It is arguable that the first perfumers were alchemists, and it goes without saying that they were natural perfumers.  

The science and intuitive art of compounding raw materials through various processes, to transform them into something greater as a whole, is certainly a fitting metaphor for what natural perfumery is about at its very basis.  

The dictum solve et coagula, to dissolve and combine, is the process through which the alchemist worked to transform body into spirit, and then spirit into body.  This was the process to volatize that which was fixed, and to fix that which was volatile.

As above, so below (and as below, so above, conversely) is an axiom that is frequently repeated in the remaining writings on alchemy.  The alchemists believed in a unity and correspondence between the physical and spiritual realms, that the cosmos was unified thusly, and that both realms operated with the same laws.

Alchemists did not have the clearly-defined distinctions, in their world, between religion, science, art, and medicine, that we take for granted today.  Matter and spirit were not viewed as the very discrete quantities we observe; the dividing line between them was decidedly hazy and open to interpretation.

In my beginning is my end...  A potent symbol for the wheel of time is that of the Ouroboros, a serpent devouring its tail as an act of self-fecundation.  Carl Jung's analysis of the Ouroboros as it relates to the alchemists was that this self-perpetuating cycle of life, and death, and life again, was symbolic of the alchemists' understanding that humanity itself is the ultimate prima materia being manipulated and fashioned into art, by means of science, or alchemy, or related overlapping modes of transformation.

Natural perfumery is very much about transformation, and of altering the physical and mental state.  

We dab on a compounding of ingredients (i.e. a finished perfume) and feel ourselves emboldened to be social butterflies.  Or we feel more approachable, and more comfortable in our own skins.  We scent ourselves to be more attractive to others, or to feel more attractive.  There is a psychological component here that the alchemists would have understood, the transformative, although their understanding would have been more holistic given their lack of clear boundaries between science (and therefore psychology), art, and reason.

In alchemy, we are part of the process and are part of the art itself.

Natural Perfumery is about using the bounty of nature as your palette of materials.

Essential oils (steam-distilled, hydro-diffused, hydro-distilled, cold-pressed), absolutes (solvent-expressed), concretes (solvent-expressed), CO2 extractions, tinctured resins and oleoresins, tinctured plant materials, infusions.  These are blended and then carried in organic perfumers' spirits, or organic jojoba.

Just as learning to draw and paint is as much about learning to actually see, and process what you are seeing, as it is about control and technique... Perfumery is very much an act of learning how to smell materials, how to process and categorize your instinctive responses to them.  Some perfumers find that their other senses are heightened when they are learning to smell and discern.  In my case, I discovered an appreciation for wine and for chocolate that I had previously not given much thought.  When you recognize nuances for what they are, you never forget them, and that this can extend into the realm of taste is actually quite sensible.

Perfumery taps into the psyche of the wearer, and of those around the wearer.  Aromachology explains how perfume affects us.  Scent stimulates the "pleasure center" of the brain, which in turn elicits feelings or sensations such as exhilaration, self-confidence, calm, happiness, nostalgia, sensuality, etc.  Maybe lavender reminds you of an aunt who grew it in her garden, or you think of the lavender-scented handkerchief that she used to wipe dirt off your face after playing outside, for example.  Perhaps the scent of jasmine elicits a purely limbic response and you feel yourself flush and get weak in the knees when you smell it.

The alchemists would likely view this phenomenon as proof that matter and spirit are essentially the same thing, and that the boundary between either is decidedly hazy.