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Chromaticism is an approach to creating music which incorporates notes from outside of the normal scale for the music’s central tonality. In basic terms, this means that the music has notes that may sound "sour" to the ears of many listeners instead of harmonious. These notes can be incorporated as part of a chord or as an element of an overlying melody. Methods of implementing chromaticism vary quite a bit, and the sour notes may be used either sparingly or very often, depending on the kind of music being played. In the hands of a gifted musician, these potentially sour notes may actually sound very pleasing due to the context or the way they are used, or they might be used specifically to create a discomforting mood.
Scales, in basic terms, are repeating note patterns that usually sound good to the human ear and generally revolve around a central tonal key. For example, the major scale has seven notes which are always a certain distance apart, and as the scale is moved to different keys, the specific notes change, but the basic pattern in terms of the musical distance between each note stays the same. The chromatic scale, on the other hand, is all 12 basic notes in sequence. For example, if someone were to hit any 12 consecutive notes on a piano, including both the black and white keys, he would be running through the chromatic scale. What this means for the purposes of this subject is that the chromatic scale has all the notes in the other scales, along with all the notes between those notes, and these are the tones that sound sour to the average ear.
Musicians throughout history have been incorporating chromaticism in small ways. For example, if a note is bent on a stringed instrument, there is a period between the start and end-point of the bend where the listener "experiences" the chromatic notes in between. The listener generally accepts this and it usually sounds OK because the musician starts and ends the bend at a point that’s in the right tonal key, making the chromaticism operate as a building of tension that is eventually released in a harmonically comfortable way. This same effect of sliding fluidly between tonally acceptable notes is a normal technique used by singers all the time, and it even exists to some extent any time there is any sort of vibrato in music.
Chromaticism is much more pronounced any time there is a full delineation of the notes instead of a sliding effect, but musicians are still often able to make the notes sound comfortable to the human ear. Most of the time, the musician will play so-called "passing notes" which are essentially chromatic notes between notes that are tonally correct. Basically, the musician will often start and usually end any musical phrases on a note that doesn’t sound sour to the listener, which makes the notes in between feel like they’ve been resolved, even though many of them may be very sour. Jazz musicians often excel at this, and it has also been incorporated by many major composers starting primarily during the romantic period and moving forward through history.
In some music, the innate sourness of chromaticism is actually embraced and there is no attempt to make the sour notes fit or make the listener comfortable. Anyone who has listened to the music on a movie score, especially horror films, has probably heard music that uses this kind of chromaticism to build a mood of unease or create a sense of chaos. Over the course of music history, many composers used chromaticism to stretch the boundaries of music, sometimes leading to music that has no tonal center at all, often referred to as "atonal" music.