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nyquist responce theory useless Condenser Microphones
Old 6th May 2006
  #1
Gear Head
 

nyquist responce theory useless

The only thing it is telling us is weather the given rate of sampling is enough to know that there is something there, but it has no idea what.

if we have a singwave at 11khz recording at 44khz it would not appear as a sign wave to our eyes or ears. It is limited to useing 3 points of reference (in a single rize and fall) to understand the signal.
the best it can do with 11khz is when the sampling is perfeclty aligned with 0 amplitude of the signal. this would create a rectangular type wave with a roof simular to the outline of a house/circus tent. However if the time of sampling is not in line with the signal at 0 amplitude it would produce an irregular shaped house with the same pattern and if the signal is modulateing slightley between frequencies we would get all sorts of irregular shapes between rise and fall and we would never know what we where looking at in those frequencies except irregular shaped patterns of different form.
However sometimes it is not the qulity of the sound that suffers it is our ears and mind! Our brain deciphers these irregularities to know what is going on in the signal if it is held long enough. short burts of recorded material always sound harsher on digital than long notes as the brain doesn't have the time to deciphere between the irregularities.

If less interaction is required form the listeners brain to understand the signal the more interaction they can have with the feeling of the music.
However the brain can also block its interaction with the higher frequencies that require to much interaction to understand and continue enjoying the music. this creates a lack of continuity because as they begin opening up their feelings wich are at many levels of frequencey the block stopes them in their tracks. the brain can provide that continuity especially if a person knows a song. gennerally though the less interaction = more effect.
Old 6th May 2006
  #2
Lives for gear
 
T.RayBullard's Avatar
 

probably should be in the Geekslutz forum.

Quote:
Originally Posted by Feelingsat24khz
The only thing it is telling us is weather the given rate of sampling is enough to know that there is something there, but it has no idea what.

if we have a singwave at 11khz recording at 44khz it would not appear as a sign wave to our eyes or ears. It is limited to useing 3 points of reference (in a single rize and fall) to understand the signal.
the best it can do with 11khz is when the sampling is perfeclty aligned with 0 amplitude of the signal. this would create a rectangular type wave with a roof simular to the outline of a house/circus tent. However if the time of sampling is not in line with the signal at 0 amplitude it would produce an irregular shaped house with the same pattern and if the signal is modulateing slightley between frequencies we would get all sorts of irregular shapes between rise and fall and we would never know what we where looking at in those frequencies except irregular shaped patterns of different form.
However sometimes it is not the qulity of the sound that suffers it is our ears and mind! Our brain deciphers these irregularities to know what is going on in the signal if it is held long enough. short burts of recorded material always sound harsher on digital than long notes as the brain doesn't have the time to deciphere between the irregularities.

If less interaction is required form the listeners brain to understand the signal the more interaction they can have with the feeling of the music.
However the brain can also block its interaction with the higher frequencies that require to much interaction to understand and continue enjoying the music. this creates a lack of continuity because as they begin opening up their feelings wich are at many levels of frequencey the block stopes them in their tracks. the brain can provide that continuity especially if a person knows a song. gennerally though the less interaction = more effect.
Old 6th May 2006
  #3
Gear Head
 

Quote:
Originally Posted by Feelingsat24khz
The only thing it is telling us is weather the given rate of sampling is enough to know that there is something there, but it has no idea what.
No, it tells us that to describe a sine wave you need at least two samples per cycle. So with CD-style sampling at 44.1kHz you can't describe a sine wave with higher frequency than 22kHz.

Quote:
Originally Posted by Feelingsat24khz
if we have a singwave at 11khz recording at 44khz it would not appear as a sign wave to our eyes or ears. It is limited to useing 3 points of reference (in a single rize and fall) to understand the signal.
No, a sine wave at 11kHz can be perfectly reconstructed from a sampling at 44.1kHz. Note the word RECONSTRUCTED. Not straight lines connecting the dots. When you know that the shape is a sine wave then all it takes are a couple of samples per cycle. Regardless of frequency.

