was Re: New file uploaded to this tuning list)

>beating is what results from these very limitations, and does not
>occur "in the air".

Care to explain how? I thought that beating did occur on the ear
drum and did not depend on spectral resolution of the basilar membrane.

>as for roughness, read this:
>
>http://www.mmk.ei.tum.de/persons/ter/top/roughness.html

"""
Rapid means that, to be perceived as roughness, the time interval
between successive events must be less than about 30 ms.
/.../
Although, as mentioned above, roughness should not be conceptualized as
being typical of modulated sounds, in laboratory experiments it is very
useful to study the roughness elicited by modulated narrow-band sounds,
in particular, AM of sine tones. A kind of "natural" AM is provided by beats, i.e., pairs of sine tones. This is why roughness was also
characterized as being the auditory sensation evoked by rapid beats.
"""

>>It is generally thought that periodicity effects (harmonic entropy)
>>are not available to the ear for frequencies over 4 KHz. and that
>>spectral effects (roughness) are dominant in this range. While both
>>spectral and periodicity effects are available below 4 KHz., there
>>is reason to believe that periodicity is dominant.
>
>it seems you're confusing theories of pitch perception with theories
>of dissonance.

No, I define dissonance as a failure of pitch perception. The
dissonance terms are in parenthesis. Take them out if you don't
like them, and everything I said is correct.

>> I suspect that minimizing roughness is the primary way in which
>> a cappella singers tune accurate JI.
>
>minimizing roughness to achieve simple JI ratios is exactly the same
>thing as minimizing beating to achieve the same simple JI ratios.
/.../
>> Roughness does occur between pure tones, also.
>
>yes, but only when they're less than a minor third apart (or further
>in the bass register).

Right, and when do they start beating?

-Carl

🔗francois_laferriere <francois.laferriere@oxymel.com>

Some further toughts and explanations

Bob:
> >beating is what results from these very limitations, and does not
> >occur "in the air".
> carl:
> Care to explain how? I thought that beating did occur on the ear
> drum and did not depend on spectral resolution of the basilar
membrane.

my pleasure:
Beating does occur in the air. Back to the basic, beating is based on
the
exact trigonometric equation:

sin( F1*t ) + sin( F2*t ) = 2 * sin( (F1+F2)*t/2 ) * cos( (F1-F2)*t/2
).

(I leave appart the 2*pi factor that is not necessary for the
explanation) Mathematically a sum of two sines with different
frequencies equate a sine with a frequency which is the average
between F1 and F2, but multiplied by a modulating enveloppe that has
frequency equating the difference between F1 and F2. If you record the
air pressure in the air (i.e. using a microphone) and trace the curve,
you will clearly see the beating.

What may be difficult to understand is that even though, the right and
the left forms are equivalent, the time->frequency domain
transformation that occurs in the cochlea (or in a Fourier transform)
"select" the left form. In other words, for any arbitrary signal, the
effect of the time->frequency transform is to decompose it into a sum
of sinus (or cosines), not a product or other combinaison of
trigonometric function.

The cochlea is a very cleverly designed device that transforms the
incomming time-domain waves into a set of stationnary waves with
maximum amplitudes on points of the basiliary membrane mapping the
frequency domain in a fairly linear way.

The amplitude of the stationnary waves obviously moves over time so
that we perceive the time evolution of the sound. Also the auditory
integrate information over a limited period of time that is analogous
to the "sliding analysis window" used in (digital) signal window.

As I explained in a previous post, if the sliding window is long
enough wrt to F2-F1, F1 and F2 are resolved as individual tones and
the average energy in the window do not vary much over time: no beat.
If the sliding window is short wrt to F2-F1 (or if the difference
between F1 and F2 is small), the amount of energy in the window vary
over time, the beat is perceived as a time domain phenomena.

But the auditory system is resourcefull and is capable of performing
simultaneously analysis in various domain and at various level of
complexity. People working on computer speech recognition painfully
know that the humain brain is unmatched to recognize and analyse
simultaneously the pitch, the phonemes, the syllabe, the words, the
sentences, the semantical content and the emotional state of the
locutor, even in extremely noisy environment: if information is
missing at any level, the gaps are filled with information comming
from many other places (knowledge of the language, of the semantical
context, phrasing habit of the locutor, name it). Brain is magic to
fill-in the blanks.

