New member here, involved in a long running parallel thread on pinkfishmedia.
I think this simple look can elucidate the great lossy/lossless debate. We are leaving MQA's "deblurring" process out for now, since this a separate debate/controversy.
Let's put some numbers on the distortion expected in the types of codecs helpfully explained by Amir. In engineering, a useful excercise is called "order of magnitude analysis." It allows one to get approximate understanding of system behavior.
Mathematically Lossless Codec:
Mathematically perfect algorithm running on a real-world computer and network, will still have an error once in a great while. Let's pick a really tiny value - 1 in a billion or 1E-9. This results in the error against the original file of
-180dB. Great performance!
Lossy codec:
Let's stipulate a very good algorithm that delivers an error of 1/10 of 1% or 0.001. This results in the error against the original file
-60dB. Not bad at all!
MQA:
From graphs posted at PFM and elsewhere, "eyeball" MQA null against LPCM looks like
-120dB, or 1 in a million (1E-6). This is clearly better than an excellent lossy codec but clearly not as good as mathematically lossless one.
https://drive.google.com/file/d/1o79kijUug1Rg3Ne0aHM35oibMMPbWRK6/view?usp=drivesdk
(Red and Blue curves used for conservatively deriving 120dB number. Yellow vs. Green maybe more relevant and seem to overlap up to 35 KHz even more. If properly averaged and weighted the final number is likely to be smaller - i.e better null).
Let's consider what above numbers mean in the context of consumer audio replay:
Leaving aside a question of when do deviations become audible, one still needs a sound system that has amplification with low enough distortion and noise to actually playback these differences.
I own modern amplifiers with very low distortion and very high power - Emotiva XPA-1 gen.2. Their specifications list Signal to Noise at 89 dB at 1 watt and 117dB at full power (600w). Let's take an average of 103dB. Added distortion, though very small (-80dB), will make the total number worse.
So on my very low distortion system, I could at least theoretically be able to hear distortion in the lossy codec. However, both mathematically lossless and MQA distortion will be below the system's noise/distortion floor and, therefore, inaudible.
They will be entirely indistinguishable from one another to the listener and are, therefore, identical. The big debate about MQA lossy/lossless status is entirely meaningless for consumer reproduction.
I note that a lot of MQA criticism is essentially someone showing you some hard to see plots and insinuating that *something* is bad. In engineering we call it "arm waving." Once you put some numbers on the observed phenomena and place it in the context of actual system operational usage, one can make informed conclusions. Simple excercise above shows that mathematically lossless and MQA are identical in the context of home listening.
I welcome mansr and others to offer a competing simple analysis that challenges above numbers in a meaningful and substantial way.