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How to test/measure the quality of dynamic range compressed audio?

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In general dynamic range, or actually I think what you mean is headroom (or also called crest factor I think?) is more indicative of the potential for listening fatigue than actual quality.

The more the dynamics are compressed the less headroom there are the and the closer the music gets to being static/noise (headroom of 0dBFS would probably be just pure static/noise).

I did read someplace (and sadly I do not remember where) that on average a humans prefer music to be within a 30dB range, not sure if this means 30dB headroom, or if it means a RMS of +/- 15dB (30dB range total, sweet spot being in the middle somewhere?)
If the range is larger than 30 then quiet and loud are so far apart that one might feel like reaching for the control at times, but in the other direction, with a too low range (Iggy Pop made a notoriously low dynamic range album) ad it might feel tiring after a while.

Your ears prefers some peaks and valleys, flow and ebb of sound. Songs that feel lively but not tiring usually is around your sweet spot (which one would assume varies a little from person to person).
Not sure if this helps clarify anything, but hopefully it is found interesting at the very least...

I guess technically speaking one could use EBU R128, and a huge survey and try and figure out what LRA (EBU R128 loudness range) people prefer and get a statistical average or mini-range or similar from that I guess, it still would not say anything about quality though, might be interesting for automation systems though, for flagging of audio that needs manual inspection if they are too far off in either direction maybe..

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