The multiplication by 2 is there so that the RMS level calculated for a 0 dBFS sine (rather than square) wave will be 0 dBFS. Without that, it would be -3.01 dBFS.
In other words, if the entire input is a simple sine wave at a constant level, the calculated dynamic range will be 0 dB. But it will be 0 dB even if only 20% or more of the input is a constant sine wave, and the rest of it is silence. Therefore, it is a pessimistic algorithm, because it will rate the track as having poor dynamic range if any substantial part of it looks like being heavily compressed. It also ignores a high peak in a single block due to using only the second highest peak value. If you take 5 minutes of high quality classical music, and paste a couple minutes of compressed metal or pop at the end of it, then the reported dynamic range will be based mostly on the latter, where the 20% highest RMS values are likely to be found.
The RMS sum is not based on the dB values, but rather on the power, which is the correct way to combine the RMS level for multiple blocks. That is, the correct overall RMS for the 12 blocks is:
10 * log10((10^(-5 / 10) * 5 + 10^(-5.3 / 10) * 5 + 10^(-5.8 / 10) * 2) / 12) = -5.25 dB
Interesting. I see. Thank you for clarifying that.
I know this is the SS section, but what would you say is an accurate measure of dynamic range? Obviously a pure sine wave is going to sound like 1 note to us, which might be the reason why the DR utility gives that a 0 rating, but music isn't just a simple sine wave. I have some chiptune music that I listen to on occasion and the DR rating is often around 3-7 (which is not unexpected for this music genre).
This particular song has a DR5 rating, and a crest factor of 6.9 I think (-9.4 dBFS RMS, -1.0 dBFS peak). If a perfect sine wave is the 0 point for the DR number, then the crest factor for this song divided by the crest factor for a sine wave (1.414) actually gets really close to the DR rating (4.8). These calculations are also a lot easier for me to understand than the math done in the DR specs.
[video]https://www.youtube.com/watch?v=KPaJLOIRJLI[/video]
I guess I've been been using the decibel units by mistake instead of the power all this time. When calculating power levels from dBFS values, what units would power be in this case? And how do I express the crest factor in terms of a decibel?
10 * log10(1.414) = 1.5 dB, but the actual value is twice that. Why is that so? I usually see 10 * log10(P1/P0), but sometimes I also see 20 * log10(P1/P0); when is 20 * used instead of 10 *?
[rule]
If I want to create a headphone measuring setup, what would be the most accurate way to do so?
From what I've seen there are two setups to do it:
- Use two microphones that measure flat and place them about a head's spacing apart; then just put the headphones over them and take measurements (the ideal headphone response in this case would be a flat line since it's just the headphone's sound being put into the microphones)
- Use two microphones that measure flat and place them about a head's spacing apart with silicone ears; then just put the headphones over them and take measurements (the ideal headphone response in this case would roughly resemble the head-related transfer function due to the pinnae amplification)
Setup #1 to me seems the most accurate because the HRTF from setup #2 can be variable depending on the ear's shape, material, size, etc. What would be the advantage of setup #2 and why is it that places like Innerfidelity and Golden Ears use a measurement setup similar to this instead of setup #1 where we know that if a headphone measures flat, it will follow the HRTF curve just like how flat-measuring speakers would be applied to our ears?