When is AI going to regenerate the lost data on recordings from cd or other digital source?

[olieb]

How many permutations of music can you produce with 8 notes?

You would be surprised. First, it's 12 notes (actually 11 without the full octave). If we only consider 7 levels of loudness (ppp,pp,p,mf,f,ff,fff) and 8 durations (1/16, 1/8, 3/16, 1/4, 3/8, 1/2, 3/4, 1) that is 616 variations of a single tone. Then you can have different ways of phrasing (legato, staccato, pedal ...) and then there is tempo.
So for starters there are much more than 1000^20 ( =10^60) possible variations for a very short pieces of 20 notes inside of a single octave and that is without taking into account that you can play two- or three- or four-part or accords (though most of these don't conform to the main stream and that is what AI will produce: 100 mio times the same thing).

 

[antcollinet]

if I remember correctly

You don't.

 

[smoking_man]

Of course you can reproduce lost data, with a probability of accuracy. It is like reading a book with a missing word or sentence, our neolithic brains can fill in these gaps with general ease, so AI would be able to do the same, when it has reached the threshold of AGI.

 

[smoking_man]

You don't.

What is the Formula for Permutations and Combinations?

 

[TurtlePaul]

Of course you can reproduce lost data, with a probability of accuracy. It is like reading a book with a missing word or sentence, our neolithic brains can fill in these gaps with general ease, so AI would be able to do the same, when it has reached the threshold of AGI.

But what is the point of guessing the 17th and 18th bits? That is 100 dB down and you can’t hear it.

For decades we have had various dithering techniques which try to extract information for the least significant bit. We also have high resolution audio formats. Nobody cares because unlike the transition from analog tape/vinyl to 16/44.1 CD, any improvement is inaudible.

What is the point of guessing the samples to go from 44.1 khz to higher sample rates? That is above 22 kHz and you can’t hear it.

For decades we have had various output filter and oversampling techniques which try to extract information right up to the Nyquest rate. We also have high resolution audio formats. Nobody cares because unlike the transition from analog tape/vinyl to 16/44.1 CD, any improvement is inaudible.

 

[Salt]

This is the End.
Not?

 

[smoking_man]

But what is the point of guessing the 17th and 18th bits? That is 100 dB down and you can’t hear it.

For decades we have had various dithering techniques which try to extract information for the least significant bit. We also have high resolution audio formats. Nobody cares because unlike the transition from analog tape/vinyl to 16/44.1 CD, any improvement is inaudible.

What is the point of guessing the samples to go from 44.1 khz to higher sample rates? That is above 22 kHz and you can’t hear it.

For decades we have had various output filter and oversampling techniques which try to extract information right up to the Nyquest rate. We also have high resolution audio formats. Nobody cares because unlike the transition from analog tape/vinyl to 16/44.1 CD, any improvement is inaudible.

I am led to believe it is called Psychoacoustic effects, making the lost audio from the 80's 90's to Present very important. Also can you guarantee a smooth line between sampling points on a cd accurate, or just guess work by a simple filter?

 

[Titurel]

On the other hand, as demonstrated by the MAL de-mixing technology* used in various Beatles-related projects there is the possibility of using AI technologies to turn mono recordings into something like genuine stereo recordings. I suspect this technology will come into play in ways both good and bad in our futures.

Along similar lines, were attempts to reconstruct Enrico Caruso's recordings. The results were interesting, but (to this singer's ear) unconvincing, since they were derived using Bjorling's (I believe) recordings as an integral part of the vocal model and mathematical models of what were believed to have been the original recording horns. Now, an AI driven physical model of Caruso's voice and technique (derived from analyses many of his recordings) should be achievable and would likely produce more satisfactory results. Re-synthesis rather than heroic remastering.

 

[antcollinet]

What is the Formula for Permutations and Combinations?

Can you google?

And we are talking permutations, not combinations - a-b-a sounds different from a-a-b etc.

