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I kind of feel like we're going in circles. The conversion of a nominal percentage-based distortion figure to dB of attenuation vs. the signal is straightforward: http://www.sengpielaudio.com/calculator-thd.htmI understand the log part. What I dont understand is why your taking the log of the distortion value. The other thing I want to draw attention too is the Fletcher Munson curves where human hearing sensitivity to frequency is fairly insensitive to bass. Reading from different sources, I was under the impression that bass frequencies were able to mask noise much more effectively than mids and high frequencies. Maybe this is the perception thing that was mentioned earlier.
Take Amir's dashboard: https://www.audiosciencereview.com/...icon-dd8-review-multichannel-amplifier.19576/
0.005090% THD+N is equivalent to 85.866dB SINAD, or is another way of saying that the sum of all distortion and noise for a 22kHz bandwidth is 85.866dB below the signal.
"Bass can have up to 10% distortion" is equivalent to "distortion can be up to 20dB below the signal (or bass note)".Since bass is at the extreme end of human hearing sensitivity, bass can have up to 10% distortion and you will not be able to distinguish it from the actual bass note.
My first reply to you was to contextualize this threshold value. I quoted a study showing perceptual thresholds express in both dB and percent for varying SPL and specific harmonic content. The way to read the table from that study is as follows:
- For a 20Hz signal ("bass note") at 80dB SPL:
- 2nd harmonic distortion (i.e., a spur at 40Hz in addition to the 20Hz signal, also known as H2) can be up to -24dB or 6% of the signal until you can hear it.
- H3 (60Hz) can be up to -36dB or 1.6% of the signal until you can hear it.
- H4 (80Hz) can be up to -43dB or 0.7%.
- H5 (100Hz) can be up to -47dB or 0.44%.
My point was that you cannot say stuff like "up to 10% distortion". It's very misleading and not useful even as a rule of thumb.
In general, it's important to get away from a kind of flat threshold thinking about sound. There are other studies that contradict the thresholds by Fielder et al that I cited. It's definitely an unresolved question, but absolute thresholds aren't as important given how effective masking is when we're listening to music.
The best we have available, in terms of a comparative standard, is the CEA 2010. However, some context is necessary. It states the following for allowable distortion thresholds vs. the fundamental (i.e., the signal or bass note):
- H2: -10dB (31.6%)
- H3: -15dB (17.8%)
- H4–5: -20dB (10%)
- H6–8: -30dB (3.2%)
- H9≤: -40dB (1%)
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