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What information in an audio file lets my iPod, home speakers, PC, and bluetooth boombox output the same recognizable “guitar” and drum sound, if it’s just a measure of the encoded amplitude values? Won’t the timbre of each instrument be lost if it all becomes numerical values between -128 and 127? Is timbre just an interpretation of air pressure?

For example:

  1. Let’s say I export an audio file that's a recording of an acoustic guitar and kick drum.

  2. When I export the audio file, the waves (amplitude) that make up the guitar’s characteristic harmonics are translated to numerical values via PCM (-128 to 127) at a fidelity dependent on my sample rate.

  3. My bluetooth boombox takes the amplitude data and moves the cone proportionally creating air pressure that I hear.

  4. Air pressure reaches my tympanic membrane and then...what? My brain interprets that air pressure as a "guitar?"

2 Answers 2

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PCM doesn't have only 127 signed values, it has at minimum [for CD-quality] 32,767 at 16-bit resolution, up to 8 million at 24-bit & 2 billion at 32-bit [the theoretical maximum is infinite.]

Each of those individual values can be thought of as a "position" - where the magnetic forces in your loudspeaker will push the cone under a specific positive or negative voltage.
Generated sound comes from each of these numbers/voltages going by so quickly that they are no longer discrete values, but become a series of physical movements - single discrete positions at 44 thousand times per second for CD or 'regular' MP3 [or higher still, the current maximum 'common' sample rate is 192 kHz]. At these speeds, the individual positions are no longer perceived as discrete events and the movement of the cone becomes audible sound.

The ability of digital audio to sample where this speaker cone should be thousands of times a second is how the particular acoustic properties of any instrument, or complex combination, are delivered.

Each sampled position contains no sonic data at all. It is simply a position the speaker cone should move to. It only becomes perceivable as sound once all these movements become too fast to recognise as discrete events. About 40 times per second is the largest gap between events that humans can hear. [We can feel it below that, but it tends to then be perceived as vibration rather than sound]. Up to 20 thousand is the maximum. [This reduces as you get older.]

A speaker cone is exactly the same mechanism as a [dynamic] microphone, but in reverse. Both use a diaphragm & a coil of wire inside a magnet. If you move a coil in a magnet it produces a voltage. If you supply a voltage to a coil in a magnet, it will move. They are exactly the same electro-magnetic principal. If you do this fast enough, it becomes sound, or an analogue of sound which we can now store as 'positions' - eg on a vinyl record as movement away from a centre point, or a tape recorder as positional variation of a magnetic field, or in digital form as numbers representing distinct voltages.

Vibrating a cone of paper will produce alternating pressures in the air… we perceive this as sound when it reaches our ear drums & makes them vibrate in time with the air movement - just like a microphone.
Even weirder… humans use electricity to transmit this information to the brain, though the microphone analogy breaks down there, it's not an identical mechanism.

Anyway - once that series of vibrations is fast enough that we don't hear individual speaker 'positions'… then it becomes indistinguishable from the natural permeation of sound from the original guitar.

Mathematics can break down any sound into a series of overlapping, interfering sine waves. The ear doesn't really do it the same way, but the perception of sound is the same for one reproduced by a speaker to that of the original instrument. Digitally sampled audio doesn't actually contain any sine waves, only individual positions, which are then recombined at the speaker to once more become "sound" with all its intricacies.

Both microphone & speaker manufacturers each try to build their devices to best recreate each absolute position to best accurately reproduce sound at all frequencies. Generally, as with all things technical, you can get somewhere close quite cheaply, but to do it exceptionally well becomes logarithmically expensive [& with a great deal of perceptual opinion in the upper echelons.]

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  • This rambles a bit - I'd never make a university lecturer - but I hope the essence of comprehension is contained within. ;)
    – Tetsujin
    Jul 15, 2022 at 16:40
  • 1
    I had numerous epiphanies reading your response, so thank you
    – but like
    Jul 15, 2022 at 18:40
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The psychoacoustics and psychophysics of sound have everything to do with the physical aspects of waves and frequency, and the biological aspects of how you ‘perceive’ the sound. The perception of an individual instrument is pretty basic based on what fundamental frequency range that instrument is in and the first few harmonics . Hence bass guitar would be a generally a plucked string with a fundamental frequency below 500hz. That’s your first acoustic clue. Same for drums - sharp transient, with quick decay. Human voice is kind of built in to the ear mechanism (cochlear) as a natural survival device - that’s why a baby cry cuts through everything. All these recognition cues are quickly learned at a young age. You hear it and your parents say what that is, and the name sticks. Past that, it gets more interesting where you are actively listening to the quality of the sound and discerning one piano from another, one bass guitar from another. Your ‘advanced’ perception of the quality of the instrument is based on many subtle clues but mostly learning to recognize the objective formant and harmonic structure of that instrument. Timbre is subjective and is the word that describes all the perceived characteristics of a sound. Anyone can recognize a violin but it takes a educated ear to pick out a Stradivarius. “Regardless of playback device” is a bit vague but most earbuds, stereos, TV sound, boom boxes will all at least reproduce 100hz-6K which will give you most of the information you need for instrument recognition but may not be able to reproduce quality cues. Medical science tells us your hearing is as good as it will ever be at 20-20kh. Take a deep breath...The audio chain is convoluted and the audio energy gets changed multiple times.The original recording is sound or air waves, goes into a microphone translating that into electrical energy or signal, goes through a Analog to Digital converter into your computer, then back out digitally through Digital to analog converter, amplified, then out to speakers that move air again and reproduce the signal. Part 1. Then more transformations - that sound from the speakers as air vibration goes into your ear canal, tympanic membrane (like a little acoustic resonator, transfers the energy to mechanical in the middle ear, then into the Cochlea (little snail like organ) transfers to liquid wave energy that moves your inner ear cells that act like in/out valves for the nerve cells they sit on and regulate the frequency of the inner ear nerves on/ off discharge. And finally, the music is back to binary electrical energy that both ears send to your brain via the auditory nerve. Your Brain/Mind perceives the nerve signals as music and that’s what you hear. Your mind has learned both the basics and advanced identification and expects those instruments to be in those audio ‘slots’. It's a miracle that the whole chain works as well as it does. I left out mountains of info on the detailed processes but hopefully it answers enough of your question. If not fully, try and be very specific and we can certainly go much deeper. I can recommend several books on the subject if you are interested.

:Introduction to the Physics and Psychophysics of Music (Heidelberg Science Library)by Juan G. Roederer | May 17, 1978

:The Physics and Psychophysics of Music: An Introduction by Juan G. Roederer | Oct 9, 2008 (updated)

:Hearing - From Sensory Processing to Perception by B. Kollmeier, G. Klump, et al. | Sep 19, 2007

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