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The most important aspects have been mentioned, however it should be pointed out that in harmonically complex passages of classically tonal music you often have to decide between two principles of writing accidentals, while being forced to ignore the other: Either you focus on vertical harmony or on the melodic line/voice leading. In the first case, as has been mentioned, you write the accidentals according to the harmonies you write. In the second case you look at where each tone moves/resolves to: Accidentals "bend" the notes in a certain direction, so you try to resolve the notes in this direction, so that flats are resolved downwards and sharps upwards. So you'd rather write the melodic line d#-e-f#-g than eb-e-gb-g. This of course only applies when a note actually moves to a neighboring half tone. You'd still rather write g-f#-e than g-gb-e for two reasons: first, it is seen as preferable to actually move to different diatonic base tones if possible and not to change tone alterations on one single tone; second, certain intervals are commonly seen as simpler than others: g-f#-e only consists of minor and major seconds, both "simple" intervals. G-gb-e however consists of an augmented unison and a diminished third, which are considered more complex and less "natural", since they aren't intervals one would commonly hear as such if played alone (i.e. if you played gb-e on a piano most people would hear it as the major second f#-e and not as a diminished third). There are many more such common "guidelines", many of which aren't formalized but just customary. Note however that these examples were made entirely disregarding the key of the piece, which would in reality matter quite a bit too of course.
However, this was to show that some of these traditional habits of voice leading are quite independant of tonality and have more to do with our notation system and readability.
But most times you don't have either harmonically oriented accidentals or melodically oriented ones, but a compromise. In a lot of traditionally tonal music it doesn't even matter, since the the two solutions are congruent, as harmonies are generally built to resolve all voices correctly. But there are still many cases where a choice has to be made and one thing sacrificed for the other. This is where you will see great individual differences between composers, some which lay their focus more on individual lines (say, Schumann/Brahms/Schönberg) and others for whom the chord constellations are more important (say, Debussy).
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