The fidelity to the original performance it totally out of reach of current technology. This is brillantly demonstrated in Floyd Tool's book "Sound Reproduction", figure 3.3 page 36, with the directionality of a violin at different frequencies.
From 200 to 400 Hz, a violin is omnidirectional. You hear the direct sound, plus the sounds reflected on the lateral walls, the wall behind the performer, the floor and the ceiling. At 425 Hz, however, the violin doesn't emit in the back-down direction. Reflection on the back wall is lower, and the secondary reflection that bounces on the floor, back wall, then ceiling is severely attenuated. At 500 Hz, however, that's the dominant direction of emission.
And the directionality changes drastically many times given the frequency range. No speaker can reproduce the same soundfield with the same directions of emission for each frequency.
And that's for violin only. Other instruments are completely different, and emit different amounts of energy towards the walls, floor and ceiling.
A practical consequence : violins used to be recorded with microphones situated aboveand a bit in front of the orchestra. In this direction, violins emit a lot of energy in the 2500 - 5000 Hz range, that is not at all emitted in direction of the audience. Therefore the recorded sound was very different from the sound emitted in the direction of the audience. Recording engineers knew that in such recordings, it was better to attenuate treble. It could be thought to be a modification of the original sound, but it was not. On the contrary, this helped to artificially remake a violin sound that sounds like the one that is percieved from the audience.
So what if we record directly from the listener's position ? This way, we capture exactly what should be heard by the listener. The problem is that the original acoustic adds up with the acoustic of the reproduction room in a way that is completely unbearable.
Therefore, recording music is an art of recreating a soundstage, given an average listening room with an average two-channel setup, that is necessarily very far from the original, but still enjoyable. For example, the reflections on the wall that is behind you can't be recorded and reproduced with a two-channels system. They are replaced by new reflections created in the listening room. Which means that it's better eliminating the original ones so that they won't add up with the ones in your own room, coming from the front.
Try to record your own hifi with a stereo microphone from your favorite listening position, and play the recording back in the hifi. No, the microphone is not crappy, that's your room that sounds that way ! Make another recording with the left and right microphones just in front of the speakers to check. This experiment was one of the biggest surprises of my audiophile life : I had the microphone in hand, closed headphones on the head, and was moving the microphone from the speaker to the listening position back and forth, and I didn't understand what was happening : why did the sound change so drastically from the microphone point of view, while it didn't if I did the same thing with my own ears ?
The answer was that the brain is extremely good at eliminating the tonal balance of the room from the listening experience.
All these things make us reconsider the original question about fidelity to the original performance. Most of this fidelity is actually in the hands of the recording and mixing engineers, that have no other choice than to recreate an artificial soundstage and an artificial tonal balance that simulates a good listeneing experience, given that it is going to be used on a two-channels system in an average room.
So we are left with fidelity to the recording instead of fidelity to the live performance. If we can define fidelity for a speaker, it is not possible for a room. In low frequencies, rooms have very strong resonances that amplify some frequencies and not others. Even anechoic rooms are not very anechoic in low frequencies. And anyway, stereo recordings, as made in studio, are not suited at all for listening in anechoic rooms. They have not enough reverberation. Making a room that is neutral in low frequencies in very difficult. Some advise the use of as many subwofers as possible, scattered in strategic positions, so that they don't act on the same resonant frequencies in the room.
For speakers, the basics of good quality are quite undertood : they must have a flat frequency response in the axis, and a smooth frequency response outside the axis. How must attenuation must they have outside the axis ? I am not sure that there is any standard about this.
Also, in France, a story goes about Cabasse loudspeakers. Some models were claimed to have an excellent frequency response, but were not appreciated by audiophiles. The reason was that they were only good at realistic listening levels. But since home listening is usually performed at lower levels, these speakers seemed to lack bass and treble, because the human ear has not the same frequency response at different levels. This is easy to see on Fletcher-Mundson curves. Thus, a coloured speaker allows a listening experience that is closer to the original than a transparent speaker at domestic listening levels.
All these parameters makes the question of fidelity a very complex one.