me: maybe im not actually autistic?

also me: if i do not tell someone about quarter comma meantone temperament i will literally die

!!! ok so quarter comma meantone is a tuning system that prioritizes major thirds above all else

western harmony prioritizes notes that fit into the harmonic series which is based off simple ratios from a fundamental pitch. twice the original pitch is an octave above, three times is an octave plus a fifth, and five times is two octaves plus a third.that gives u a major chord

so a major triad in root position has a fundamental and then ratios of 5/4 and 3/2, and in so-called 'just intonation' all twelve notes are built off these ratios. the problem is that there are multiple ways to get to different notes

eg, if you stack two perfect fifths (3/2 x 3/2) you get a ninth. hence a major second is defined as a ratio of 9/8. if you stack two seconds you get a major third. but that gives you 81/64. not 5/4.

the interval between these, 81/80, is small but not imperceptible. it is called a syntonic comma. there are many approaches to fixing this including (shudder) equal temperament. what quarter comma meantone does is exactly what the name suggests.

redefine the fifth so that it agrees with the major third. how? well if you can get a major third (plus two octaves) by stacking four fifths on top of each other, simply reduce the size of each by a quarter of the difference. hence quarter comma.

the result is a tuning system that has hella nice major thirds (mostly) and slightly flat fifths. problem solved!

except no. not exactly.

lets say you are building your tuning system and you really like D. for no particular reason. you want the major third on D so you know where to put F sharp. you also know where to put A (up 5) and G (down 5), and you want those M3s to be nice so you also get C sharp and B

and you should also be able to play in closely related keys so let's throw in E (M3 of the IV in G) and also G sharp (M3 of the V in A). we also want to be able to play in minor keys and relative majors so that tells you where to put F...

... which is down a major third from A, B flat, which is down a major third from D, and E flat, which is down a major third from G. and those are all the notes! you did it!

except no u didnt! going down a major third (x 4/5) should be the same as going up two major thirds and then down an octave (5/4 x 5/4 x 1/2). but obviously. 25/32 is not the same as 4/5. like. waaayyy off.

you made a scale that has precisely 8 wonderful, in tune major thirds and 4 awful, terrible, screeching major thirds. oh and also the fifth built on G sharp isnt a fifth but is instead down two thirds, up a fifth, and down another third, then up an octave, resulting

in one of the ugliest intervals you have ever heard. its called the wolf fifth and it makes me cry.

this scale plays really really well in D and closely related keys. and it is absolutely horrible in anything else. which is fine if you have say, a harpsichord and can just retune everything. not quite so good if you have, for instance a pipe organ

meet the split sharp keyboard

this bad boy has separate keys for G sharp and A flat. the A flat is made to be a major third below the C. you also get both an E flat (already defined) and a D sharp (major third above B)! this solves the wolf fifth problem and also gives you two more major thirds to work with

this is all just for one kind of tuning system! there are so many of them that were created its kind of intimidating!

*slaps roof of quarter comma meantone* this bad boy can fit so many major thirds in it

also if you were wondering the tuning system we use today is super boring, relatively speaking. you take the octave and cut it up into twelve evenly spaced steps. ie a half step is a ratio of 2^(1/12). as a consequence all keys sound equally good, but

basically the only perfect intervals are octaves. eg a major third is four half steps so 2^(1/3). this is noticeably sharper than a justly tuned major third. again if youtube was working i would post a link with these different sounds. as it is youll have to take my word for it