Emotional modulation means to reduce the intensity of an emotional experience or the length of time one experiences a dominant emotion. Most people recognize that anger is part of life. But most people also recognize that if a person goes often into an uncontrollable rage, it is toxic to that person and those around him or her. Likewise experiencing anger over a prolonged period of time leads to a chronic hostility that is destructive. Limiting the extremes, while it may not be real crux of emotional health, is a valuable capability.
Moreover, one person can modulate the emotions of another. Mothers do this for small children, and if emotional development proceeds well, children take over the function for themselves. Still, everyone, at times of crisis, benefits from the modulating help of others. Women are especially adept at and inclined toward modulating the upset of men. Not for a complete stranger, but within a relationship, a man that is upset can provide a deep instinctive pull to a woman to get more involved. When the upset is constant, then of course the task is futile, but the strong instinctive cue remains.
Emotional modulation is also one of the few ways to influence from an oppressed position. Movies and books are full of plots that depict 'the bad guy' being modulated and eventually disarmed by the intended victim. In an abusive relationship, however, if modulation works, it is only until the next upset.
Having to modulate constantly for the primary aggressor, the survivor can become trapped by the feeling that she is essential for the primary aggressor's well-being, because this role becomes a source of meaning even in a very painful larger picture. The problem is one, there is no rest from this role, and two, the survivor comes to view her effectiveness by how 'in control' the primary aggressor seems. The survivor may unknowingly start minimizing the abuse herself, to bolster self-esteem.
Early in a relationship, having to do a lot of emotional modulation should be a warning sign that something extreme is operating. Getting drawn into investing a lot of emotional modulation can hasten the bonding.