There is a possibility of addressing this question historically... My understanding (which is possibly apocryphal) is that mf
came before mp
, and originally meant "normal volume". To explain, "forte" has two meanings, in the same way that the English word "loud" can both
- Mean "high volume" — as in "play it loud" — and
- Refer to the concept of loudness more generally — as in "how loud is this note?", to which an acceptable answer could be "not very", "quiet", "moderately loud", etc.
And so mf
was originally taken to mean "with medium loudness"; and mp
came about later on, as a sort of reinterpretation of what mf
meant. Do I have any proof for this? Nothing but sketchy recollections from a music history class.
Overall, I'd lean towards mf
being closer to "medium volume" than mp
, although of course what that means is subjective and will vary based on the piece, as others have indicated. I wouldn't think this usage is entirely set in stone, though. For example, Boulez used twelve dynamic markings for serialising dynamics (pppp
, ppp
, pp
, p
, quasi p
, mp
, mf
, quasi f
, f
, ff
, fff
, ffff
), while Mozart used six (pp
, p
, mp
, mf
, f
, ff
); as far as these and similar practices indicate, it doesn't seem like there's a reliable symbol for "exactly medium volume". Even MIDI velocity can't encode something exactly between 0 (minimum) and 127 (maximum), which would be 63.5.
But, this shouldn't worry us too much. If a composer wants to notate dynamics that precisely, they will probably make that clear in the score. Otherwise, it is open to interpretation...