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Especially for something like this http://imgur.com/ROj1kBN (which is originally in D Major), how do I know that it doesn't constitute a key change? A more general question would probably be how do I identify key changes in sheet music in general?

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The composer starts in D major, as you say, but temporarily wants to put some D minor flavour in. As it's only on a temporary basis, and he's returning to D major, it's a modulation rather than a key change. So it's easier for everyone if the key signature stays the same, and accidentals are used to signify changed notes.

A proper key change would involve two naturals, at the beginning of the new key, often with a double bar line, and the new key signature put in place. If the new key is C/Am, it looks a little odd, as there would be the naturals, followed by seemingly no key signature.A look at the next few notes should give sufficient clues, though.

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There are modulations, and there are key changes. When a piece includes a "development" section, harmonic excursions will generally use accidentals. When it's more of a set of variations, each may get its own key signature. Or a composer may change key signature for purely pragmatic reasons, to make a section easier to read. The ultimate Key Change is the "up a semitone for the last chorus" device, common in popular music. This will definitely get a new key signature!

Is the Ring Cycle a series of modulations - it begins in Eb and also ends there, several evenings later - or are there key changes? Does Bach's 'Minuet in G' modulate to D, or change key? Would we be dissatisfied if the Ring didn't "come home"? What about the Bach? Do you find the unresolved modulation in "Unforgettable" magical, or vaguely unsatisfying?

You wanted an answer and I'm just offering more questions :-) Questions on how to label something often end up like that.

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  • Another question - where exactly does Unforgettable modulate? – Tim Jul 17 '16 at 13:35
  • Nat King Cole sings it in F. The song takes some pleasing harmonic detours but remains firmly rooted in F until the final four bars when it settles on a definite Bb, the subdominant key. It's odd, and to my ears rather unsatisfactory. Works best when the refrain's sung just once, as on the YouTube clip of Nat's TV show. The duet version with Natalie goes back for a second try, and has to jump through some harmonic hoops - a half-chorus instrumental in Db then a rather contrived slip back into F for the ending. Great melody, but structural problems that I find hard to spin into virtues. – Laurence Payne Jul 17 '16 at 23:04
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    Written in, well, the jury seems to be out! I have dots with a G major key sig., but others with a C major key sig. The duet may be like that as it was done post mortem, so there may only have been certain recordings of Nat to use. The original song sounds o.k. to me, with no perceivable modulation. For secong time around, I usually play a bar of the V of the original 1st chord, which makes it sound as if there's a key change there. – Tim Jul 19 '16 at 9:20
  • All of Nat's contributions to the duo recording are in F. The inherent modulation in the basic song may not worry you, but I'm surprised you don't perceive it. – Laurence Payne Jul 20 '16 at 9:54
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For your particular example, there is no clear way of telling, because it lacks context. In general, the key has changed when music feels more or less "at home" in a key different than the previous one. For this to happen, the new key has to be properly established, and music has to remain in this new key for some time. Therefore it depends on what there is before and after. In any case, the concept of key change (modulation) is kind of a theoretical simplification; in practise, analysis of a musical score is not always white or black.

This is a complex topic, that involves understanding well the concept of Key, function of different chords, etc… If you want to get it right, study a good harmony text. I strongly recommend you Arnold Schönberg's Harmony book. Chapter 9 talks about modulation, but reading previous chapters might also be usefu/needed.

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