I've always said that nothing beats live music...
by Kbyrnes (2018-12-12 09:36:10)
by Kbyrnes (2018-12-12 09:36:10)
In reply to: I guess this could go in circles for many iterations as ther posted by mjv8198
...I went back and re-read the math PhD's article. I wasn't a math major, so beware of the following! The digital approach is indeed a sampling, so kind of an average, but the phenomenon is more like integration, where the number of divisions is made smaller and smaller to approximate the smooth curve of whatever function you're dealing with.
There are graphic comparisons of analog to digital that could be quite misleading, like this one:
One sine-wave period corresponds to the stated frequency; if we're talking about A 440 (the note A on a piano above middle C), then one period of the sinusoidal wave form is considered to represent 440 hertz. The highest note on a conventional acoustic piano, C8, has a frequency of about 4200 Hz (in equal temperament).
So going back to that image above, if one period is for A 440, the period last for 1/440 of a second. The graphic image shows about a dozen divisions, so about 440 x 12 = 5,280 components per second. But sampling rates are commonly over 50,000 Hz, meaning 50,000 components per second. So imagine those 12 boxes in the image each sliced into about 10 narrower pieces.
Current digital technology samples the sound data at rates far above the ability of the human ear to hear (about 20,000 Hz). In live music, the sounds combine pure tones into a complex tangle with harmonics reaching well above what our ears can hear. It would be interesting to take recordings done on wide-track tape recorded and played back at high speed to digital recordings at, say 96,000 Hz and ask people with experienced ears to compare. Not to mention--digital recording still often uses analog components; e.g., "digital" microphones with diaphragms, etc.
Sound reproduction is a fascinating field. A few years ago I valued the Pritzker Pavilion in Millennium Park, Chicago, and was given a mini-lecture on and demonstration of their outdoor sound system, which serves people seated up front and then sitting on a lawn that extends several hundred feet back and away from the stage. They fashioned a system with delayed sound reinforcement using LARES technology, so that the sound from the speakers, wherever they are placed, arrives at the auditor close to the same time as the actual sound from the stage. See link for a little story about that.