Quote:
Originally Posted by Feelingsat24khz
Our brain deciphers these irregularities to know what is going on in the signal if it is held long enough. short burts of recorded material always sound harsher on digital than long notes as the brain doesn't have the time to deciphere between the irregularities.
I don't know if you're trolling or not, but lets assume not. Then your misunderstanding of the models behind digital audio is quite impressive. Unfortunately you're far from alone. This idea that, within the audible range, the more samples you have the closer to the original wave form you get is wrong. A bass tone is not better described than a treble tone within the audible range. So increasing the sample rate to 88kHz or 96kHz makes zero difference below 20kHz in the digital domain. The only thing it does is to extend the frequency range by one octave above the audible range. One extra octave a few octaves above the highest note on a piano.

You need to read up on elementary calculus and calculus in general leading to transforms. In particular the Fourier transform. Then you will see that any wave form can be described as the sum of sine waves of different frequencies. The limit imposed of 44.1/48/88.2/96 kHz sample rate sets the limit for the highest frequency component of this sum. All sine waves below this limit are smooth and perfectly shaped sine waves. As sine waves are. Regardless of frequency. Sum them and you get the original complex waveform back. Using this as a model, combined with the sample theorem means that complex waveforms can be perfectly described within the audible range by CD-quality sampling at 44.1kHz.

best regards
Lars
Old 6th May 2006
  #4
Old 7th May 2006
  #5
Gear Head
 

[QUOTE=larsfarm]No, it tells us that to describe a sine wave you need at least two samples per cycle. So with CD-style sampling at 44.1kHz you can't describe a sine wave with higher frequency than 22kHz.
a sine wave at 11kHz can be perfectly reconstructed from a sampling at 44.1kHz. Note the word RECONSTRUCTED. Not straight lines connecting the dots. When you know that the shape is a sine wave then all it takes are a couple of samples per cycle. Regardless of frequency.




How can only a couple of samples accuratley reconstruct an infinate number of possible curves for a signwave.
a very sharp 22khz signwave curve would then be reconstructed as a 18khz signwave or even a small square wave. a 22khz signwave connot be measured correctley at 44khz (maybee a small chance that it will be reconstructed correctly). only pure square waves can really be measured. Sign waves and triangular waves have an infinate number of amplitudes as aposed to a square waves.





I don't know if you're trolling or not, but lets assume not. Then your misunderstanding of the models behind digital audio is quite impressive. Unfortunately you're far from alone. This idea that, within the audible range, the more samples you have the closer to the original wave form you get is wrong. A bass tone is not better described than a treble tone within the audible range. So increasing the sample rate to 88kHz or 96kHz makes zero difference below 20kHz in the digital domain. The only thing it does is to extend the frequency range by one octave above the audible range. One extra octave a few octaves above the highest note on a piano.




When i sample at 96khz. My mics/preamp can only hear 20khz. when i have a close look at the waveforms of cymbals and drums whose attack contains alot of high amplitude frequencies at 20khz and above it is clear to see that the signal is all over the place and can only really construct square waves. still sounds respectable though.



You need to read up on elementary calculus and calculus in general leading to transforms. In particular the Fourier transform. Then you will see that any wave form can be described as the sum of sine waves of different frequencies. The limit imposed of 44.1/48/88.2/96 kHz sample rate sets the limit for the highest frequency component of this sum. All sine waves below this limit are smooth and perfectly shaped sine waves. As sine waves are. Regardless of frequency. Sum them and you get the original complex waveform back. Using this as a model, combined with the sample theorem means that complex waveforms can be perfectly described within the audible range by CD-quality sampling at 44.1kHz.e


this might work most of the time when recording a complex waveform with little dynamic range eg rock /pop. electric guitar rock drummer.
but when the dynamics of the source are greater than the very small difference seen in most of todays compressed music the detailed attacks of accoustic instruments become distorted.

I dont care how much proccessing power and algebra a computer uses to reconstruct a waveform with only a few snapshots. No waveform pattern is like any other... ever. just like snow flakes.

Thanks lars.

Regards,

Bill.
Old 7th May 2006
  #6
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Harley-OIART's Avatar
 

....Is that a Troll I see under the bridge?


...But of course assuming this is a legit post -> Proceed with Caution
Old 7th May 2006
  #7
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DirkB's Avatar
 

Quote:
Originally Posted by Feelingsat24khz
How can only a couple of samples accuratley reconstruct an infinate number of possible curves for a signwave.
Hmmm, so you are saying there are more than one sinewave curves for a particular frequency?

