In medieval & renaissance religious music, ie what got recorded, use of certain intervals was banned, like the flattened fifth nicknamed 'the devil's tritone'. It was considered discordant, sinister. But, it's widely used now, & we don't have the same association.
We think of notes in relation to vibration of plucked strings, but it's interesting to see the effect on a surface as visualised with a cymascope. There are constructive & destructive interferences, for sure.
Detailed schemes have been made of the moods of different keys, but there are many exceptions, & many songs that change key using notes that overlap (ie between associated major/minor keys). This paper summarises some of the main early theories, consonance, &c: The Affective Character of the Major and Minor Modes in Music. You may also find this preprint interesting: Harmony Explained:
Progress Towards A Scientific Theory of Music;
The Major Scale, The Standard Chord Dictionary, and The Difference of Feeling Between The Major and Minor Triads Explained from the First Principles of Physics and Computation; The Theory of Helmholtz Shown To Be Incomplete and The Theory of Terhardt and Some Others Considered.
A lot about music is cultural, learned, associative. The experience of listening to Balinese gamelan orchestras, with no introduction, no framing, is a good way to see this. Balinese players raised with this music, surely experience it differently.
That's not to say there are no intrinsic or deeper factors. This paper is interesting: Shaking Takete and Flowing Maluma. Non-Sense Words Are Associated with Motion Patterns. More generally we can look at the link between synaesthesia & onomatopeia.
It is nearly unique to humans to spontaneously dance when hearing music. There has been a long interplay between music and language, with some theories singing together rather than words drove our ability to vocalise. And tonal languages seem to have continued to push genes for better pitch discrimination. It is notable that few people have perfect pitch, we need a reference tone or to hear several tones, to get the key. When we hit whole tones, and perfect intervals, you might say we resonate with each other.
Sacred Harp singing is an interesting glimpse into choirs without an audience, and the social impact of singing together. Perhaps the deepest reason for an emotional connection, is music linking us to our prelinguistic selves, and connecting through song.