First of all, what key is it in? The key signature (2 sharps) suggests D major, but the tonic, if there is one, is surely G major. So is the key or mode really G Lydian? In some sense, yes, though it bears little resemblance to earlier (pre-1650) modal music.
It does, however, tie in with the 19th-century ‘revival’ of Medieval and Renaissance modes, as much as it does with the new idea at the time about eliminating emotion and desire as much as possible in music. The two ideas were linked by a misunderstanding of pre-tonal music as floating and emotionless, lacking the build-up of harmonic tension and its subsequent resolution that is so fundamental to music of the so-called common-practice era (roughly 1700-1900).
In fact, the desire for resolution and the resulting emotional response (discussed in much music psychology) has its core in the tension- and resolution-pattern given by the dominant 7th resolving to the tonic. But in Satie's piece the major 7th (so not a dominant 7th) in the opening chord does not resolve: it merely becomes the 3rd in the following chord, another major 7th chord, which also doesn't resolve in any traditional sense, but instead forms a kind of pendulum with the first.
To experience the effect of this more clearly, have a look at the video (above), where Satie's original version is followed by a slightly altered one in ‘standard’ G major, utterly banal by comparison! Both are deliberately played by ‘emotionless’ MIDI to remove any aspects of interpretation in performance.
So why does this music feature so heavily on ‘Relaxing Classical’ playlists? One reason is that it does not exhibit the tension associated especially with late Romanticism in music (for example Wagner, Richard Strauss or even Scriabin). This is why it must be considered revolutionary, as Satie was among the first to create such ‘emotionless’ yet beautiful music: ‘L'art pour l'art’ (Art for art's sake).
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