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I have learned music theory from the internet but I have this question that how to come to know that where one key starts and other ends? (When I am reading the music sheet)

For example, in Minuet In G, the minuet starts in G Major but in the middle it changes to D Major. Now how should I come to know that where did D major start?

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You mean when you listen to a song or when you see the music sheet in front of you? –  Shevliaskovic May 2 at 12:32
    
@Shevliaskovic When I see the music sheet music in front of me. –  Kartik May 2 at 12:55
    
Little bit off topic, but here's a scientific paper on detecting keys with computer programs. ccrma.stanford.edu/~craig/papers/05/p3d-sapp.pdf For many cases, some training and visual inspection will be easy enough, but it's still interesting. –  Roland Bouman May 10 at 10:59

3 Answers 3

up vote 10 down vote accepted

What you mean is not a change of scale, but rather a change of key. A change of key is called a modulation. Modulation is usually established by a full cadence into the new key. If a piece in G major modulates to D major, then you'd expect to see a progression of

D | G | A | D

which would be

I IV V I

in the new key of D major. Sometimes you won't find this entire progression but you will typically find the progression from A to D.

The A chord has a c#, which is not part of the scale of G major, so this is where the listener has the first sense that the tonal center is changing.

Note that in this case G and D are very closely related keys - they have 6 out of 7 scale tones in common, and this is why it is relatively easy to make this change of key.

So you can try and spot modulations by looking for accidentals. So in this case, G major, you want to look for an accidental raising the c to c#. I can see one immediately in measure 20. Also in the following measures, we see c# rather than c. The first occurrence of c natural is measure 24 in the left hand part. Chances are that the key is back to G major at that point. The actual modulation back from D to G will be in that measure or just before or after it.

Now that you found the accidentals, you have to analyze the harmony to figure out what chords are there, and what progression they make. Only after that step you can know for sure at which point exactly the modulation occurs. Of course, you should use your ears too; in many cases the change is clearly audible.

If we take a look at measure 20 (where we first spotted the c#) you can see that the chord is essentially A there. Same goes for the next measure 21. There are plenty of notes in the melody there that are not part of the A chord, but since the bass is A, it still sounds mostly like a chord of A. And in measure 21, the strong beats of the melody are a, c#, e which are in fact chord tones of A. So measure 21 really feels like an A chord.

It is also interesting to look a little further back to measures 17 - 19. As you can see, these three measures avoid the use of c as well as c# - The chords for these measures are G, D, Em. These are all preparation for the A chord introduced in measure 20. The Em chord in measure 19 acts as a so-called secondary dominant, making a transition to A smooth, and then measure 20 "reveals" a change of key is happening by introducing the c# rather than a c natural which one would expect if the tonality was still in G.

In measure 22, 23, 24, 25 the chords are

G D A | D F# A | D D7 | G

So what we see here is that after the introduction of the A chord in measures 20 and 21, we get a brief confirmation of the key of D in measure 23, which is again prepared by the last A chord in measure 22. And again, last chord in measure 23 is A, followed by a D in measure 24. But then measure 24 surrenders back to the original key of G again, by using a c natural. In the chord of D, this c natural is a 7th degree, making this a D7 chord. This is the dominant chord in the key of G. The dominant has a very strong tendency to fall back to the tonic chord, and indeed in this case it returns to G, which is the first chord we find in measure 25. The piece then continues in G.

So all in all, the escape from G to D is really rather brief; probably too brief to call it an actual modulation, it is more a temporary departure than a structural change of key.

In larger pieces, the key change will be explicitly marked by a double line and a key signature. For smaller pieces, the change of key is only temporary and transient, and normally this is not explicitly denoted - they simply write accidentals instead.

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"Of course, you should use your ears too; in many cases the change is clearly audible." Do you think this has something to do with one's training? i.e. after learning all the chords by heart, playing them, it becomes instinctive to a musician to hear the key change; but is it something naturally evident, or only to one who has the chords ingrained in their experience? (I hope it's clear what I'm trying to get at here) –  Jeffrey Kemp May 2 at 15:49
    
When just listening to a piece, I can pick out a key change easily. But to others, they don't necessarily pick it out, although they might feel the music "lift" a bit without knowing why it feels that way. –  Jeffrey Kemp May 2 at 15:50
    
The only thing I would add to Roland's excellent explanation is that the natural sign is written out on the C in measure 24, when it doesn't have to be (it would still be C natural if not written out, because there is no C# earlier in the measure). This is to draw attention to the fact that we are on our way back to G. –  BobRodes May 2 at 15:53
    
@BobRodes thanks for the kind words. Indeed - you are absolutely right. The natural sign is added to the score as a matter of courtesy. It would have been a natural c even without the natural sign. That said, courtesy signs are in many cases present, which is great. –  Roland Bouman May 2 at 17:05
    
@JeffreyKemp I meant even casual listeners sense something is going on. They are usually not capable of explaining what it is they hear, but they often do hear someting happened. By "using your ears" I meant you should - and almost always can - sing the local tonic, and this sense of tonic is what should serve as guide to understand what key, or rather, center of tonality, is currently in power. Just reading the score doesn't always cut it, esp. if the piece is modal rather than diatonic in nature. –  Roland Bouman May 2 at 17:08

In general there are a couple of beats where chords are shared between the two keys. You can think of these chords as belonging to both keys and establishing the transition. Once you hit a new chord or tone that does not belong to the first key, at this point you are definitely in the new key. so whether you decide to label this the "start" of the new key, or if you decide to label the transition passage the start of the new key, is up to you.

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+1 Yes, very true. –  Roland Bouman May 3 at 0:07

Often, a change of key will be noted with a new set of static sharps or flats, and then it is easy to spot.

In your example, this is not the case as the sharp for C's that indicates a key of D major is just noted with accidentals where the C# notes appear.

The reason for this notation could be one of the following:

  1. The section with the new key is just temporary, so it would be more of a confusion to the player that reads it to make a static key change twice.

  2. The composer feels that the melody still belongs to the D major just with some accidentals to make things more interesting, which in this case just happens to be C# that would normally indicate the key of D major if you add everything up.


As of how to spot where the key change occurs, I think Rolands answer is quite excellent.

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Thanks @awe, much appreciated :) –  Roland Bouman May 10 at 10:56

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