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Sampling rates higher than 44.1Khz?
WmAx
post Feb 9 2006, 15:32
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QUOTE (bug80 @ Feb 9 2006, 05:48 AM)
QUOTE (WmAx @ Feb 9 2006, 07:22 AM)
Did you note the relative level of the intermodulated product? It was only a few dBs above the noisefloor, when I generated the 30kHz and 32kHz tones at -3dBFs!
*

So you added two sine waves with an amplitude of -3dBFs? In that case the result will clip and that may explain the tone you heard..
*



I am sorry, I made a typo earlier. The final waveform peak amplitude as viewed after mixing the two signals was -3dBFs, not the two individual signals before mixing. Please note that the 2kHz *tone* was not audible unless very specific conditions were present, as I previously specified.

-Chris

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krabapple
post Feb 9 2006, 18:13
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more on the 'beating' issue, from James Johnston:

A Graphical Explanation involving Sampling
http://www.audioasylum.com/audio/general/messages/43134.html

Opener:
"The questions about modulation of sine waves near the Nyquist limit seem to be common and repeated. The image URL here has a plot that, I think, explains how the "beating" comes about due to adding in frequencies that are solely above the Nyquist limit, and thus how filtering them out removes any "beating" one observes in raw, unfiltered data from a DAC (before the anti-imaging filter)."
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SebastianG
post Feb 9 2006, 18:17
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QUOTE (Grand Dizzy @ Feb 8 2006, 11:06 PM)
This thread is fascinating! But most of it is too techy for me unfortunately.

Could anyone try again to explain how these byproduct tones/beats come about? And what is the low pass filter's involvement in this? (What is a low pass filter anyway?)
*

Fascinating? Hmm.... May seem so. But I think that some posts here are actually a bit misleading/misinformed.

QUOTE (hdante @ Feb 7 2006, 10:27 PM)
QUOTE (SebastianG @ Feb 7 2006, 04:29 PM)

Why may I hear something like that ?
*

[...] Mathematically, cos(32KHz)+cos(30KHz) = 2*cos(31KHz)*cos(1KHz). Add the time in equation and you have a 1 KHz harmonic with a variable intensity of 2*cos(31KHz*t). [...]
*


So what ? Just because there's suddenly a cos(1kHz*t) in a product you think you should be able to hear this one? Do you realize that you can also interpret your formula as a 31 kHz sinusoid with an amplitude modulation at a rate of 1 kHz ? Truth is: It does not matter whether a product representation contains usually audible signals. The first form (cos(32kHz)+cos(30kHz)) is the really interesting one. Why ? Because we've a bunch of filters in our inner ear (hair + hair cell) seperating frequencies -- every hair (depending on its location/length) has a certain resonance frequency and acts like a bandpass filter. From signal theory we know such filters are linear and time-invariant (LTI system theory, please check the linearity property on this site).
The linearity suggests that if you can't hear a single tone at 30 or 32 kHz, you also cannot hear anything when cos(30kHz*t)+cos(32kHz*t) is "in the air".


QUOTE (mandel @ Feb 7 2006, 11:51 PM)
That's really interesting actually.  I just created a 96khz wav file with a 30k and a 32k tone and could hear a beat frequency as you say.  Though at 2khz not 1khz
*

This is likely due to one of these things:
- improper anti alias filtering of your sound reproduction system
- non-linear distortions of your sound reproduction system (including clipping)


edit: typos

HTH,
Sebi

This post has been edited by SebastianG: Feb 9 2006, 18:22
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hdante
post Feb 9 2006, 18:34
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There's too much interpreting here. I've found a "third-party" argument which mirrors my original statement and I hope it is pretty understandable. However, I insist that the 2 KHz was wrong and 1 KHz would be the correct result (there's the same error in the quote that follows).


QUOTE (mika @ music player)
(...)
3. The third theory of recording at 96kS/s has to do with high frequency information during the mixing process.

Whenever two audio signals are combined, the result is a harmonic structure that produces additional frequencies as a combination of the summing of the two. If a note is played at 100Hz and another is played at 150Hz, there will be two additional frequencies produced as a result. One at 50 Hz (B-A) and the other at 250Hz (B+A). It is the first - the subtractive - that we shall discuss here. If two frequencies are produced at 30k and 45k, the effect will produce a harmonic overtone at 15k - well within the human hearing spectrum (at least for those of us in our 20's).

