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So what makes punk, disco, new wave, heavy metal, grunge? Is that not subject to technical analysis?
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This is gonna be really general, because categories cross over and sounds can be blended.
Heavy metal is characterized mostly by power chords, where the guitarist plays the 1st and 5th notes of the chord (leaving out the 3rd). That is, instead of playing GBGBDG for a G chord, he’ll play GDG — perfect fifth and perfect fourth intervals, no sixths or thirds.
Since it is the state of the B in the scale of G that decides whether it’s G major (B natural) or G minor (B flat), heavy metal is kinda neither major nor minor. Melody-wise, the singer can sing the normal B or the bluesy B flat without committing to “happy” major or “sad” minor tonality.
Typically a heavy metal song relies most on the I, IV and V — the tonic, subdominant and dominant chords of the key. In the key of G, that would be G5, C5 and D5. Because it is neither major nor minor, heavy metal can also leap to the subtonic — that is, in the key of G, the F is usually sharp, but the subtonic would be F natural.
Those intervals of 4ths and 5ths really stand out and they don’t turn muddy or garbled when you distort 'em, so they’re a clean, loud, powerful choice for that particular style.
Good example: “Problem Child” by AC/DC.
Grunge has many of the same musical qualities as heavy metal, but since it’s descended from punk music, it’s slightly more committed to minor tonality and dissonance — they knew, like heavy metal guitarists, that the 3rds and 6ths and suspended 4ths sound dirty and muddy when distorted, but the grunge guys wanted that kind of sound that you could get with thirds, suspended fourths + major seconds, and so on.
Instead of sticking with the big 3 (I, IV and V), they were free to wander off into other chords. “Smells Like Teen Spirit” is in F minor (where the I-IV-V progression would normally be F5, Bb5, C5) but instead plays F5, Bb5, Ab5, Db5. There is no V chord — they don’t play C5 during the verses, but instead play Db5 which is a half-step difference — so the song doesn’t have a musical resolution where it goes to the C5 dominant, making it sound restless and dissatisfied.
You could also characterize grunge from punk by the dynamic variations that grunge seemed to enjoy (soft and minimalist bits, then loud rockin’ bits).
Disco is much more brazenly harmonic than heavy metal or grunge; not content with a simple C chord (C-E-G) you might hear a C major 9th chord (C-E-G-B-D), or a C9 (C-E-G-Bb-D) or a C minor add 9 (C-Eb-G-Bb-D) by the rhythm guitar. You may also hear a syncopated bass line — like the one in “Stayin’ Alive” that starts on the 1 beat, and goes like this:
1 & 2 & 3 & 4 &
x x x y-- x y-- x x x
where you see that note Y, the one that gets held out and emphasized, does not happen on the beat, thereby preceding the drums and guitar by half a beat.
The disco beat is generally in quarter notes or eighth notes on the high-hat, hitting closed-open-closed-open, making a sound like tk kssss tk kssss tk kssss tk kssss tk kssss.
Add to that some electronic synth (or real) strings playing octaves (C, then a C above that), some fat horns, and give it a tempo you can dance to.
New wave was a marketing term applied to a whole bunch of different kinds of musicians who sort of inherited the spiritual mantle of punk music, but who took it in a more keyboard-and-harmony direction, and with cleaner (read: digital) recording and post-processing techniques. Musically speaking, there isn’t much about the notes themselves that makes it a “new wave” sound. As Wordman suggested, and I agree with, it’s mostly about the engineering sound and the recording equipment rather than the notes.
Are these universal truths for every band, every song? Hell no. Surely someone will come along and say, “Remember that one forgettable band who had that one song that used that technique, and they weren’t a ____ band!” These are very general statements, and yeah, they’re broken all the damn time. 
Next week: reggae, blues, and the mu major chord of Steely Dan. 