Not seen much of Harmonia in this so I thought I’d throw in my thoughts.
While Harmonia may come from the term harmony, and thus may represent different forces or people coming together to create something beautiful, there are actually a few other things in the story to emphasise this concept and the use of the name. In Harmonia, colour is used often to describe how one feels (e.g. orange is happiness, blue is sadness etc…), and each of the main characters are associated with these feelings (Shiona is always happy and thus orange, Tipi is always sad and thus blue). I thought this was relevant because those elements are prominent throughout the story and the term ‘colour’ has some meaning in music.
The term ‘tone colour’ (also known as timbre) is used in music to describe properties of sound outside of pitch and rhythm – it’s what distinguishes the difference between a flute and a clarinet. So if each character represents a different emotion/colour and one considers each of these characters to be a different timbre, then the union of these characters can create a harmony.
On a similar note, there are also cases of people with synaesthesia associating harmony with colour (A famous example is the composer Olivier Messiaen who has literally described elements of his music as a specific colour). So there is a literal aspect of this association between colour and music as well that should be considered.
Another thing that I thought should be mentioned is how music naturally provokes an emotional response based on different elements such as harmony, so if Harmonia has an emphasis on feelings then it makes sense that the title should be related to something that creates emotions. Even the line ‘You taught me how important feelings are. There is an everlasting song.’ supports this idea. The everlasting song symbolises the constant emotions one has and how they can never go away.
So while there may be some musical elements in the story such as the music box, they’re just used as an emotional catalyst. The title of Harmonia is used to represent all the ways of communicating emotions from one person to another and since music (and more specifically harmony) communicates this concept is several different ways it makes sense that it would be the basis of the title.