While this 15k signal would be picked up on a microphone in the room during a live classical performance, the issue has to do with multitrack performances where the music was tracked on separate microphones in isolated facilities. There would be no opportunity for this high frequency information to be mixed and reproduce these lower harmonic overtones because at 44.1k, the highest frequency recordable is at about 22k.

Theoretically, if we put two oscillators in a room - one at 30k and one at 45k, a microphone would pick up a 15k harmonic that we could hear. If we had the same oscillators in different rooms and recorded them both at 44.1k and mixed them we would not hear this phenomena. If, however, we recorded them at 96k (assuming the filters on the converters rolled off at 48k and not earlier) and mixed them we would once again hear this 15k overtone. This is supposedly an example of where recording and mixing at 96k can achieve different sonic characteristics even if the recording was to be reproduced on a 48k medium. The overtones discussed above would be produced in the mixing process and would endure the downsampling process.

Upon trying to put together this test I had a difficult time finding scientific enough equipment to produce and measure these frequencies. The theory is plausable, but the effect would be fairly minimal as these overtones are at very low amplitude. Regardless, the theory has a chance of holding water if a valid test can be done. I have heard of no such tests. Perhaps we could Roger to oblige us.
(...)



The text is at http://www.musicplayer.com/ubb/Forum2/HTML/001473.html
There's a link there with info about some instruments harmonics. (There's life above 20 kilohertz). By visual inspection, the article doesn't talk about the cited argument. However, it seems to have info on the amount of energy many instruments have above 20 KHz, which may be interesting for those who were considering that the effect (which could be a feature, not a bug) is unlistenable.
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krabapple
post Feb 9 2006, 18:45
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JJ again , at even greater length and detail, on high frequencies in audio and other matters generally. I see he even engaged 'RockFan' (who was on this thread earlier)
on pretty much the same issues he's brought up. Whihc makes me believe there's llittle point arguing them further.

http://www.skepticforum.com/viewtopic.php?...6385681595377ed

(For those unaware, Mr. Johnston, retired from Bell/ATT labs, was a co-inventor of MP3)

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hdante
post Feb 9 2006, 18:46
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QUOTE (SebastianG @ Feb 9 2006, 03:17 PM)
So what ? Just because there's suddenly a cos(1kHz*t) in a product you think you should be able to

I'm not thinking anything, I'm just repeating what I've just read.

QUOTE (SebastianG @ Feb 9 2006, 03:17 PM)
hear this one? Do you realize that you can also interpret your formula as a 31 kHz sinusoid with an amplitude modulation at a rate of 1 kHz ? Truth is: It does not matter whether a product
representation contains usually audible signals. The first form (cos(32kHz)+cos(30kHz)) is the really interesting one. Why ? Because we've a bunch of filters in our inner ear (hair + hair cell) seperating

Remember that when we want to tune a guitar, if we have a reference (tuned) string, we tune the others by listening to the beating. And I believe that music professionals may also tune it by listening to the deviating mean frequency. Both things are at the right side of the equation, not the linear one. I can surely tune a guitar by listening to the beatings. If the beating is non-linear so what ? I listen to it.
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bug80
post Feb 9 2006, 18:54
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QUOTE (hdante @ Feb 9 2006, 07:46 PM)
Remember that when we want to tune a guitar, if we have a reference (tuned) string, we tune the others by listening to the beating. And I believe that music professionals may also tune it by listening to the deviating mean frequency. Both things are at the right side of the equation, not the linear one. I can surely tune a guitar by listening to the beatings. If the beating is non-linear so what ? I listen to it.
*

Yes that's correct. BUT the beating we hear is not a "tone" it is the actual tone going up and down in amplitude. So if we can't hear the original tone, we also cannot hear it changing in amplitude. So you cannot hear a 32 kHz tone "beating".

