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I studied Ogg Vorbis posts hard and it is still unclear for me:
1. What quality setting do I have to use to get encodings not worse than with LAME 3.90.3 APS? (I think q6, am I right?)
That is subjective and depends on the person's ears. So you'll get different responses from different people.
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2. What is the difference in stereo encoding between q5.99 and q6.00?
q 6 is when lossless stereo coupling occurs. Essentially Vorbis saves bits by transmitting the differences between channels. It usually works well until we hit the low bitrates where we get 'stereo collapse', and it sounds rather mono. At q 6, there is no 'loss' there. Unless your hearing is very sensitive to stereo separation, I doubt you will hear much difference between 5.99 and 6.00.
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3. Is it safe to use q6.13 or q5.24? Or they can produce worse quality than q6 and q5?
AFAIK, fractional qualities are very safe to use.
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4. Is Ogg Vorbis better than LAME 3.90.3 APS in classical music in most cases?
If I remember, guruboolez pointed out some problems with Ogg Vorbis on classical music. Since GT3b1 is based on Vorbis 1.0, these will remain unfixed. However, I suspect they only affect low bitrates. So at the quality values that GT3b1 is typically used (>= 5), the artifacts will be different. People have reported that Vorbis suffers from a high frequency boost on all q values. Some find this annoying, some find this negligible, and some find it makes it sound better than the original.