>
> >as for roughness, read this:
> >
> >http://www.mmk.ei.tum.de/persons/ter/top/roughness.html
>
> """
> Rapid means that, to be perceived as roughness, the time interval
> between successive events must be less than about 30 ms.

AND TO THE POINT!!!

We can reasonnably assume that the auditory system performs its
primary analysis simultaneously with many "window size". There is not
a fixed frequency or duration where, "click", the brain switch from
one analysis mode to the other (discrete event to tone, time to
frequency etc.). So IMHU, beat and roughness (at least wrt to
intonation) are basically the same, but the beat is clearly
time-domain, while the roughness is in the twilight zone where various
analysis modes cooperate in the auditory system. 30 ms is only a
figure for a point somewhere in the middle of this zone.

END OF THE POINT

Another example of the capability to fill the blank is the "virtual
pitch". This is well known, that in the traditional telephone bandwith
(300Hz-3300Hz) male voice pitch is totally absent (or was, telephone
quality has made some progress). It seems that whenever there are few
frequency evenly distributed with a missing root, the brain "invent"
it. In a way it is like visual illusion where we complete the contour
of familiar shapes. That may occur at a more or less upstream point of
the auditory system not as a non-linear phenomena occuring in the
middle ear or in the cochlea.

Am I correct to assume that "virtual pitch" and "difference tone" is
the same thing?

Bob:
> >minimizing roughness to achieve simple JI ratios is exactly the
same
> >thing as minimizing beating to achieve the same simple JI ratios.
> /.../
> >> Roughness does occur between pure tones, also.

I suspect that roughness between pure tones can only be perceived by
highly sophisticated and educated ears (I was quite lousy to hear any
diffrences between the "jerries" files) ;-)

> >yes, but only when they're less than a minor third apart (or
further
> >in the bass register).

Carl:
> Right, and when do they start beating?

That was, in a way, my question when I asked:

Francois previously:
> By the way, is there a perception of beat when using pure sine tones
with
> ratio slightly off 1:2, 2:3 and so on? If so that would be a good
argument
> in favor of difference tone.

I mean difference tone for JI tuning of course

SO....
If roughness and beat are the same, using one ore the other for JI a
cappella tuning is the same. My problem is that if it is so, I do not
understand how singers can use them for ratio above 6:5, because as
far as I can explore actual voice recording, upper frequencies (let
say above 5-6th harmonics) are not very accurate and can probably not
provide reliable beat (or roughness). Or perhaps I work only with bad
recordings? Or perhaps what is perceived of the singer own voice is
more reliable than what is picked up by the microphone?

or roughness is something else than beat, or the mechanism for a
capella JI tuning is something else (memory of intervall?)

Yours truly

François Laferrière

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., Carl Lumma <carl@l...> wrote:
> >beating is what results from these very limitations, and does not
> >occur "in the air".
>
> Care to explain how? I thought that beating did occur on the ear
> drum and did not depend on spectral resolution of the basilar
membrane.

read francois' posts again. whether two tones close in pitch will be
perceived as two tones, or as one tone beating, depends on the time-
domain resolution. this, in turn, depends on stuff "deeper in" than
the ear drum.

right -- any slower, and you have beating/impulses, rather than
roughness.

> /.../
> Although, as mentioned above, roughness should not be
conceptualized as
> being typical of modulated sounds, in laboratory experiments it is
very
> useful to study the roughness elicited by modulated narrow-band
sounds,
> in particular, AM of sine tones. A kind of "natural" AM is provided
by beats, i.e., pairs of sine tones. This is why roughness was also
> characterized as being the auditory sensation evoked by rapid beats.
> """

yup!!

