I'm looking for help with respect to where I could start learning music in general as a guitarist. I can play some simple songs and melodies I taught myself, understand what notes map to which frets/strings, etc. I also understand the chromatic scale, and roughly how it maps to piano keys, etc (ie: why there is no
E#/Fb), but that's where it ends. I've read a few books, including Music Theory for Beginners, but it wasn't helpful to me. I come from a strong math background (understand harmonics, pitch, semi-logarithmic scaling, etc), but have zero music background beyond enjoying it in general.
I'm attempting to learn scales, chords, and basic music theory, in hopes that I can read music sheets rather than just guitar tabs I download online.
I understand that chords are just combinations of notes played simultaneously to give a "richer" sound, and that scales are just sequences of notes following a set pattern, and they aren't necessarily symmetric (ie: some scales are played differently going up versus down in pitch).
What is the significance of scales in playing songs? If I pull a sheet of music up, it sometimes has the chords I'll be using, so I know what finger positions to use in advance. Does knowing the "scale" or "key" that that song is played in have any similar effect (ie: I know which notes/frets I'll be using, and which ones I won't, example below)?
I've tried playing scales as part of daily exercises, and it's improved my dexterity and fretting speed, but I can't see how they impact the songs I play. What are scales and keys used for if I just want to pick an arbitrary song and play it?