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Transposition is simple: C in C major reads as G in G major, but if that very C is C4, what G (G4 or G5) is the corresponding G? What is the rule to figure out the octave?

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This is impossible to answer, up-transpose is as legitimate as down-transpose. It completely depends on the purpose of the transposition. For a singer the adjustment may be necessary to match his or her vocal range. It then depends, whether the high notes were the problematic ones or the low ones.

The only simple cases are adjusting a given score for a transposing instrument: then the diffrerence between the sounding note and the written one is clearly defined.

  • Well, you've (somehow) answered it: "depends on the purpose".But, let's imagine that we want to know how a given MIDI piece in, say, C major sounds in, say, G major. It would make sense to down-transpose here, as to minimize the overall distances between notes (as c is closer to the g one octave below). Such a general scenario is where I'm framing the question. – nightcod3r Jan 8 '16 at 22:56
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    As @guidot implies, the decision is based more on /why/ you're transposing than /what/ you're transposing. Even in your example, if your MIDI piece is designed to be played on a piano soundfont and the melody is already in the bass register, down-transposing will make the melody much muddier than up-transposing. And so the decision would be based on how much you value a clear melody versus a deep, rich bass tone. As it is, there are barely any hard-and-fast rules in writing, playing, or recording music. It's more than a little optimistic to hope to find such a rule for modifying music. – Babu Jan 8 '16 at 23:59
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    It also depends on the instrument tone you get after transposing. You may even consider transposing different parts of the piece up and down to get better sounding tones in every part of the piece. – Guney Ozsan Jan 9 '16 at 13:40

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