Let me see if I can add a little context to this discussion. The piano is so ubiquitous that it is used as a reference point when discussing the octave numbers. So, the lowest C on the piano is designated C1. When playing a C flute, the lowest C for that instrument can also be designated C1 from the perspective of the player.
But, to put that into context, with the flute C1 sounding in the same octave as middle C on the piano, we get that flute C1= piano C4. Now to confuse things even more, a bass flute is an octave below the C flute. So, on bass flute the lowest C can also be designated C1 from the flutist point of view and the bass flute C1 = piano C3. And just to confuse things a bit more, a C flute C1 = bass flute C2 = piano C4.
If we consider a transposing instrument like an Eb alto sax, its lowest C can also be designated C1 from the saxophonist's perspective. However, because it is a transposing instrument, alto sax C1 = piano Eb3. And the piano middle C means piano C4 = alto sax A2.
So, if we consider the piano as the reference point, the bottom line is that the octave designations of various instruments are all relative to the piano octaves. That means the flute's low C is four octaves above the piano's lowest C. The alto sax's low C is three octaves + a major 6th above the piano low C.
Have I confused everyone enough?
