fake bass and the missing fundamental

This is probably not the right group, but a lot of people here seem
pretty deep in acoustics, so I'll proceed ...

The ear has a characteristic that if you ply a series of harmonically-
related tones but leave out the fundamental, the brain will fill it in
for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
will perceive the missing fundamental at 25 Hz. Many bass-enhancement
algorithms use this trick (although one has to question what happens
in the case where the bass energy is not single-frequency!).

What I would like to know is how far up in frequency this effect
occurs. It seems as if the ear transitions from waveform mode at low
frequencies to envelope mode at higher frequencies, so it seems
doubtful that the missing fundamental effect still occurs at higher
frequencies. For example, if I mix 2Hz, 3KHz and 4 KHz do I hear 1
KHz?

Thanks for any replies!

Bob Adams

Robert Adams wrote:
> This is probably not the right group, but a lot of people here seem
> pretty deep in acoustics, so I'll proceed ...
> 
> The ear has a characteristic that if you ply a series of harmonically-
> related tones but leave out the fundamental, the brain will fill it in
> for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
> will perceive the missing fundamental at 25 Hz. Many bass-enhancement
> algorithms use this trick (although one has to question what happens
> in the case where the bass energy is not single-frequency!).
> 
> What I would like to know is how far up in frequency this effect
> occurs. It seems as if the ear transitions from waveform mode at low
> frequencies to envelope mode at higher frequencies, so it seems
> doubtful that the missing fundamental effect still occurs at higher
> frequencies. For example, if I mix 2Hz, 3KHz and 4 KHz do I hear 1
> KHz?

That's an interesting ponder-piece. I just played a C-E-G chord on the 
piano. No lower notes popped out at me.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Robert Adams wrote:

> This is probably not the right group, but a lot of people here seem
> pretty deep in acoustics, so I'll proceed ...
> 
> The ear has a characteristic that if you ply a series of harmonically-
> related tones but leave out the fundamental, the brain will fill it in
> for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
> will perceive the missing fundamental at 25 Hz.

Just another audio fallacy. Dissmiss it.
If some people eagerly want the things to work in that way, it doesn't 
mean the things actually work in that way.
You can get peculiar effects by mixing the frequencies, but it is not 
the same thing as the fundamental.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Vladimir Vassilevsky wrote:
> 
> 
> Robert Adams wrote:
> 
>> This is probably not the right group, but a lot of people here seem
>> pretty deep in acoustics, so I'll proceed ...
>>
>> The ear has a characteristic that if you ply a series of harmonically-
>> related tones but leave out the fundamental, the brain will fill it in
>> for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
>> will perceive the missing fundamental at 25 Hz.
> 
> Just another audio fallacy. Dissmiss it.
> If some people eagerly want the things to work in that way, it doesn't 
> mean the things actually work in that way.
> You can get peculiar effects by mixing the frequencies, but it is not 
> the same thing as the fundamental.
> 


The "fundamental" may be the wrong term in many cases, but this is a 
genuine phenomenon. It is relied upon by orchestral wind players (such 
as myself) to ensure the whole section is in tune. It is also (as I 
think I may have mentioned before) how we can hear pseudo-bass notes out 
of a tiny lofi speaker (as in a small portable radio).

It is called a "resultant tone" or a "difference tone". I demonstrate it 
to my flute students at their first lesson.  It requires tones 
sufficiently pure, and sufficiently powerful, and sufficiently high 
(e.g. C and E 2 octaves above middle C) . It also requires sufficient 
control over pitch to overcome the inherently out-of-tuneness of equal 
temperament. If the notes we are playing comprise any of the first six 
natural harmonics, the pseudo-fundamental will be very apparent (in this 
example - middle C itself). Unless we play our notes according to 
natural tuning (i.e. ~pure~ thirds, etc), that bass resultant tone will 
be horribly out of tune with other instruments playing it. Once we 
depart from these intervals, the resultant tone become more complex, and 
less immediately related to a fundamental or even to notes of the scale. 
In particular, chords such as the diminished seventh chord (four notes 
separated by minor thirds) as a whole universe of resultant tones, 
giving an inevitably disturbing feeling (usually the whole point of that 
chord).