Perhaps you should forget about nyquist and look at the math behind sine waves. Very basic stuff actually...

Greetings,
Dirk
Old 7th May 2006
  #8
Gear Nut
 
dorisinger's Avatar
 

I don't think the real issue is whether oversampling more accurately desribes the sine wave in question, it's that undersampling introduces artifacts. Aliasing. Like wagon wheels turning backwards in the old Western movies (As the wheels begin to spin, the film frame rate is sufficient to describe the wheel spokes. But, as the wheels speed up, the film frame/second is lower than the Nyquist frequency of the turning wagon wheels - so an undersampling artifact is introduced making it appear as if the wheels are turning backwards. Eventually, the wheels turn so fast that the individual spokes all blend together, so the aliasing that is occurring isn't visible. It's not that undersampling renders a square wave, it's that the undersampling at less than the nyquist frequency constructs the wrong wave). As Lars points out, at 44kHz, there is no aliasing anywhere within the audible spectrum.
Old 7th May 2006
  #9
Gear Head
 

Quote:
Originally Posted by DirkB
Hmmm, so you are saying there are more than one sinewave curves for a particular frequency?

Perhaps you should forget about nyquist and look at the math behind sine waves. Very basic stuff actually...

Greetings,
Dirk


an audio signal with an absolute fundamental high frequencey of any given khz can have an infinate number of curves wich define the higher overtones of that frquencey. these higher overtones are what determine the exact shape of that frequencey.

a band with many instruments creats one signal through the air. in that signal we have an absolute fundamental high frequencey wich is characterized by its higher overtone frequencies. to understand the shape of a "fundamental high frequencey" we need to break it up into at least 7 or 12 seperate harmonics wich correspond to the musical scale. so to get a clear image of an audio signal at a given khz we need to be at least 7 to 12 times faster.
Old 7th May 2006
  #10
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yes with lower sampling rates thhe waveform is different, thats because the computer breaks up a sinewave into tiny little samples that if u look really but really close youll see is not a straight sine wave but a sine wave built on steps. the lower the sampleing rates the bigger those steps will be and thus , the sound will be degraded.
most if not all sound sources have a fundamental tone and its harmonics. most of those harmonics we cant listen cause they exceed our listening range 20khz. so
the computer sampling at 44.1 doesnt know what to do with those highfrqeuncies so it folds them back to under 20khz creating aliasing. to overcome this you sample at higher levels. better at 88.2khz so in dithering the math will be simpler and give a better outcome.
so, the higher the sampling rate the more acurate picture of the waveforms youll have and to your ears sound better and to your heart a better reception of the soul inside the music performed.
Old 7th May 2006
  #11
Rep
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Rep's Avatar
Quote:
Originally Posted by larsfarm
. This idea that, within the audible range, the more samples you have the closer to the original wave form you get is wrong. A bass tone is not better described than a treble tone within the audible range. So increasing the sample rate to 88kHz or 96kHz makes zero difference below 20kHz in the digital domain. The only thing it does is to extend the frequency range by one octave above the audible range. One extra octave a few octaves above the highest note on a piano.

All sine waves below this limit are smooth and perfectly shaped sine waves.
As sine waves are. Regardless of frequency. .

best regards
Lars
Exactly ...
It gets really Tiresome trying to explain this to each New PT recruit,
...as they are trying to get a HD setup , to get that "sound" , they are Looking for,
that they think only 192khz will do ...
And Digi feeds the fuel, just call up and ask,
...they say It WILL represent the "LOWER'" Hz and FQ's , better as WELL !?!
Old 7th May 2006
  #12
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brianroth's Avatar
 

Dan Lavery has a rather extensive paper:

http://www.lavryengineering.com/docu...ing_Theory.pdf

Bri
Old 7th May 2006
  #13
Lives for gear
 
DirkB's Avatar
 

Quote:
Originally Posted by Feelingsat24khz
an audio signal with an absolute fundamental high frequencey of any given khz can have an infinate number of curves wich define the higher overtones of that frquencey.
Don't confuse signals and sinewaves.

