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I agree with your conclusion wholeheartedly. And certainly "steps" is just a convenient presentation. But, think of the people this article is aimed at. It's an acceptable way to present it that does not convey any patently false information, except at a mathematical detail level that the...

Thanks for all your comments. It's great to generate discussion. I appreciate it.

Certainly in practice that's true. I mention in the article that the mathematics are a essentially an oversimplification for purposes of generating a theoretical target.

Good to know...thanks for sharing. Seems a bit tangential to what I'm proposing though. Feels like a general discussion of recreating functions through a series equation: Fourier, etc. My discussion is more about how physical properties mimic digital properties in some respects and so that...

When small enough you can use step and point pretty much interchangeably with very little difference in the mathematical results between them. Where is the mistake? All modern approximations using calculus utilize this same approximation method.

Certainly...but if you PREFER the analog sound, what would you need to do in your digital system to mimic it? I make the case that there is basically "sampling noise" in analog sound based on the physical properties of the medium used. Then it's simply a matter of determining what effective...

When "step" size becomes small enough, at the limit as it reaches the smallest possible physical dimension for example, the step becomes essentially a point of negligible size. This is the basis of calculus.

I just posted an article going through the mathematical exercise to show what would be required from digital system to perfectly mimic a vinyl LP. In case you're interested - https://bandzoogle.com/blog/could-digital-audio-ever-outperform-analog

Stumbled on this forum discussion almost by accident. Enjoyed reading the comments and discussion. There's a lot of different sides to the loudness vs dynamics story for sure. Often times it gets blamed on the mastering. As a long time mastering engineer (nearly 20 years, over 50,000 tracks)...