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I've been working on an orchestral piece for a while and I want to include a key change. For example, from Bb major into Eb major. How could one go about changing keys in a way that makes the music flow smoothly while keeping the same tone and feel?

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There are several ways. One easy one is to use a pivot chord; this is a chord that is diatonic in both keys; one approaches the chord in the first key and exits the chord in the target key. In your case, Bb to Eb, one could use Cm. It's the ii chord of Bb and the vi chord of Eb. A possibility (not necessarily the best) is to play a Gm chord (also diatonic in both keys) followed by a Cm, a Bb7, and then Eb. The key of Eb needs to be "confirmed" by playing something like an Ab or Fm chord; these have an Ab in Eb as opposed to an A in Bb. (That sentence sounds weird.) Schoenberg calls this "neutralizing" the A. Of course one could take the shortcut of playing Bb7 (the dominant seventh of Eb) followed by Eb.

Besides the usual harmony books, there are several (older) books on modulation. These can be found on the Wayback Machine or the Internet Archive. One is Arthur Foote has one called "Modulation." Max Reger has another called, "Modulation." A third one is Frank Shepard's "How to Modulate." Reger's book is a list of modulations from C to every other key and from Am to every other key. Foote and Shepard concentrate more on the theory behind modulation.

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Yes, B♭ major to E♭ major is trivial. Just stick in some A♭ notes. Shall we be a bit more adventurous?

A lot of discussion on modulation concentrates on the chord progression. Melody is also important. Here's a simple transition from C major to E♭ major. It's carried by repetition of a simple melodic phrase.

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Also consider the 'just do it' modulation. Don't try to smooth it out, dramatise it! You can imagine Beethoven doing something like this. 'I'm done in C major for now. Let's try F♯ major!'

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If you want something a little less abrupt, the ii - V -I sequence is incredibly powerful. Write one in the old key, repeat it in the new. Literally any new key will work. Try! Here's an example, C major to E major, followed by a condensed version.

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B♭ major and E♭ major are very closely related. In fact, there's only one diatonic note that changes - A♮ becomes A♭ when the key changes to E♭ major.

So I doubt there could be a more subtle, unnoticable key change. In fact, there are many instances in pieces where the music modulates in that way, and most people would not consider there's much of a move.

The note that is pivotal to E♭ is its leading note - D. That is part of the dominant chord in E♭, which is B♭7. So playing a harmony using that chord is exactly what's needed to introduce the new key. And the note which isn't diatonic to key B♭ is A♭. That's what'll lead the piece into key E♭.

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