However, the good news is that except for these higher notes, the 
resultant tones are too low ( i.e. within the "critical bandwidth") to 
be heard as pitches; instead they just give a sort of muddying quality 
to the sound. This is why in good orchestration, low notes are widely 
spaced, and upper notes can be much closer together. So while in theory 
you will get that 24Hz resultant tone as suggested, it is borderline 
below our perception of pitch, and we will be more aware of that 
muddiness. The notes would have to be at a fairly high SPL to get the 
effect, which would also be very uncomfortable.

I suggest getting some musicians to demonstrate all this to you (I will 
do so myself, for the usual fee and expenses), before dismissing it as a 
"fallacy".

Richard Dobson

Jerry Avins wrote:
..
> 
> That's an interesting ponder-piece. I just played a C-E-G chord on the 
> piano. No lower notes popped out at me.
> 
> Jerry

See my other post. The piano is not a suitable instrument to test this 
- inherently out of tune (the dreaded Equal temperament - the pipe organ 
presents similar problems  here), and the noes are not strong enough to 
give the effect. You need sustained tones, upper-mid frequency range.
Synthesise two tones at 1000Hz and 1250, and play them back at a decent 
level, and you should, hear the low fundamental clearly (a flat middle C).

Richard Dobson

Richard Dobson  <richarddobson@blueyonder.co.uk> wrote:

>Vladimir Vassilevsky wrote:

>> Robert Adams wrote:

>>> The ear has a characteristic that if you ply a series of harmonically-
>>> related tones but leave out the fundamental, the brain will fill it in
>>> for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
>>> will perceive the missing fundamental at 25 Hz.

>> Just another audio fallacy. Dissmiss it.

>The "fundamental" may be the wrong term in many cases, but this is a 
>genuine phenomenon. It is relied upon by orchestral wind players (such 
>as myself) to ensure the whole section is in tune. It is also (as I 
>think I may have mentioned before) how we can hear pseudo-bass notes out 
>of a tiny lofi speaker (as in a small portable radio).

So far as I can tell, informally, it's a true phenomenom.

I wonder what standards of proof of this effect would be
accepted by Vladimir?  (Double-blind studies, perhaps?)

Steve

On Jul 3, 4:13�pm, spop...@speedymail.org (Steve Pope) wrote:
> Richard Dobson &#4294967295;<richarddob...@blueyonder.co.uk> wrote:
>
> >Vladimir Vassilevsky wrote:
> >> Robert Adams wrote:
> >>> The ear has a characteristic that if you ply a series of harmonically-
> >>> related tones but leave out the fundamental, the brain will fill it in
> >>> for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
> >>> will perceive the missing fundamental at 25 Hz.
> >> Just another audio fallacy. Dissmiss it.
> >The "fundamental" may be the wrong term in many cases, but this is a
> >genuine phenomenon. It is relied upon by orchestral wind players (such
> >as myself) to ensure the whole section is in tune. It is also (as I
> >think I may have mentioned before) how we can hear pseudo-bass notes out
> >of a tiny lofi speaker (as in a small portable radio).
>
> So far as I can tell, informally, it's a true phenomenom.
>
> I wonder what standards of proof of this effect would be
> accepted by Vladimir? &#4294967295;(Double-blind studies, perhaps?)
>
> Steve

Thanks for the replies. I have heard the effect working at low
frequencies; I just didn't know if it works at high frequencies as
well.

But I have a bit of a problems when it comes to using this effect to
get an increase in apparent bass response from a small speaker. If all
bass energy were single tones, then I could see that adding some
harmonics might give the perception of a lower tone. However, unless
you listen exlusively to pipe-organ music (ei, you are a very lonely
guy), it seems that if you apply a more typical complex spectrum to a
non-linearity designed to produce harmonics, it will just make a big
mess of intermodulation tones, which will make for very muddy bass.
But maybe the saving grace is that there ear has pretty poor
resolution at these low frequencies, so it's hard to distinguish band-
limited intermod products from actual low-frequency signal content.