I was talking about a sinewave.

Read again what Lars explained. That's how I understand it and it is accurate.

Now, whether sampling an additional octave above the audible range leads to a perceived improvement of sound, because of this extra octave... That's another lifetime worth of study...

Greetings,
Dirk
Old 7th May 2006
  #14
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One possible advantage of a higher sampling rate than 44.1 kHz is the fact the *required* Nyquist A-to-D low pass filter is moved well above the audible range.

There's nothing quite like having a 100000000000000000000000 dB/octave filter inline at just over 20 kHz <g>.

Bri
Old 7th May 2006
  #15
Gear Guru
 

Quote:
Originally Posted by Feelingsat24khz

How can only a couple of samples accuratley reconstruct an infinate number of possible curves for a signwave. .
a sine wave is a particular shape with certain mathematical properties - it has only one possible curve. only one possible sine wave can be drawn to pass through two points, just like only one straight line can be drawn between two points.

any sound wave, no matter how complex, can be analyzed as a collection of sine waves. It's all sine waves! Recent research indicates that the ear/brain analyzes sound this same way.

Read the information that has been linked. Do a search. At the moment you don't even seem to understand what a "signwave" is.

This has been gone over so many times, that some people in this thread are thinking you might be a troll, or are posting smilies that seem to say 'not again!!'.

That should tell you something.
Old 7th May 2006
  #16
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IS THIS HIGH-END GEARSLUTZ SUBJECT ???stike
Old 7th May 2006
  #17
Gear Head
 

yes it is all sign waves and if we can reconstruct a sign wave of 22khz recording at 44khz recording it would be easy to assume that we can reproduce the audio signal correctley for that frequencey however what i am saying is. You need to have at least a multiple of 7 or 12 or 24 etc to understand exactly what is happenning to that frequencey otherwise it does not have a point of reference. for example we would know the frequency in its basic form but would not have much idea of its real charachter/overtones. you may think that the measurment of these overtones are only related to frequencies out of our hearing however these higher octave frequencies are what determine the character of the frequencies an octave below.


Yes this is in the wrong post.
Old 7th May 2006
  #18
Gear Addict
 

Hi Feelingz,

My name is Rob. I'm having a little trouble understanding your posts.
I have a feeling that English is not your first language. There are members
on this forum from all over the world. If you like; you may type in your native tongue and I'm certain someone will accomadate a translation which will better help the message you are trying to communicate.

Cordially,

Rob.
Old 7th May 2006
  #19
Gear Addict
 
dub3000's Avatar
Quote:
Originally Posted by Feelingsat24khz
if we have a singwave at 11khz recording at 44khz it would not appear as a sign wave to our eyes or ears. It is limited to useing 3 points of reference (in a single rize and fall) to understand the al.
the best it can do with 11khz is when the sampling is perfeclty aligned with 0 amplitude of the signal. this would create a rectangular type wave with a roof simular to the outline of a house/circus tent. However if the time of sampling is not in line with the signal at 0 amplitude it would produce an irregular shaped house with the same pattern and if the signal is modulateing slightley between frequencies we would get all sorts of irregular shapes between rise and fall and we would never know what we where looking at in those frequencies except irregular shaped patterns of different form.
I'm a bit horrified to see so few "proper" responses to this guy, btw. Anyway, this used to bother me until i had it explained, here's a simplified explanation:

One way D/A's can work is they hold the sample at a level until the next sample comes in. This means you get a wave that looks like stair steps. As it turns out, the components of the wave that make it look all stepped will be above the sampling frequency/2 (i.e. 22kHz). So you apply a 20kHz brickwall filter and those steps disappear - what comes out at the end is actually going to be a really close approximation of that original wave - with an ideal filter, it'll be identical.

Of course, there is no such thing as a realtime ideal filter, so you're going to have artifacting up there at the limits of hearing. But the actual theory part works really well. This stuff is covered in a lot of university level digital courses, it's worth hunting down info on this (I've seen it on a oscilloscope, and it works).

Btw, this is the best reason to be working above 44kHz for regular recording stuff - you can move the D/A filter up much higher so you can have a gentler slope and less degradation.

