the harmonic series is the notes that you get from a brass instrument without changing the length of the tube.
while the trombone and trumpet change length of tube with slide and valves respectively, the bugle is just a single length of tube
that’s why Last Post that you might hear on Remembrance Sunday is written using only the notes of the harmonic series
if you take a string it can give you a note.
the 2nd harmonic is an octave above. it’s also half the length of the string. then as you go to a third, quarter, fifth of the length of string you go up the harmonic series and so on.
12th fret on a guitar or bass is therefore always halfway along the string.
this understanding is why some people can pick up a fretless bass or whatever and just play it in tune. it’s a mathematical relationship that determines where notes are, so some people can just sense it.
the system of notes that’s been developed by the west is called equal temperament, where every note inside the octave is equally apart
it is based on the octave as a vital concept. in the harmonic series, every note that’s not octave equivalents of the bottom note is out of tune according to western temperament
but they’re only out of tune by a tiny amount - which is why it all works out ok with eg. brass instruments
when I first learned about equal temperament it really bothered me, the idea of of just intonation with its pure ratios seemed much more preferable. but seems like there has to be some out of tune-ness as the circle of fifths is actually a spiral of fifths and if we want it to end where it begins it needs to be fudged, fudging all the notes slightly seems better than fudging a few notes a lot, though I am interested in hearing what those old systems that prioritised the purity of some intervals at the expense of some being really out of tune sound like, so now i’m fan of equal temperament never should have doubted it, the book didnt convince me.
in terms of whether it is arbitrary, think the big intervals, octave, perfect fifth and major third are pretty universal, as they represent the simplest ratios that our ears and brains like, how the rest of the scale is divied up varies between cultures, with some having more granular scales with microtonality relative to ours and some retaining the pure ratios of just intonation, the western way has its advantages, enable harmonic chord progressions and modulations between keys to happen, other cultures traditional music doesnt even have that as a concept. Indian classical music is pure melody, with octaves and fifths as drone as the only harmony, they dont change chords, but because of that the melody is less restricted. So wouldn’t say it is quite arbitrary, there are somethings that are naturally occurring and crop up everywhere, but then there is considerable variation between cultures in what to do in the spaces in-between.
feel like i ask this about once a year but you guys got any recommendations for a starter synth for a total noob? wanna get away from soft synths and start twiddling knobs. i love warm pads and rubbish string sounds.