And then you have to define permutations of what. How many selections out of how many. Consider the aforementioned 3 minute song. 60bpm, so a total of 180 beats. Each beat can be a single crotchet at any of the 88 notes on a keyboard. Or you could spread a minim over that beat and the next. Or a semibreve srpead over four of them. Or you could have a beat consisting of two quavers, or four semiquavers, of 8 demisemi quavers, or any mix of those lengths. Or a rest (no note) of any of those lengths. Or any combination of those things (eg a a quaver followed by two semi quavers)

So now you have to divide each beat into 8 possible positions for a note (anything up to 8 demisemiquavers), each one of which could be any of 6 different lengths and differing combinations of those lengths. That gives you around 88x8^6 different options for every beat of a song. (guessing a little here, 'cause i've not bothered to work out exactly what the number of permutations of 6 different note lengths over 8 positions of a beat could actually make sense, but lets just assume I've got it about right)

(EDIT : In any case, I could point out there is also a hemidemisemiquaver which would result in 16 positions per beat instead of just 8, making the calculation 88x16^6 = up near 1.5 billion options per beat instead of a mere 23 million - but let's not go there, hey?)

So just taking note length and pitch into account, each beat of the song can have 88x262144 different permutations..


So now you have to calculate the permutations of 23million+ options at each beat position for 180 beat positions. So now we are up to 23,068,672^180 = my scientific calculator can't do that - but it is around 23x10^1080

Now consider there are only around 10^82 atoms making up the observable universe - So feel free to consider this number the same as infinity.

And that is without considering that each beat will normally have multiple notes played at the same time - so you have another power of 2 or 3 or something like in there.

Then there is intensity of each note, sustain from one note, to the next - or across any number of notes or beats. Look at a piece of sheet music - every symbol on there including the clefs and timing notation changes the sound of the piece. Then you have interpretation by the musician, arrangements for a band - or for an orchestra.

How sure are you now that an AI can generate every possible combination of notes for a 3 minute song before the heat death of the universe?

 

[TurtlePaul]

Also can you guarantee a smooth line between sampling points on a cd accurate, or just guess work by a simple filter.

I guarantee it. (but it is also generated by a simple filter)

If you understood sampling theorem then you would understand why it is guaranteed, subject to Nyquist frequency limitations.

 

[mhardy6647]

Re-synthesis rather than heroic remastering.

...and, doubtless, we'll then hear Caruso sing Hit Me Baby One More Time.

 

[smoking_man]

Can you google?

And we are talking permutations, not combinations - a-b-a sounds different from a-a-b etc.

And then you have to define permutations of what. How many selections out of how many. Consider the aforementioned 3 minute song. 60bpm, so a total of 180 beats. Each beat can be a single crotchet at any of the 88 notes on a keyboard. Or you could spread a minim over that beat and the next. Or a semibreve srpead over four of them. Or you could have a beat consisting of two quavers, or four semiquavers, of 8 demisemi quavers, or any mix of those lengths. Or a rest (no note) of any of those lengths. Or any combination of those things (eg a a quaver followed by two semi quavers)

So now you have to divide each beat into 8 possible positions for a note (anything up to 8 demisemiquavers), each one of which could be any of 6 different lengths and differing combinations of those lengths. That gives you around 88x8^6 different options for every beat of a song. (guessing a little here, 'cause i've not bothered to work out exactly what the number of permutations of 6 different note lengths over 8 positions of a beat could actually make sense, but lets just assume I've got it about right)

So just taking note length and pitch into account, each beat of the song can have 88x262144 different permutations..


So now you have to calculate the permutations of 23million+ options at each beat position for 180 beat positions. So now we are up to 23,068,672^180 = my scientific calculator can't do that - but it is around 23x10^1080

Now consider there are only around 10^82 atoms making up the observable universe - So feel free to consider this number the same as infinity.

And that is without considering that each beat will normally have multiple notes played at the same time - so you have another power of 2 or 3 or something like in there.

Then there is intensity of each note, sustain from one note, to the next - or across any number of notes or beats. Look at a piece of sheet music - every symbol on there including the clefs and timing notation changes the sound of the piece. Then you have interpretation by the musician, arrangements for a band - or for an orchestra.