--dan http://remaincalm.org/
Old 7th May 2006
  #20
Gear Head
 

thanks for the info guys.

it has led me to believe that even though we do not hear a specific frequency does not mean our hearing does not respond to it.
digital converters can respond to specific frequencies depending on their rate however the highest frequencie will have no differentiating detail or point of reference to be judged upon so they will all sound the same.
so even though we can still reconstruct signwaves at 22khz with a 44khz recording i do not belive it is possible to have any defining detail within a recording where the fundamental frequency of an instrument is 22khz.
the fundamental frequency tells us its time domain and the higher overtones tell us how it is interacting with matter.
if music or a note from an instrument was a perfect signwave then i think we can count on our mesurments. but the timbre of any sound is determined by its higher and lower harmonic overtones. that would mean that if we sampled a
musical note with a fundamental low frequencey of 10khz with a 20khz recorder we should according to my theory have little or no ability to differentiate between different timbers in that recording. we would only hear the fundamental frequency.
Old 7th May 2006
  #21
Gear Head
 

it is very unlikley that the evolution of biology can lead to useless perception.

it would be very usless to hear a sound and not have any idea where or what it is.

Our ears can respond well above what we hear in order to differentiate that which we can hear.
Old 7th May 2006
  #22
Gear Head
 

I now know what a signwave is and will not confuse it with audio signals or frequencies.
Old 7th May 2006
  #23
Gear Maniac
 

What instrument has a fundamental of 22khz??? I defy you to name one that has fundamentals even as high as 10khz. Do you know what a fundamental is? I dont think you do.

You say we need to hear higher harmonics to give us a reference to understand the fundamental. Do we not get any reference from lower harmonics, which are invariably present in music? In your theoretical example of a sound with a fundamental of 22khz, how do you propose we can hear even the 2nd harmonic at 44khz, let alone 7-12 octaves above this?

What is your point? That all recording devices so far invented are imperfect?

We know this...

Or is it that no recording device so far invented sounds realistic?

Thats bull****...Id say if your recordings are not sounding good its opperator error, not a lack of understanding on the part of the physicists and engineers who designed the gear and the principals that make it work.


M
Old 7th May 2006
  #24
Gear Maniac
 

Quote:
Originally Posted by Feelingsat24khz
I now know what a signwave is and will not confuse it with audio signals or frequencies.

Sinewave!
Old 7th May 2006
  #25
Gear Head
 

Quote:
Originally Posted by moogus
What instrument has a fundamental of 22khz??? I defy you to name one that has fundamentals even as high as 10khz. Do you know what a fundamental is? I dont think you do.

You say we need to hear higher harmonics to give us a reference to understand the fundamental. Do we not get any reference from lower harmonics, which are invariably present in music? In your theoretical example of a sound with a fundamental of 22khz, how do you propose we can hear even the 2nd harmonic at 44khz, let alone 7-12 octaves above this?

What is your point? That all recording devices so far invented are imperfect?

We know this...

Or is it that no recording device so far invented sounds realistic?

Thats bull****...Id say if your recordings are not sounding good its opperator error, not a lack of understanding on the part of the physicists and engineers who designed the gear and the principals that make it work.


M

it is not about hearing the 2nd harmonic at 44khz it is about how that harmonic can change your perception of the sound.
it is only an example. use half of that figure even 1 tenth if you want to work with the example within the audible range.
Old 7th May 2006
  #26
Gear Nut
 
DivideByZero's Avatar
You must have some pretty fancy microphones if you're concerned with picking up harmonics in the 40k range. This is truly the High End forum in every sense of the word.
Old 7th May 2006
  #27
Gear Maniac
 

Quote:
Originally Posted by Feelingsat24khz
it is not about hearing the 2nd harmonic at 44khz it is about how that harmonic can change your perception of the sound.
it is only an example. use half of that figure even 1 tenth if you want to work with the example within the audible range.

So youre saying that a sound we cant hear can change our perception of a sound we can? Where is your evidence for this?

If we do transpose that freq down by a factor of ten, then we still have several octaves of bandwidth before a 44.1k system runs out anyway, so what is your theoretical problem? Once again, do you think you can percieve freqs far above 20k?

