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Modulation means getting between keys, so let's say you are playing in the key of C, but you want to get to the key of Eb smoothly, without jarring the nerves of the listeners. There are lots of ways to do it, but the main point is that you have to get to the V7 chord of the new key. So from the key of C to the key of Eb, that means getting to Bb7. How do we do that smoothly? We look for chords with common notes. Since the V of the V of the new key would be Fm7, we have C as a common note. So we hold the C in the C chord, and move the rest of the C chord to Fm7, then Bb7, then Eb, and presto -- we are there! I realize that may be a bit hard to follow with just printed words to follow, but if you saw it happen you would understand it instantly.
There are basically 3 ways to transpose:
1. by intervals
2. by scale degrees
3. by solfege -- the movable "do" system.
But since solfege applies mostly to singers, we will ignore that possibility and just take up the first two:
1. Intervals: If the new key is an interval of a minor 3rd above the old key, then all notes in the song will also be an interval of a minor 3rd higher. In other words, if you are transposing from the key of C to the key of Eb, which is a minor 3rd higher (or major 6th lower -- whichever way you want to look at it), then all melody notes will also be a minor 3rd higher:
"G" in the key of C would become "Bb" in the key of Eb. "E" in the key of C would become ":G" in the new key of Eb. "A" would become "C", "B" would become "D", and so on. All chords would also move a minor 3rd higher. The "C chord" would become the "Eb chord", the "F chord" would become the "Ab chord", and so on.
2. Scale degrees: Each key you play in has it's own scale degrees. In the key of C the scale degrees are: C=1, D=2, E=3, F=4, G=5, A=6, B=7, C=8. In the key of Eb, however, Eb=1, F=2, G=3, Ab=4, Bb=5, C=6, D=7, Eb=8. So if I want to transpose Silent Night, for example, from the key of C to the key of Eb, I need to notice what scale degrees I am using in the key of C, and then use those same scale degrees in the key of Eb. For example, Silent Night starts on the 5th degree of the scale, goes up to the 6th, back to the 5th, then down to the 3rd. In the key of C that is: G-A-G-E. But in the key of Eb it is Bb-C-Bb-G. Why? Because the scale degrees 5-6-5-3 are constant -- we just need to apply them in each key. What about chords? Same idea. If the chord progression on Silent Night is the I chord followed by the V chord, followed by the I chord, followed by the IV chord, etc. -- then in the key of C that means C-G-C-F-etc., but in the key of Eb it means Eb-Bb-Eb-Ab-etc.
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