I don't really follow the idea that "midi is lossy" in the sense described. Because it uses note-on/note-off pairs? I don't see the problem there. Certainly the idea that a score somehow has more information in it than a midi recording is ridiculous. A score always requires interpretation. The midi is, in contrast, fully specified, very little room for interpretation.
A midi recording contains pretty precise velocity info for each note (0-127) that is either not present at all in a score, or is present only in the form of a limited number of dynamic markings[1], which govern the flow of dynamics imprecisely, and almost not at all on a per-note basis.
With tempo it is similar to dynamics: midi will precisely determine when notes turn on and off, down to the millisecond, in the process resulting in the midi performance having a precise tempo. In contrast, musical scores have limited means to indicate proper tempo[2], necessitating (as with dynamic markings in a musical score) much interpretation by the musician.
All of this is not to say that a midi performance is somehow "better" than a score. There are good midi recordings and bad ones. A good recording will generally be made by an accomplished musician who in making the recording records fairly precisely a particular (and good) interpretation of the score. Likewise, a bad recording would generally be the result of a poor interpretation of a score. But whatever the case, the midi recording is far more precise than the score itself.
> Certainly the idea that a score somehow has more information in it than a midi recording is ridiculous
A midi file is designed to contain different kinds of information than a score, so it can absolutely contain less information (of a certain kind) than a score.
Imagine a group of notes that are attacked very close together in time in a midi file - is it meant to be a chord played without arpeggiation? A chord arpeggiated as fast as possible? A chord arpeggiated to a specific tempo?
When a composer writes (say) a chord with an arpeggiation sign next to it, it specifies that the notes are to be played in a certain order, and quickly. There are multiple possible performances that comply with this "specification". MIDI cannot encode this information (the information being the set of acceptable performances).
Thanks, yes, I would agree that a midi recording and a score to a large extent encode different types of information. The score has less of some of the kinds of information that are in fact present in midi. And the midi, of course, doesn't specify anything about ranges of interpretation; it simply represents a specific interpretation of a score.
A midi recording contains pretty precise velocity info for each note (0-127) that is either not present at all in a score, or is present only in the form of a limited number of dynamic markings[1], which govern the flow of dynamics imprecisely, and almost not at all on a per-note basis.
With tempo it is similar to dynamics: midi will precisely determine when notes turn on and off, down to the millisecond, in the process resulting in the midi performance having a precise tempo. In contrast, musical scores have limited means to indicate proper tempo[2], necessitating (as with dynamic markings in a musical score) much interpretation by the musician.
All of this is not to say that a midi performance is somehow "better" than a score. There are good midi recordings and bad ones. A good recording will generally be made by an accomplished musician who in making the recording records fairly precisely a particular (and good) interpretation of the score. Likewise, a bad recording would generally be the result of a poor interpretation of a score. But whatever the case, the midi recording is far more precise than the score itself.
[1] https://www.aboutmusictheory.com/music-dynamics.html
[2] https://en.wikipedia.org/wiki/Tempo#Basic_tempo_markings