>
> >>It is generally thought that periodicity effects (harmonic
entropy)
> >>are not available to the ear for frequencies over 4 KHz. and that
> >>spectral effects (roughness) are dominant in this range. While
both
> >>spectral and periodicity effects are available below 4 KHz.,
there
> >>is reason to believe that periodicity is dominant.
> >
> >it seems you're confusing theories of pitch perception with
theories
> >of dissonance.
>
> No, I define dissonance as a failure of pitch perception. The
> dissonance terms are in parenthesis. Take them out if you don't
> like them, and everything I said is correct.

it's a matter of debate. there are still quite a few extreme
periodicity theorists, and a few extreme anti-periodicity theorists,
occupying prominent positions in the psychoacoustic community.

> >> I suspect that minimizing roughness is the primary way in which
> >> a cappella singers tune accurate JI.
> >
> >minimizing roughness to achieve simple JI ratios is exactly the
same
> >thing as minimizing beating to achieve the same simple JI ratios.
> /.../
> >> Roughness does occur between pure tones, also.
> >
> >yes, but only when they're less than a minor third apart (or
further
> >in the bass register).
>
> Right, and when do they start beating?

when the beat rate is slow enough to be made out as distinct
impulses, rather than a blurred roughness sensation. it seems that
33Hz is an acceptable generalized figure for the border between
beating and roughness, though the two effects kind of blend into one
another rather than there being a sharp boundary.

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> my pleasure:
> Beating does occur in the air.

kind of misleading . . . the air has nothing to do with it.

Back to the basic, beating is based on
> the
> exact trigonometric equation:
>
> sin( F1*t ) + sin( F2*t ) = 2 * sin( (F1+F2)*t/2 ) * cos( (F1-F2)
*t/2
> ).

> What may be difficult to understand is that even though, the right
and
> the left forms are equivalent, the time->frequency domain
> transformation that occurs in the cochlea (or in a Fourier
transform)
> "select" the left form. In other words, for any arbitrary signal,
the
> effect of the time->frequency transform is to decompose it into a
sum
> of sinus (or cosines), not a product or other combinaison of
> trigonometric function.

i don't know why you say this. clearly if F1 and F2 are close enough,
the cochlea "selects" the right form, not the left form. one hears a
single pitch, varying in amplitude at the rate F1-F2.

> The cochlea is a very cleverly designed device that transforms the
> incomming time-domain waves into a set of stationnary waves with
> maximum amplitudes on points of the basiliary membrane mapping the
> frequency domain in a fairly linear way.

right, but these 'maximum amplitude' regions can overlap
significantly, or almost entirely, if F1 and F2 are close enough.

> The amplitude of the stationnary waves obviously moves over time so
> that we perceive the time evolution of the sound. Also the auditory
> integrate information over a limited period of time that is
analogous
> to the "sliding analysis window" used in (digital) signal window.
>
> As I explained in a previous post, if the sliding window is long
> enough wrt to F2-F1, F1 and F2 are resolved as individual tones and
> the average energy in the window do not vary much over time: no
beat.
> If the sliding window is short wrt to F2-F1 (or if the difference
> between F1 and F2 is small), the amount of energy in the window vary
> over time, the beat is perceived as a time domain phenomena.

right. it is the length of the sliding window, as compared with F2-
F1, that "chooses" the left or right side of your equation. now since
this sliding window is a function of cochlea and/or brain, how on
earth can you claim that beating occurs 'in the air'?

> We can reasonnably assume that the auditory system performs its
> primary analysis simultaneously with many "window size". There is
not
> a fixed frequency or duration where, "click", the brain switch from
> one analysis mode to the other (discrete event to tone, time to
> frequency etc.). So IMHU, beat and roughness (at least wrt to
> intonation) are basically the same, but the beat is clearly
> time-domain, while the roughness is in the twilight zone where
various
> analysis modes cooperate in the auditory system. 30 ms is only a
> figure for a point somewhere in the middle of this zone.

exactly!!

> That may occur at a more or less upstream point of
> the auditory system not as a non-linear phenomena occuring in the
> middle ear or in the cochlea.

virtual pitch occurs at a higher (later) level of processing, as it
can be evoked binaurally (spectral components fed to separate ears),
while non-linear phenomena occur (mostly) *separately* in each ear.

