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I always start with the piano,

writing the melody and the chords of the song.

After when I finish all parts,

I want to arrange my songs with other instruments.

But I don't know how to harmonize all other instruments together.

Is there any some type of theory for this ?

closed as too broad by Todd Wilcox, Shevliaskovic, ex nihilo, MattPutnam, Tim Oct 29 '18 at 13:11

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The harmonies generally will transcribe from what happens on piano to other instruments. If the harmony in a particular bar is around an F# chord, then all the instruments will need to be playing mainly the notes F# A# and C#. Not necessarily at the same time, but maybe the clarinet for example, could play A# and C# in that bar, half and half, while the trumpet plays F# G# and A#.

Look at it all vertically, bar by bar, checking that the main notes contained therein mostly constitute the underlying chord, as indicated in the original piano accompaniment.

Arranging a song is far more complex, with different mixes of instruments, coming in and going out, but that question is hinted at in the question as posed. It's another one for another day.

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There is a music theory topic Orchestral Instruments, learning this will help you use more instruments in your music, This classifies instruments into families like Brass, String and Wood, each of these instrument families have instruments classified into different voices like in Brass family Trumpet for Soprano, French Horn for Alto, Trombone for Tenor and Tuba for Bass.

Example lesson here

Example 4 part music that uses Brass family here

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