Here’s an attempt at a short answer. “Beauty” is a vague term enclosing a manifold of diverse experiences. Trying to define it as one kind of thing (property or whatever) makes little sense. It is mostly in a certain pattern of behaviour and experience – How beautiful! – that beauty comes to play its part. And since those experiences are among those that are most worth having, yes, it matters.
And here are a few reflections around the short answer.
Beyond the how beautiful! experience it seems a bit strained to make it into an abstract noun – this “thing” called “beauty”. What could it be?
According to a long philosophical tradition that goes back to Plato and beyond, beauty is a matter of unity in multiplicity, the unity that may be grasped beyond the manifold of experiences, simple relations, “harmony” in a broad sense.
Is harmony the domain of beauty?
It is not only the mathematician or scientist who calls out how beautiful! when calculations turn out right; when connections are suddenly revealed; when loose pieces join to make a whole. On the other hand, isolated from that experience of discovery, that revelation-out-of-complexity, what beauty could there be in a geometric shape, in 2+2=4?
It is when coming out of confusion that we may experience simplicity as beauty. It comes with an emotion that might best be described as wonder. Because of this (minimal) emotional touch, how beautiful! implies: how moving! But how moving! does not imply: how beautiful!
I would be senseless to cast away beauty because all that counts is emotion. That may even sound like an absurd proposition, but what I found in a recent book on musical rhetoric comes close. “I catch myself sometimes describing a work of art as “beautiful” when what I really [!] mean is that it has touched my heart,” writes the oboist Bruce Haynes in The Pathetick Musician (2016). (The shoddily produced ebook has no page numbers.)
Is the experience of being emotionally touched more “real”, or profound, than the experience of beauty?
Let me look for a moment at one of the pieces of music that first come to my mind when thinking of the experience of beauty. The second movement of Ravel’s G major piano concerto, in E major, starts with a long piano solo, a tender, familiar-yet-enigmatic unendliche Melodie that ambiguously hovers between 3/4 and 6/8 time. When it finally comes to a conventional trilled cadence, the flute’s entry on a high C-sharp seductively deflects it away, towards a restful but fleeting A major. I won’t try to analyse why, but for me the flute’s entry is one of the strongest frisson-provoking moments in all music, not weakened by rehearings but enriched by the memory of those past experiences. How beautiful!
What seems to be a stable ingredient in the various emotional mixes that come with the experience of beauty, is that element of wonder. If Ravel’s music were merely expressive, causing no wonder, it would be just one of those countless pieces expressing something or other.
So, Haynes was right in arguing that calling something beautiful involves an emotional component. But he was wrong in discarding beauty for emotion or expression, as if that’s all that counts.
But speaking of “beauty” in the abstract we may give the phenomenon a significance and coherence that is lacking from the mere that’s beautiful! – which may mean various things: handsome, attractive, nice, pleasant, you-name-it.
And what provokes our interest in these handsome-attractive-nice-pleasant-you-name-it-things may be very different causes. As I wrote previously, we may call a face beautiful, a landscape, a vase, the sound of wind in the leaves, a mathematical formula. In a certain context it may be convenient to think of all of this as involving “beauty” (rather than mere “attractiveness” or “pleasantness”). And I’m inclined to think that wonder should be part of that context. If so, how beautiful! means more than: I like it, or: how touching. And wonder is one of the best emotions we can have, because it involves an opening up, a cessation of hostilities, of distrust, of reservation or mere boredom; maybe, too, something like harmony.