Attempting to cheer up a person who is deeply sad using external methods that clash with their emotional state is often useless and can even be destructive. This mismatch is illustrated through two vivid images of incompatibility.
The first image involves clothing on a freezing day, which commentators understand in two main ways. One perspective views this as a person taking off their clothes in the cold, or wearing worn out, torn garments that offer no warmth at all [רש״י, אבן עזרא, ביאור שטיינזלץ, עמנואל הרומי]. Another approach suggests it refers to a person wearing thin, highly decorated garments on a bitter winter day. While these clothes may look beautiful, they provide absolutely no protection against the freezing temperatures [רלב״ג, אלשיך, מלבי״ם, מצודות].
The second image describes a destructive chemical reaction involving natron, a soft earth historically used as a cleaning agent, a base for soap, or a material for delicate pottery [רש״י, אבן עזרא, מצודת ציון, מלבי״ם]. Pouring vinegar on this earth creates a harmful reaction. The vinegar dissolves the soil, ruins its cleaning properties, and causes the material to crack on the outside and crumble from within [רש״י, אלשיך, ביאור שטיינזלץ, מצודת דוד].
These two images serve as a metaphor for singing joyful songs to someone with a broken, miserable heart [אבן עזרא, מצודת ציון, ביאור שטיינזלץ]. The primary approach among commentators is that playing happy music for someone deep in grief does not help. Instead, it angers them, weighs them down, and worsens their emotional state. Even if the sad person tries to force a smile outwardly to please those around them, inside they feel suffocated by a growing sadness, much like the natron that bubbles and dissolves from the inside out [אלשיך, מצודת דוד, מלבי״ם].
Taking this concept to a spiritual level, some apply it to the act of teaching Torah to a wicked student who is unwilling to accept it, or attempting to calm the evil inclination with pleasant words. These efforts are doomed to fail because the core elements simply do not connect [רש״י, אלשיך, מלבי״ם].
However, a completely opposite approach views these metaphors as a positive process of healing. According to this perspective, just as wearing a decorated garment over warm clothing adds beauty, and just as combining vinegar and natron can actually complete a cleaning process and release a pleasant scent, singing to a sad person can ultimately be beneficial. A repeating melody can disconnect a person from their negative thoughts, successfully pierce through their heavy sadness, and eventually bring true joy that drives the grief from their heart [רלב״ג, עמנואל הרומי].