> Am I correct to assume that "virtual pitch" and "difference tone" is
> the same thing?

no!!! they can often be slightly but measurably *different* in
pitch!! this is important for inharmonic timbres . . .

>
> Bob:
> > >minimizing roughness to achieve simple JI ratios is exactly the
> same
> > >thing as minimizing beating to achieve the same simple JI ratios.
> > /.../
> > >> Roughness does occur between pure tones, also.
>
> I suspect that roughness between pure tones can only be perceived by
> highly sophisticated and educated ears

not so! any naive ear can hear roughness between two pure tones, say
(for example) at 700 Hz and 740 Hz.

🔗emotionaljourney22 <paul@stretch-music.com>

🔗robert_wendell <rwendell@cangelic.org>

🔗francois_laferriere <francois.laferriere@oxymel.com>

I apologize for the misquotation

> Whoever this Bob is, I want to clarify that it is NOT Bob Wendell -

Carl? (not Bob):
> minimizing roughness to achieve simple JI ratios is exactly the
> same thing as minimizing beating to achieve the same simple JI
ratios.
> > > /.../
> > > >> Roughness does occur between pure tones, alsoC.
> >
> > I suspect that roughness between pure tones can only be perceived
by
> > highly sophisticated and educated ears
>
> not so! any naive ear can hear roughness between two pure tones,
say
> (for example) at 700 Hz and 740 Hz.

whoever...

I failed to make myself clear, sorry. I never questioned the fact that
roughness is perceived by everybody between off 1:1 pure tones (even
though, the exemple is slightly above the "limit" of 33Hz). My
question is about other slightly off other ratio (1:2, 3:2 and so on);
do they lead to generally perceived sensation of roughness? If so that
makes roughness a good candidate for a upper level phenomena because
it has no physical basis on interference.

By the way, the 700, 740 Hz exemple makes me realize that 33Hz is, in
middle octave, (C3 to C4) of the order of magnitude of the semitone
(in fact it varies from a full step to a semitone) amazing!!!

> Jon:
> Could anyone post the universally agreed upon definitions of both
beating and
> roughness? Beats certainly are a term that I am familiar with, as
are many
> musicians, but 'roughness' seem to be much more of a descriptor and
not a
> phenomenon or artifact.
>
> I did some playing around with soundfiles today based on Paul's
post, and will
> comment once I see that it won't devolve into semantic
circle-dancing...

I Think it may lead to interresting but not that productive
discussion. IMHO difference between beat, roughness and dissonance may
be much like difference between blue, violet and red (to not talk
about mauve, purple, lilac and magenta).

But I may be wrong, I am open to discussion ;-)

François Laferrière

🔗Carl Lumma <carl@lumma.org>

>Carl? (not Bob):

It was Paul.

>I failed to make myself clear, sorry. I never questioned the fact that
>roughness is perceived by everybody between off 1:1 pure tones (even
>though, the exemple is slightly above the "limit" of 33Hz). My
>question is about other slightly off other ratio (1:2, 3:2 and so on);
>do they lead to generally perceived sensation of roughness?

At amplitudes where difference tones are not present, roughness
between pure tones should only occur within the critical band.
It's almost the definition of roughness. There are two three things
I'll mention here, though:

() On the harmonic entropy list, when we were listening to chords of
tones with harmonic content, at least two of us reported hearing a
"warbling", "pulsing" at a rate which could only have been caused by
the presence of virtual pitches (not combination tones).

() A few experiments have found that listeners can pick out just
ratios between pure tones. Vos is a researcher who got this result, according to Paul. other experiments have found that listeners
can't pick them out (Plomp & Levelt, I think).

() According to Paul there's something called 2nd-order beating.
What's that?

> Jon:
>Could anyone post the universally agreed upon definitions of both
>beating and roughness?

Anybody?

>IMHO difference between beat, roughness and dissonance may
>be much like difference between blue, violet and red (to not
>talk about mauve, purple, lilac and magenta).

I think you meant from red to blue, but dissonance isn't high-
frequency roughness. Dissonance (or discordance) is a combination
of roughness and tonalness (or harmonic entropy).