How sure are you now that an AI can generate every possible combination of notes for a 3 minute song before the heat death of the universe?

You are exaggerating. The notes are the important part and there are only 8 of those. I rarely hear an original song these days. I believe that is because we have reached a tipping point in the fact that any selection of the 8 notes has already been played in another song.AI Could squeeze a few more out but repetition would occur by the nature of the limited scale.

 

[smoking_man]

I guarantee it. (but it is also generated by a simple filter)

If you understood sampling theorem then you would understand why it is guaranteed, subject to Nyquist frequency limitations.

I do not need to have knowledge of this. Higher frequency bands will fill these unnatural perfect lines between samples. This would provide you with a non linear line between the two sample points. It is common sense. This will be more prominent as you go up in frequency.

 

[antcollinet]

You are exaggerating. The notes are the important part and there are only 8 of those. I rarely hear an original song these days. I believe that is because we have reached a tipping point in the fact that any selection of the 8 notes has already been played in another song.AI Could squeeze a few more out but repetition would occur by the nature of the limited scale.

If it were true that only 8 notes mattered we wouldn't see an instrument with more than 8 notes.

But even if I were to change my calculation to only include the 12 notes in a single octave, the permutations for a song only drop to 3x10^1080.

You really need to get a grasp of how permutations can mathematically grow rapidly out of control when you are accounting for complexity before continuing with this - frankly ridiculous - thought experiment.

 

[Nopiano]

I rarely hear an original song these days.

I think that’s more about what sells ‘pop’ music rather than the mathematical possibilities!

 

[smoking_man]

If it were true that only 8 notes mattered we wouldn't see an instrument with more than 8 notes.

But even if I were to change my calculation to only include the 12 notes in a single octave, the permutations for a song only drop to 3x10^1080.

You really need to get a grasp of how permutations can mathematically grow rapidly out of control when you are accounting for complexity before continuing with this - frankly ridiculous - thought experiment.

Can you reveal the maths that took you to your conclusion?

 

[smoking_man]

Going back to AI if you could predict the location of every molecule of air in a recording studio or live venue then you will be able to recreate the exact musical performance on your music reproduction equipment. That would not be a speaker because it only moves the air in a 1 dimensional piston like movement. The same limitations would apply to microphones too.

 

[Berwhale]

Higher frequency bands will fill these unnatural perfect lines between samples

It's Monty time...

 

[antcollinet]

I do not need to have knowledge of this. Higher frequency bands will fill these unnatural perfect lines between samples. This would provide you with a non linear line between the two sample points. It is common sense. This will be more prominent as you go up in frequency.

Clearly you do need to have knowledge - because what you believe to be "common sense" is anything but.

Start here - watch over again until you understand what it is showing you - only then come back with questions about it

******
An excellent video explaining the basics of how digital audio works, in particular, busting the myth that it is has "stair steps"

Monty uses all analogue test equipment together with a low end DAC to show how even this DAC perfectly reconstructs sound waves, perfectly smoothly. He shows how bit depth (resolution) only impacts the audio in terms of quantisation noise - rather then increasingly jagged steps - even going down to 8 bit audio to show this. He also demonstrates how dither and noise shaping used during sampling (or resampling) can dramatically reduce the audibility (and objectionability) of this noise.

First - is the demo (at 5:35) of a perfectly reconstructed 20kHz sine wave with 44.1kHz sample rate - even thought there is only just over 1 sample per half cycle.

Second - (at about 20:50) is the demo that time resolution is not limited to sample rate. The edges of a square wave can be placed on a sample, on the next sample - OR - anywhere in between. No time resolution problems (at least not at the sample rate level)

This is a must watch for anyone who can't mathematically prove the sampling theorem backwards, but nevertheless wants to gain a near intuitive understanding of just how well it works.

EDIT : Ninjad by @Berwhale

 

[Jcrow]

I think even if the ‘lost’data is probabilistically reinstated by AI, I doubt we would be able to tell since CD quality is more than enough for our ears.