However, my guess is that if you tried this trick with very small
speakers at much higher frequencies, the intermod products would NOT
be negligable. In other words, you can add harmonics to a 50Hz tone to
make it through a speaker that can't repoduce 50Hz, but I doubt the
same effect applies at 500Hz without severe audible artifacts.


Bob

On Jul 3, 1:10&#4294967295;pm, Richard Dobson <richarddob...@blueyonder.co.uk>
wrote:
> Jerry Avins wrote:
>
> ..
>
>
>
> > That's an interesting ponder-piece. I just played a C-E-G chord on the
> > piano. No lower notes popped out at me.
>
> > Jerry
>
> See my other post. The piano is not a suitable instrument to test this
> - inherently out of tune (the dreaded Equal temperament - the pipe organ
> presents similar problems &#4294967295;here), and the noes are not strong enough to
> give the effect. You need sustained tones, upper-mid frequency range.
> Synthesise two tones at 1000Hz and 1250, and play them back at a decent
> level, and you should, hear the low fundamental clearly (a flat middle C).
>
> Richard Dobson

Don't you just love it when musicians spout total crap!

On Fri, 3 Jul 2009 13:57:46 -0700 (PDT), HardySpicer <gyansorova@gmail.com> wrote:

>On Jul 3, 1:10&#4294967295;pm, Richard Dobson <richarddob...@blueyonder.co.uk>
>wrote:
>> Jerry Avins wrote:
>>
>> > That's an interesting ponder-piece. I just played a C-E-G chord on the
>> > piano. No lower notes popped out at me.
>>
>> > Jerry
>>
>> See my other post. The piano is not a suitable instrument to test this
>> - inherently out of tune (the dreaded Equal temperament - the pipe organ
>> presents similar problems &#4294967295;here), and the noes are not strong enough to
>> give the effect. You need sustained tones, upper-mid frequency range.
>> Synthesise two tones at 1000Hz and 1250, and play them back at a decent
>> level, and you should, hear the low fundamental clearly (a flat middle C).
>>
>> Richard Dobson
>
>Don't you just love it when musicians spout total crap!

Without wanting to put words in Richard's mouth, I would assume he refers (in part) to the
fact that at "decent" levels, the 250 Hz really is heard (intermodulation product) rather
than being filled in by the brain. We all need to continue to cut musos some slack - many
genuinely want to be more technically aware, but  their information comes from a mountain
of crap created by other musos, and it just gets messier and messier.
Tony

Steve Pope wrote:
> Richard Dobson  <richarddobson@blueyonder.co.uk> wrote:
> 
> 
>>Vladimir Vassilevsky wrote:
>>>Robert Adams wrote:
> 
> 
>>>>The ear has a characteristic that if you ply a series of harmonically-
>>>>related tones but leave out the fundamental, the brain will fill it in
>>>>for you; in other words, if you mix 50Hz, 75Hz, and 100Hz together you
>>>>will perceive the missing fundamental at 25 Hz.
> 
> 
>>>Just another audio fallacy. Dissmiss it.
> 
> 
>>The "fundamental" may be the wrong term in many cases, but this is a 
>>genuine phenomenon. It is relied upon by orchestral wind players (such 
>>as myself) to ensure the whole section is in tune. It is also (as I 
>>think I may have mentioned before) how we can hear pseudo-bass notes out 
>>of a tiny lofi speaker (as in a small portable radio).
> 
> 
> So far as I can tell, informally, it's a true phenomenom.
> 
> I wonder what standards of proof of this effect would be
> accepted by Vladimir?  (Double-blind studies, perhaps?)

It is not possible to get a real bass from a small speaker by doing some 
sort of DSP black magic with harmonics. No matter what the authors of 
the "bass enhancers" are trying to claim. Although it is possible to 
create interesing audio effects that could entertain the listener for 
some time. The value of those effects is in reducing of the listener 
fatigue. Once you tired of listening the music, you can engage some 
audio effect and this makes the "new" sound. But the effect can't 
replace what is not reproduced.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com