What are the important elements of harmony, rhythm and orchestration in composing relaxation or spa music?
Try sustaining the 1 and 5 of the key while you change the bass note. Or try sustaining the tonic in the bass while the right hand changes chords. Lots of sustaining things, lots of repetition. Find a simple repetitive motif and repeat it o. Every chord change.
Here's how to know what chords go together. Usually stick with the 1 2m 4. 5 and 6m
https://wordpress.com/post/ofonechord.wordpress.com/76 (I'm speaking from the perspective of a keyboardist, but you can take these concepts to other instruments.)
My immediate thought for archetypal 'relaxation' music would be the 'Ambient' genre.
a few tips if following this style:
harmony : you may want to avoid 'chord progressions' in the traditional sense. Exploring the possibilities within a single scale, but with a fixed harmonic root note or drone is common. It's often good to have some interesting and dissonant moments to prevent the music being too saccharine.
rhythm : you may want to avoid a strict pulse or percussive rhythm, but still have some sense of cyclic movement within the piece. Try to create patterns that are natural and unsurprising without being too predictable and oppressive.
orchestration : effects like reverb and delay, and synthetic sounds can help in transporting the user to 'another world', as can foreign / world instruments.
All this might sound like a complete cliche and a recipe for 'cheese' but it does somewhat depend how well you do it!
FWIW if I were going to a spa now I think I would like them to play me some Charles Mingus, which is a bit different to what I've described!
Anything using the major pentatonic scale as your melodic lead should come close to the relaxing compositions you're looking for