In other words you can hear the following (the 1 kHz tone, at least):

(tone of 32 kHz) + (tone of 1 kHz)

but you can NOT hear the following (which is the case here):

(tone of 32 kHz) * (tone of 1 kHz)

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ChiGung
post Feb 9 2006, 19:00
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QUOTE (hdante @ Feb 9 2006, 05:34 PM)
QUOTE (mika @ music player)
(...)
Whenever two audio signals are combined, the result is a harmonic structure that produces additional frequencies as a combination of the summing of the two. If a note is played at 100Hz and another is played at 150Hz, there will be two additional frequencies produced as a result. One at 50 Hz (B-A) and the other at 250Hz (B+A). It is the first - the subtractive - that we shall discuss here. If two frequencies are produced at 30k and 45k, the effect will produce a harmonic overtone at 15k - well within the human hearing spectrum (at least for those of us in our 20's).

laugh.gif That is quite nonsense Im afraid hdante. The poster is roughly calculating beat frequencies between tones and confusing them with new tones that have the frequency of the beat. Mind a beat in a tone (or between tones) is definitely not a new tone and doesnt 'look' like a tone in a PCM record or sound like tone in RL. SebG put it like this:
QUOTE
you can also interpret your formula as a 31 kHz sinusoid with an amplitude modulation at a rate of 1 kHz

(the amplitude modulation can be seen in the pcm record as a 2kHz pulsing of the tone.)

Now sebG is one of those who doesnt like people talking about this stuff or attempting to enquire outside of contemporary academic language and references, hence this statement:
QUOTE
Fascinating? Hmm.... May seem so. But I think that some posts here are actually a bit misleading/misinformed.

Unfortunately hes not been inspired to actualy point out any particular misleads or misinforms -which are par for the course in open forum whatever the Tos. And I fear if him or his like do choose to elaborate it will be in a frustrated manner, so watch out for that wink.gif

good luck'

This post has been edited by ChiGung: Feb 9 2006, 19:01


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bug80
post Feb 9 2006, 19:08
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Here is a little Matlab code for anyone who likes to try the experiment of adding two ultra sonic tones. Make sure your hardware supports a sampling rate of 96 kHz.

I heard a tone, by the way, which is probably due to imperfections (non-linearities) in my hardware (the speakers for example).

Warning: be carefull with cranking up the volume, this is generally not good for hi-fi equipment.

CODE
% Ulta-sonic experiment

Fs = 96000;                 % Sampling frequency

f1 = 25000;                  % Frequency of 1st tone
f2 = 26000;                  % Frequency of 2nd tone

T = 5;                      % Length of signal
A = -6;                     % Amplitude (dB)

% Construct tones
N = round(T * Fs);          % # samples
t = (0:N-1)' / Fs;          % Time axis

B = 0.5 * 10^(A/20);        % Amplitude per tone
p1 = B * sin(2*pi*f1*t);
p2 = B * sin(2*pi*f2*t);

p = p1 + p2;                % Total tone

sound(p,Fs)


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ChiGung
post Feb 9 2006, 19:11
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QUOTE (bug80 @ Feb 9 2006, 06:08 PM)
Here is a little Matlab code for anyone who likes to try the experiment of adding two ultra sonic tones. Make sure your hardware supports a sampling rate of 96 kHz.

I heard a tone, by the way, which is probably due to imperfections in my hardware (the speakers for example).

If its handy, could you try it at 24bits? If not ill try later.


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bug80
post Feb 9 2006, 19:15
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QUOTE (ChiGung @ Feb 9 2006, 08:11 PM)
QUOTE (bug80 @ Feb 9 2006, 06:08 PM)
Here is a little Matlab code for anyone who likes to try the experiment of adding two ultra sonic tones. Make sure your hardware supports a sampling rate of 96 kHz.

I heard a tone, by the way, which is probably due to imperfections in my hardware (the speakers for example).

If its handy, could you try it at 24bits? If not ill try later.
*


My Matlab version (6.1) doesn't support 24 bits for the 'sound' command. I could try to use the DAQ toolbox, though, but I don't really feel like it because I know we cannot hear the beating as a "tone" anyway smile.gif
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ChiGung
post Feb 9 2006, 19:21
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QUOTE (bug80 @ Feb 9 2006, 06:15 PM)
QUOTE (ChiGung @ Feb 9 2006, 08:11 PM)
QUOTE (bug80 @ Feb 9 2006, 06:08 PM)
Here is a little Matlab code for anyone who likes to try the experiment of adding two ultra sonic tones. Make sure your hardware supports a sampling rate of 96 kHz.

I heard a tone, by the way, which is probably due to imperfections in my hardware (the speakers for example).

If its handy, could you try it at 24bits? If not ill try later.
*


My Matlab version (6.1) doesn't support 24 bits for the 'sound' command. I could try to use the DAQ toolbox, though, but I don't really feel like it because I know we cannot hear the beating as a "tone" anyway smile.gif
*


Ok, ill try with audacity. I think it might be coming from rounding error...


