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... with a certain degree of confidence / corridor of accuracy.

What do I mean? Case in point: There is the huge archive of digitized Edison wax cylinder recordings.

They have annotations, usually year of recording, sometimes producer of recording. Assuming that, with a good likelihood, grouping the intersection of e.g. one year of recording and a geographic area or even company yields sets of recordings very likely made with the same model / iteration of the technology within a set, given how slow-paced development was back then:

Could one infer the rough frequency response curve of an imaginary "average recording device" of those times from such a narrowed-down set of recordings?

My not exactly DSP expert naive train of thought went like this:

  1. if I have a great enough number of as diverse as possible audio recordings, their sources (i.e. before entering the brass horn to be recorded) should have an average spectrum roughly resembling white noise. This probably means using broadly set up orchestral recordings, not so much "solo singer with background accompaniment", which is weighted too much to vocals in the spectrum.
  2. with a good likelihood of being made on the same model of recording apparatus, an "average spectrum" calculated e.g. with FFTs over the whole set of recordings as described above, should yield the rough response curve of the imaginary recording device

Now, if premise 1. is already wrong, then I'm out of luck. And 2. could be wrong if the spread of characteristics between individual exemplars of devices of a series is too great - although I guess that's a bit of a question with regards to "what do I need". Anyway, this was just to show I made some effort thinking about this. If it doesn't work the naive way I am imagining:

Is there a way to do that, only from recordings, without being in possession of an actual device of that type (for measurement)?

The amount of distortion by e.g. saturation within the mechanical recording process can probably not be inferred just from recordings?

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  • $\begingroup$ Recorded sound doesn't resemble white or pink noise in any way. Have a look at an RTA of any recording. The bandwidth depends on the instrumentation, and on the microphone or horn or whatever transducer got the sound into the apparatus: and its distribution depends on the orchestration and the conductor, or the voice or whatever is being recorded. Melba isn't going to look like Caruso on an RTA, or Stokowski like Toscanini. $\endgroup$ – Marquis of Lorne Dec 1 '19 at 21:39
  • $\begingroup$ That's why I wrote, the average of many, as diverse as possible, recordings - not one recording. But I guess it's still hard to assemble a good mix of recordings (if you don't have the "uncolored" sources, can only guess what is somewhat even). Yeah, maybe it's not possible to put the perfect colelction together, it was stated as an ideal, hypothetical base to start my thought experiment from. $\endgroup$ – user1847129 Dec 1 '19 at 22:58
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Yes, that's definitely possible. The key would be to find recordings where it's reasonably easy to find an acoustic reference. Great candidates for this would be classical or big band recordings. Let's say you have wax cylinder of Beethoven's 5th, you can try to create a reference by analyzing a dozen or so recent recordings of the same piece. The standard deviation would give you a "margin of error" for the reference and than you can simply divide the spectrum of the wax cylinder by the reference spectrum. Repeat for as many recordings as you can find good references for.

should have an everage spectrum roughly resembling white noise

No. It's certainly not white: closer to pink but with more high end roll off. Hence you need a known good reference to determine exactly what it is.

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    $\begingroup$ I'll add: A buddy, upon discussing this, just mentioned that, if lucky, somewhere in those archives there may be a recording of a reference that's still in existence today prety much exactly (of cours still with an own recording curve, but we're talking ballpark idea of a really quirky recording device...), like the bell of the Big Ben, the start of which (when the thing that hits the bell, well, hits it) might have quite a broad spectrum... Now I'm off to searching homework... $\endgroup$ – user1847129 Dec 1 '19 at 16:48
  • $\begingroup$ This won't strictly result in an approximation of an average recording device so much as an average recording regime. The device is almost certainly the most important component of this, but the way performances were delivered for the recording would have been altered somewhat to compensate for the shortcomings of the recording device. The curve you get will be the right one for transforming a modern recording - but not necessarily a recording of an old arrangement using modern equipment - to sound like an older recording. Perhaps this is the real intent of the question anyway. $\endgroup$ – Will Dec 2 '19 at 10:40
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The amount of distortion by e.g. saturation within the mechanical recording process can probably not be inferred just from recordings?

Actually, amplitude and rate saturation would be fairly easy -- just play them back, and look for the waveform flat-topping (which tells you about amplitude saturation), then look for the slopes never going beyond a certain amount (which tells you about rate saturation).

It might work a whole lot better if you start with a few wax cylinder recorders in good condition, and characterize them for nonlinearities. Then you'll know what you're most likely looking for in the old ones.

This would actually be a good Master's or PhD thesis topic -- so perhaps start with a literature search, to see if it's been done.

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