If roughness really is high-frequency beating, I was wrong. But I
was right that difference tones aren't high-frequency beating (I
think).

-Carl

🔗jonszanto <JSZANTO@ADNC.COM>

🔗Carl Lumma <carl@lumma.org>

🔗jonszanto <JSZANTO@ADNC.COM>

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> I failed to make myself clear, sorry. I never questioned the fact
that
> roughness is perceived by everybody between off 1:1 pure tones (even
> though, the exemple is slightly above the "limit" of 33Hz). My
> question is about other slightly off other ratio (1:2, 3:2 and so
on);
> do they lead to generally perceived sensation of roughness?

no they do not (except, to a very small degree, the 1:2). look up the
classic plomp and levelt experiment -- it's the basis of the
whole 'sethares school' of dissonance theory.

> I Think it may lead to interresting but not that productive
> discussion. IMHO difference between beat, roughness and dissonance
may
> be much like difference between blue, violet and red (to not talk
> about mauve, purple, lilac and magenta).
>
> But I may be wrong, I am open to discussion ;-)

francois, please have a look at roederer's introductory book on
psychoacoustics, or hall's book _musical acoustics_ (last three
chapters), or something similar. the phenomena of beating and
roughness, at least, have been studied at great length, and are
pretty well-defined, even fairly well quantified for human
experimental subjects (yeah, i know, yucky conditions for a musician
to be concerned with, but it's something). jon szanto is right that
we need clear definitions, and while the terhardt site that i linked
to gives much of the important information, i could probably find
something more simple and concise . . . stay tuned.

🔗emotionaljourney22 <paul@stretch-music.com>

francois wrote,

> >I failed to make myself clear, sorry. I never questioned the fact
that
> >roughness is perceived by everybody between off 1:1 pure tones
(even
> >though, the exemple is slightly above the "limit" of 33Hz).

francois, above the "limit" of 33Hz, you indeed have roughness, in
fact this is more "pure" roughness, since any "beating" is too fast
to perceive as a train of distinct impulses.

> () On the harmonic entropy list, when we were listening to chords of
> tones with harmonic content, at least two of us reported hearing a
> "warbling", "pulsing" at a rate which could only have been caused by
> the presence of virtual pitches (not combination tones).

i don't remember this being our conclusion. could you point us to
this discussion again? perhaps on the harmonic entropy list
itself . . .

> () A few experiments have found that listeners can pick out just
> ratios between pure tones. Vos is a researcher who got this
result, according to Paul. other experiments have found that
listeners
> can't pick them out (Plomp & Levelt, I think).

neither experiment concerned "picking them out". but you're right,
vos found "purity maxima" for pure tones at 2:3 and 4:5, while plomp
and levelt didn't find "roughness minima" for pure tones at these
ratios. perhaps differing experimental conditions, particularly
different amplitude levels (which have a non-linear impact on the
amplitudes of the combinational tones) explain why the results were
different.

> () According to Paul there's something called 2nd-order beating.
> What's that?

it's a sort of beating which is due to higher-level neural processing
in the brain (and is thus perceptible for two tones presented
separately to the ears), rather than the usual critical-band-induced
mechanism within each ear. check out roederer's introductory book, if
at all possible -- then follow up with the references roederer
provides, if you're interested . . .

> > Jon:
> >Could anyone post the universally agreed upon definitions of both
> >beating and roughness?
>
> Anybody?

i'll look into it!

> If roughness really is high-frequency beating, I was wrong. But I
> was right that difference tones aren't high-frequency beating (I
> think).

yes, you're right. i've been discussing this with bob offline, and he
agrees that the two aren't the same thing, though he's never heard
the latter without also hearing the former. the non-linearities that
create difference tones are inescapable, in his view. i noted to him
that, according to the research i perused, the only combinational
tone that does not rapidly vanish in amplitude for decreasing input
levels, is the cubic 2a-b combinational tone, but this was for some
particular range of intervals, and for sine tones rather than the
harmonic-rich human voices bob is used to working with.