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bug80
post Feb 9 2006, 19:25
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QUOTE (ChiGung @ Feb 9 2006, 08:21 PM)
QUOTE (bug80 @ Feb 9 2006, 06:15 PM)
QUOTE (ChiGung @ Feb 9 2006, 08:11 PM)
QUOTE (bug80 @ Feb 9 2006, 06:08 PM)
Here is a little Matlab code for anyone who likes to try the experiment of adding two ultra sonic tones. Make sure your hardware supports a sampling rate of 96 kHz.

I heard a tone, by the way, which is probably due to imperfections in my hardware (the speakers for example).

If its handy, could you try it at 24bits? If not ill try later.
*


My Matlab version (6.1) doesn't support 24 bits for the 'sound' command. I could try to use the DAQ toolbox, though, but I don't really feel like it because I know we cannot hear the beating as a "tone" anyway smile.gif
*


Ok, ill try with audacity. I think it might be coming from rounding error...
*


In that case I would expect a noise-like sound instead of something that sounds like a composition of several pure tones. But still you can try to do it in Audacity. smile.gif
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SebastianG
post Feb 9 2006, 19:25
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QUOTE (ChiGung @ Feb 9 2006, 07:00 PM)
Unfortunately hes not been inspired to actualy point out any particular misleads or misinforms -which are par for the course in open forum whatever the Tos. And I fear if him or his like do choose to elaborate it will be in a frustrated manner, so watch out for that wink.gif
*


I consider "if you play cos(30kHz*t)+cos(32kHz*t) you also may hear cos(1kHz) because cos(30kHz*t)+cos(32kHz*t) = 2*cos(31kHz)*cos(1kHz)" to be misinformation.

I consider "That's really interesting actually. I just created a 96khz wav file with a 30k and a 32k tone and could hear a beat frequency as you say. Though at 2khz not 1khz" to be misleading. Although that may be the case it may lead ppl to think that what hdante said is true whereas the reasons for mandel hearing something is likely related to non-linear distortions or improper D/A conversion.

I might have exaggerated things though. tongue.gif

Sebi
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hdante
post Feb 9 2006, 19:39
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QUOTE (ChiGung @ Feb 9 2006, 04:00 PM)
laugh.gif That is quite nonsense Im afraid hdante. The poster is roughly calculating beat frequencies between tones and confusing them with new tones that have the frequency of the beat. Mind a beat in


Ok, I think we reached the point. What the two links I posted here (about which I've realised my unfortunate belief that they were authoritative) are probably sugesting is that the beat is what is outside the hearing limits, while the tone is what is inside the hearing limits.

The beat, in the guitar tuning sense, is what is off the low hearing limit (eg 5Hz). The beat, in the ultra sonic sense is what is above the high hearing limit, (eg 31 KHz).

About the thing with Sebastian, I've just confirmed. At 440 Hz + 450 Hz I do listen both the 445 Hz tone and the beating.

Now you, ear engineers, say something about those.

Henrique Dante de Almeida
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ChiGung
post Feb 9 2006, 19:40
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Points well made sebG - seems you are cool blush.gif

-Tried 24 bits in audacity, the noise was even louder than with mandels 16bit file. Could be audacity, my laptop sound card or anything.

Seems the exact cause of this noise is intractable to me, but the well learned ones I think would agree that it is an artifact and shouldnt be heard in ideal circumstances.

many regards'


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hdante
post Feb 9 2006, 19:42
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QUOTE (SebastianG @ Feb 9 2006, 04:25 PM)
I consider "if you play cos(30kHz*t)+cos(32kHz*t) you also may hear cos(1kHz) because cos(30kHz*t)+cos(32kHz*t) = 2*cos(31kHz)*cos(1kHz)" to be misinformation.

I consider "That's really interesting actually. I just created a 96khz wav file with a 30k and a 32k tone and could hear a beat frequency as you say. Though at 2khz not 1khz" to be misleading. Although that may be the case it may lead ppl to think that what hdante said is true whereas the reasons for mandel hearing something  is likely related to non-linear distortions or improper D/A conversion.

