Thanks from heart for the great response to all of you,

To answer the question above, I need the RMS (incl Equal Loudness Contour, ELC) to be able to "to get commercially mastered tracks to play in sequence at the same apparent loudness". I need to be able to change that loudness.

Usually that loudness measures from -16 to -12db in Pop music, average. It's the overall loudness of a track, not its peak levels.

Also, on a bit lower level than CD, I need to be able to get my backing tracks at a similar (but loud) level so I can perform in venues not having to adjust the volume on every track.

Now, to my personal experience, it's good to be able to measure a track, get the average RMS (with and without ELC, and then make decisions about the final normalize levels based on the ear and the knowledge of what is recorded in.

The ELC (Equal Loudness Contour)  takes in account one 'imperfection' of our ears: we can't hear lower and higher frequencies at lower loudness levels. That's why, in the old Hi-Fi amplifiers one finds the 'loudness' knob. That knob adds bass+high at quiet levels, but does no change the audio spectrum at louder levels.

So, one measures the average loudness of a track and if there is a lot of bass in it, one knows that if the RMS is high, is due to the presence of bass. Then we look at the RMS with ELC. Then we decide whether to equalize out some low frequencies or live with them and have an overall quieter track, etc

Also, we don't need to do mathematically precise equal loudness on an album - if one track is -14db (RMS) and another -15.5 and they sound pretty close, and their bass frequencies are similar, then no adjustment is usually done.

Thus, here, as everywhere, technology works hand in hand with ears and experience and knowledge of what frequencies are recorded in that track.

Finally, the answer to the question is  something that would measure the average RMS (with ad without ELC) and then the RMS could be adjusted - for a whole track, per channel or only for parts of a track.

Now, about the apps mentioned in this thread:

1. Jamin is a very good tool and I am using it, but it does not give measurement of the actual RMS. It does not give average values of a whole track as well. It's meant fore something different, for mastering, not for normalizing, I believe.

2. Audacity only does peak normalizing, as well as Ardour

3. Adaptive Normalize in Rezound is good, but no measurements there as well.

3. Normalize(-audio) is something I didn't know before. That tool does the job, one can measure the levels (quite fast, as there is no GIU!) and decide what level to apply per track (or even batch, for less important projects). I can't change the loudness of a part of a track, though. Also, there is no measurement taking in account the Equal Loudness contour

4. ReplayGain does not work with wav files, I believe. Also, it does not change the gain, only gives instructions to Amarok (am I right here?) by writing some code to the ID3 tag of an mp3 file.

Thanks to all for your replies - if you come to some other ideas, please do write.

Viktor