Are you still saying youve never heard a CD recording that sounds very realistic? Let alone a vinyl or tape recording...


M
Old 7th May 2006
  #28
Gear Addict
 
skygod's Avatar
Where have all the garage bands gone?

Quote:
Originally Posted by Feelingsat24khz
The only thing it is telling us is weather the given rate of sampling is enough to know that there is something there, but it has no idea what.


Excellent! Your gung fu is very perceptive, but the truth is that it goes beyond audible perception. The entire body chemistry is involved. Ever wake up feeling great, that first cup of coffee, open the window and breathe in the glory of the morning, take a shower, get dressed, get in the car feeling on top of the world like you could run thru a troop, and BAM!, some prick runs a stop sign and cuts you off, has the balls to stop, then call YOU a mother-fakkuh, gives you the NJ bird salute, and your entire demeanor changes on a dime? Or the opposite, you are feeling lower than the dregs of life and suddenly an old song comes across the airwaves and that guitar riff goes thru your bones and your body chemistry changes on a dime and you are way into wellness again?

Some years back I remember an article diatribe rant I read by Neil Young, where he talked about how much he hated digital recorded audio compared to tape recorded audio, and how he turned the tape player on and got the band to start jamming/playing for hours from where all the musical ideas came from … and how he would never over his dead body … yada yada That’s how we all did it. Ask that great African American band Aerosmif, or ol’ Slowhand, or Rush, or Yes, or the Rolling Dead, or Page, or David Gildouche ... and if they deny they did it, then they’re a bunch of lying hypocrites. The best material comes came in spurts of magical moments of creativity. And when you listen to aging fusion or jazz players and rockers today who are boring to watch and listen to, it’s because they are not hungry anymore, and have lost their creative magic. We’ll with the advent of 24 bit 96kHz (and I’m not sold on any bit rates or sampling rates higher than that other than wasted 1s and 0s despite what the poser merchandiser and marketers have to say about that) ol’ Neil might have a problem convincing others of his audio position on in this century, unless he qualifies it with ....

The garage band mentality is the essence of creative talent. We have lost it in great part because we just can’t turn on the tape player anymore, unless, you are a dinosaur like me who still uses one, or more, because digital media does not lend itself to hours of endless recording. Storage requirements become the issue so people now come up with meaningless riffs and loop them, and when they are out of ideas, which is probably, 99.99999 percent of their miserable professional lives, are looping somebody else’s ideas. What a stinking rat race huh? Critically listen to country radio or rock radio or nu metal radio or rap radio for a week at a time and take notes of intros, riffs, solos, and endings. There is almost a ring binder out there now, not unlike a restaurant menu, that permit artists can go into a studio and say I want my song to start and sound and end like this one. Voila, cookie cutter, instant song. They now all sound the same … maybe 24-36 different patterns out there to choose from. This is the industry today in a nutshell, where the analog God has been banished and replaced by the devil god relegating mortals to a CPU, monitor, control surface, AD/DA converters, modeling crap, storage medium, software manager, and burner. A digital mouse replaces the creativity.

And what about high headroom preamps like the Pacifica that has ungodly headroom, what is it 5H to 400kHz or something stupid like that … way out of the human audible shelving limits at both ends, and yet, everything sounds better thru these than anything else out there? Now why is that? Because it is it an entire body experience my gearslutz whuas? No ****heads, not an out-of-body existentialist upper room experience … I’m talking about “In-body Chemistry 101” a’cappice?



-------
And if you are unhappy about being unhappy …
then your gung fu is very weak and miserable
-------
Old 7th May 2006
  #29
Gear Head
 

Quote:
Originally Posted by moogus
I defy you to name one that has fundamentals even as high as 10khz.
Organ.
Old 7th May 2006
  #30
Gear Head
 

if we are perceiving a sound at 20khz is is because our responce is at least 7 to 12 times higher.

it would be usless to hear a 20khz frequencey if our hearing responce only goes to 20khz as that sound would not have any information to tell us how it is interacting with it's environment.

our brain acts like a filters that removes frequencies that have no deffining charachter.

If only the lower overtones exist it would be like haveing a past but no future. and without a future the sound dies right there and then. and it will give no life or indication of anything. just confusion and emptiness.
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