: How do I transpose an orchestral piece if it will push some of the instruments out of their range? Chord inversions seem to be the obvious choice, but sometimes it changes the overall harmony or disturbs the voice leading.

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One option is to re-orchestrate the work; we also call this "arranging."

By changing around the instrumentation, you can move the various lines to other instruments that might have different range characteristics. Just be careful that this re-orchestration doesn't ruin the balance of the work: often inexperienced musicians will re-orchestrate something such that the melody can no longer be heard.

Lastly, I would caution against changing the chord inversions. They are a vital part of the musical structure that help determine the form, the flow, and the emotional content of a work, and changing them up could actively harm your transcription.

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Transposing orchestral pieces mostly produces unsatisfactory results, but it's often done, particularly to accommodate singers. If you transpose up too much the result often sounds thin, and if you transpose down too much the sound can get very muddy. A major third is normally about the maximum you can get away with.

Most orchestral instruments don't have a hard upper range limit, but they do have a hard lower range limit, and these limits are often used in orchestral writing, so transposition downwards is slightly more problematic than upwards. There are several strategies to cope with out-of-range notes:

Single notes or whole passages can be transposed an octave. This only works if it doesn't mess up the chord inversions.
Out-of-range notes can be given to other instruments.
Another instrument from the same family can be substituted. A low range second clarinet part transposed down might work on bass clarinet. A high flute part transposed up might work better on piccolo.
In unison lines it can often make sense to just leave out individual instruments where they go out of range.
In really difficult cases it might be necessary to completely redistribute the orchestration of a section of music.