I might have exaggerated things though.  tongue.gif

Sebi
*


If you read more carefully, I have already stated that I don't believe that the 2 KHz is correct. I understand that you are able to realise that I think it's a bug in his headphones or something.
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hdante
post Feb 9 2006, 19:45
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QUOTE (ChiGung @ Feb 9 2006, 04:21 PM)
Ok, ill try with audacity. I think it might be coming from rounding error...
*


As long as anyone here doesn't own a 96 KHz ready studio, we'll have a hard time doing this.
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bug80
post Feb 9 2006, 19:51
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QUOTE (hdante @ Feb 9 2006, 08:39 PM)
Ok, I think we reached the point. What the two links I posted here (about which I've realised my unfortunate belief that they were authoritative) are probably sugesting is that the beat is what is outside the hearing limits, while the tone is what is inside the hearing limits.

Sorry, I do not think those articles are very authoritative. smile.gif

QUOTE
About the thing with Sebastian, I've just confirmed. At 440 Hz + 450 Hz I do listen both the 445 Hz tone and the beating.

And how exactly did you do that? If you add two tones of 440 Hz and 450 Hz you should not end up with a 445 Hz tone, since addition is linear. You should hear a superposition of both tones (you should hear them both at once), plus a beating effect, which is again just a temporal change in amplitude, not in frequency.

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ChiGung
post Feb 9 2006, 19:55
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QUOTE (hdante @ Feb 9 2006, 06:45 PM)
QUOTE (ChiGung @ Feb 9 2006, 04:21 PM)
Ok, ill try with audacity. I think it might be coming from rounding error...
*


As long as anyone here doesn't own a 96 KHz ready studio, we'll have a hard time doing this.
*


Not really, high quality equipment shouldnt theoreticaly make the noise.
Its made in by laptop and desktops sound chipset alright.
Seems a good advertisement for not using high samplerate on standard equipment.

Just reminded' maybe take the samples offline, could burn out a few tweeters with passing noobs playing them louder and louder to see if they have the noise ?


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hdante
post Feb 9 2006, 19:58
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QUOTE (bug80 @ Feb 9 2006, 04:51 PM)
And how exactly did you do that? If you add two tones of 440 Hz and 450 Hz you should not end up with a 445 Hz tone, since addition is linear. You should hear a superposition of both tones (you should hear them both at once), plus a beating effect, which is again just a temporal change in amplitude, not in frequency.
*


You may try it also.
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bug80
post Feb 9 2006, 20:06
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QUOTE (hdante @ Feb 9 2006, 08:58 PM)
QUOTE (bug80 @ Feb 9 2006, 04:51 PM)
And how exactly did you do that? If you add two tones of 440 Hz and 450 Hz you should not end up with a 445 Hz tone, since addition is linear. You should hear a superposition of both tones (you should hear them both at once), plus a beating effect, which is again just a temporal change in amplitude, not in frequency.
*


You may try it also.
*


I did and I absolutely don't have a clue what you're talking about. I can even give you the spectral results in a figure. If you add two tones with different frequencies, you end up with a superposition of those tones. That's all there is to it.
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hdante
post Feb 9 2006, 20:09
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QUOTE (bug80 @ Feb 9 2006, 05:06 PM)
I did and I absolutely don't have a clue what you're talking about. I can even give you the spectral results in a figure. If you add two tones with different frequencies, you end up with a superposition of those tones. That's all there is to it.
*


I meant listen to it. Listen to a 440 Hz tone, listen to a 445 tone, listen to a 450 tone, an then listen to a 440+450 tone.
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bug80
post Feb 9 2006, 20:16
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QUOTE (hdante @ Feb 9 2006, 09:09 PM)
QUOTE (bug80 @ Feb 9 2006, 05:06 PM)
I did and I absolutely don't have a clue what you're talking about. I can even give you the spectral results in a figure. If you add two tones with different frequencies, you end up with a superposition of those tones. That's all there is to it.
*


I meant listen to it. Listen to a 440 Hz tone, listen to a 445 tone, listen to a 450 tone, an then listen to a 440+450 tone.
*


... yes? I still hear a 440 and a 450 tone together? It is hard to discriminate what the frequency of the highest note is, however, because of an effect called masking in the frequency domain which is a psychoacoustic effect, quite different from the "beating" effect what you were talking about earlier.

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hdante
post Feb 9 2006, 20:23
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QUOTE (bug80 @ Feb 9 2006, 05:16 PM)
... yes? I still hear a 440 and a 450 tone together? It is hard to discriminate what the frequency of the highest note is, however, because of an effect called masking in the frequency domain which is a psychoacoustic effect, quite different from the "beating" effect what you were talking about earlier.
*


I'm sorry, I hear the base frequency above 440 Hz. I may take that back, however. I may keep with the beat, only.
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