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For example a chord progression in the key of G that have the chords G Major - C Major and D Major and you want to transpose to the key of B

Slide the new key B under the old key G.  The new chords are B Major - E Major and Gb Major

Example 1

Example 2

For example a chord progression in the key of G that have the chords G Major 7 - Bb minor 6 - A minor 7 and D7 and you want to transpose to the key of B

Slide the new key B under the old key G.  The new chords are B Major 7 - D minor 6 - C# minor 7 and F#7

Example 3

In example 3 the Roman Numerals are showing the notes of the Bb/A# Major Scale and underneath are the Scale Chords that could be used.

The Red arrows show the I - IV - V the most common chords used in many songs, the pink arrow shows the relative minor