The_Complete_Idiot%27s_Guide_To_Music_Theory

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Part 4: Accompanying
The original melody, marked up with intervals.
Transposing your melody one interval at a time.
Now, you start composing your “new” melody in the new key. The first note in
the new key (which you have to manually figure out) is a C, and the interval
between that note and the second note is a major second—which makes the second
note a D. The next interval is another major second, which makes the next
note an E. The next interval is a major second down, which makes the next note
a D. And so on, until you’re done.
This method doesn’t work as well when you’re transposing chords, because it
doesn’t tell you what type of chord comes next—major, minor, or other. I suppose
you could augment this interval-based approach by noting the chord type
from the original version, but that gets a tad complex; there are easier ways to
transpose chord progressions.
Software-Based Transposition
Thanks to modern computer technology, you may be able to avoid manual
transposition completely. Almost all computerized music notation programs,
such as Finale and Sibelius, let you enter your music in concert key; all you have
to do is click a button (or select a menu item) to automatically transpose one or
more staves to another key.
For example, the Finale program (from Coda Music Technology) has a drop-down
menu option that enables you to determine whether a given part is noted in
concert key or the instrument’s native key. Depending on the option you select,
your score can show all instruments in concert key, or the specific keys for each
instrument. The nice thing about this option is that you can do your original
composing in concert key and then automatically transpose the parts to their
own keys when you’re done writing—which is easier than trying to manually
transpose all the parts while you’re composing.
Finale also lets you transpose a part from any one key to any other key, just by
selecting a few options in a dialog box. When you want to change keys, you can
instruct the program to transpose the original notes up or down, as appropriate,