That our ears are not just hearing vibrations or waves of compressed air, but that our brains are actually "doing unconscious math" to the point where we (nearly everyone, not just trained musicians) can tell by "how it sounds" if the math of that waves of compressed air is geometrically and proportionally sound. That utterly blows my mind every time I think about it. Octaves, 3rds, 5ths, and all of harmonic structure is math, geometry, fractions, percentiles, proportions, all in the air and instantly computed by our brains from the signals our ears send. And that is not even including timing, tempo, rhythm and meter.

I'll try to break it down into something that makes it easy for a beginner. I wouldn't personally call myself an expert in the field by any means, but I have completed three college courses in music theory and taught myself a lot about it before hand. In my personal opinion the best way to begin to learn music theory, at least as it pertains to guitar, is to forget about specific keys for the time being; applying what you learn about scale degrees and whatnot can later be applied to any key. Instead focus on the numbers. For now I'll also disregard the pentatonic scales. So for instance regardless what the specific scale or mode is it will always have 7 notes in it, and the 8th note is the same note as 1 just at a different octave; the difference in the scales and modes is where you place the half steps. We'll start with the major scale. - = Whole step / = Half step 1 - 2 - 3/4 - 5 - 6 - 7/8(1) There will almost always be 2 half steps in any given scale or mode; I say almost because there are instances where this rule is broken such as Harmonic, Melodic, and Pentatonic scales. But I won't get into that for now. Now out of that scale you can begin to make chords; for the time being we'll assume chord means triad, or three note chord. There are many others, but these are of course the most commonly used. The difference between a Major and minor chord is the the third note in the chord. If it is flat(b) it is a minor chord, if not it is a Major chord; as with any language this rule is of course broken at times for instance a diminished chord has a flat 3rd, but it also has a flat 5th as well; and an Augmented chord has a natural 3rd, but also has a sharp(#) 5th. This may sound a little confusing, but it really isn't once you sit down put the theory on the instrument. Back to the scale; if you take the 1st, 3rd, and 5th degrees of the scale and play them in unison it will be a Major chord. It is important to note that any triad you play from the scale will be every other note; for instance 1 - 3 - 5; 2 - 4 - 6; 3 - 5 - 7, etc. (As a foot note, regardless of the chord you are playing the first note in the chord is always referred to as the 1 even if it is the second, third, fourth, etc. not in the scale; it is just easiest to give a visual representation by saying for example 2 - 4 - 6) Do that a minute and I guarantee you that you will be able to pick out which chords are Major, minor, and the single Diminished chord in the scale; but here it is anyway just in case you would like a visual representation: M = Major m= Minor D = Diminished M(1) - m(2) - m(3)/M(4) - M(5) - m(6) - D(7)/M(8) It is good practice to play through your scales and modes (I'll get to those next) with chords. Now if you recall, I said earlier the difference between a Major and Minor chord is the third note; well this is also true of a Major or Minor scale. Play the same notes of the major scale using the same half steps, but start on a different degree; say the 6th degree. You'll notice that it sounds minor. This is in fact the Natural minor scale of the Major key; and every note in the scale has its own scale known as a mode. Ionian (Natural Major scale) 1 - 2 - 3/4 - 5 - 6 - 7/1 (8) Dorian 2 - 3 /4 - 5 - 6 - 7/1(8) - 2(9) Phrygian 3/4 - 5 - 6 - 7/1 - 2 - 3 Lydian 4 - 5 - 6 - 7/1 - 2 - 3/4 Mixolydian 5 - 6 - 7/1 - 2 - 3/4 - 5 Aeolian (Natural minor scale) 6 - 7/1 - 2 - 3 /4 - 5 - 6 Locrian 7/1 - 2 - 3/4 - 5 - 6 - 7 Now those are all working with the same key. If you wanted to play the same mode using the same starting note you simply just place the half steps where they need to go for each mode. To really get the half steps ingrained into your head it is good practice to play each mode starting at the same place. Ionian (Natural Major scale) 1 - 2 - 3/4 - 5 - 6 - 7/8 (1) Dorian 1 - 2/3 - 4 - 5 - 6/7 - 8(1) Phrygian 1/2 - 3 - 4 - 5/6 - 7 - 8(1) Lydian 1 - 2 - 3 - 4/5 - 6 - 7/8(1) Mixolydian 1 - 2 - 3/4 - 5 - 6/7 - 8(1) Aeolian (Natural minor scale) 1 - 2/3 - 4 - 5/6 - 7 - 8(1) Locrian 1/2 - 3 - 4/5 - 6 - 7 - 8(1) There is a whole lot more I could write about; I didn't even get to the circle of fifths, prefect fifths, dissonant dyads and triads, seventh chords, leading tones and their connection to harmonics, and many other things, but this should give a pretty good starting point. Whenever you learn a new song, try to figure out the theory behind it and what makes it work mathematically based on this and other things you'll pick up and you're sure to learn a lot and begin to be able to pick up songs a lot quicker as well as write your own with relative ease.

If you play punk rock, literally nothing. If you play anything else, basic scale structure (major and minor) and relative major/relative minor relationships will take you a long way. Do a YouTube search for Marty Schwarts. He's got very user friendly beginner and intermediate instructional videos that aren't nearly as boring as most guitar vids out there

Scales m8

SCALES

Learn treble bass and tenor. Learn the other clefs now so you don't have to improve when they expect you to know it. Work on some exercises for finger independence, squeeze that thing (Idk the name but you've probably heard of it/have it.) and make sure to do patterns like 1st and 3rd, as well as independent fingers. I like to do 1st and 2nd, 1st and 3rd, etc on all the fingers.