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I'm trying to figure out how a key influences a song's pitch.
Let's say I have a song in C major. If I transpose it to D major does this necessarily mean that my song will have a higher pitch? Or is this assumption wrong because we could have been playing it one octave lower in D major. In other words, when someone tells you they're playing in one key versus another key, you can't make any assumption if the pitch will go up or down (?)
I think it might make more sense to ask how transposition affects the pitches of a piece.
Usually a piece is transposed for a specific reason. The two most common reasons are to make it more comfortable for a singer or singers and to make it possible or easier to play with different instruments. In either of those cases, whether the piece is transposed up or down depends on exactly which instruments are going to be used and/or the ranges of the singers.
For example, it's not uncommon for a person with a high voice to sing a part an octave higher than the original, while a person with a low voice may sing an octave lower than the original.
When pieces are played on different instruments, it's usually called a transcription, because more than just a straight transposition is necessary. For example, the classical guitar version of "Leyenda" (often called "Asturias") by Isaac Albeniz involves transposition to a different key from the original as well as moving the lowest notes up or omitting them and moving the highest notes down. Also, the chords are arpeggiated. These changes are necessary because of the major differences between the guitar and the piano (the original instrument).
So in the end, a transposition to a different key might simultaneously involve some instruments playing higher and others playing lower than the original piece, or even some notes being played higher and other notes played lower on the same instrument, when compared to the original.
'Transpose from C major to D major' doesn't tell us whether to go one up or seven down. Or nine up - which might well be the requirement if a song for bass voice was being transposed for soprano!
As anyone who has bought a song copy from one of the online music publishers will have discovered, the ability to have it 'in your key' can be a mixed blessing. Even without octave shifts, a piano accompaniment can become clunky surprisingly easily when transposed more than a few semitones. And where other instruments are involved, it's easy to fall foul of the absolute possible range, not just the most effective one. A piano part transposed down may sound muddy. A flute asked to play below middle C just can't. (OK, maybe B, as we're such a lot of pedants here.)
I think of pitch as the rate at which something vibrates. So a D note a whole step above a C will be higher in pitch. C can be higher, lower or the same as another C.
Transpose means you are playing it in a different key. If everything else was the same, like I am literally just shifting everything up a whole step all the pitches will be higher and you will go from the key of C to D. If you shift everything down from C to a lower D all the pitches will be lower and you will transpose to the key of D.
