i would LOVE to explain this to you, it's so peak and i'm kinda dedicating a decent portion of my life into understanding it
so it starts with tuning systems
normally we have 12 equally-spaced notes per octave of course, which is a tuning system called 12edo
however you can arbitrarily choose any number there, like 6, for the 6edo tuning system (also known as the whole tone scale)
you can choose things 12 is divisible by for options you can play as a subset of 12edo, like 4 (which is just a diminished chord), 3 (augmented chord), 2 (just octaves and tritones), 1 (1 note per octave, the only intervals are multiples of octaves), and the previously mentioned 6
but you can also choose, say, 24
24edo has every note 12edo has, and the notes directly between them, for example between a major third and a minor third, 24edo has an interval called the neutral third, which is 3.5 semitones
yes this means there are half-flats and half-sharps now, they're called shats and flarps, deal with it :3
another example is 7edo ! since it has 7 steps just like diatonic scales (like the major and minor scales and all the modes), it can be treated as an equalized form of them, all of them combined and averaged out, so there is no difference between major and minor, and all the triads are the same neutral one
each of the numbers in that image are actually these tuning systems ! and the lines that cross over them are various properties, often known as "temperaments"
but before i explain this i have to explain JI, also called "just intonation", which means we have to go back to root pitch
when dealing with raw Hz, intervals are stacked by multiplication, not addition
the octave is 2 (usually written as 2/1 in this context), so 880Hz is exactly an octave above 440Hz
2/1 is the octave in JI. it's also the octave in all these other systems including normal 12edo, which is why it's so familiar. the rest aren't though, since no equally-spaced tuning system has pure JI except the interval it's divided by (which in this case is the octave)
3/1 is the tritave, an interval of around 19.02 semitones
thus, 3/2 is 7.02 semitones, and is the pure JI perfect fifth !
and 5/4 is around 3.85 semitones, making it the JI major third
now here's the cool bit: the reason intervals sound consonant in normal 12edo and every other tuning system is because they're really close to relatively-simple JI intervals
however they do some weird stuff JI doesn't
for example, in 12edo, you can stack 4 fifths, reduce by 2 octaves, and the result is a major third
but if you try (3/2)^4 / 4/1 in JI, the result is 81/64, not 5/4, despite said interval still being the closest to 5/4 by a lot
that's because in 12edo, 5/4 and 81/64 are the same thing
this property is a temperament, called "Meantone", which is actually, a line in that graph above
every edo tuning system where the meantone line passes through has the same property, you can stack 4 fifths and reduce by 2 octaves and you get the simple better major third everyone likes
which is actually why edos with meantone are so good and part of why 12edo is so popular and widespread, as 12edo is based on a really good set of scales known as diatonic (usually the major and minor scales), and meantone makes the major chords in those scales consist of 5/4 rather than 81/64
meantone isn't the only temperament though, there many *many* more, like dicot !
dicot is the temperament where 5/4 and 6/5 (minor third) are the same thing, and it has its own line on the right side of the graph
an example of an edo with dicot is 7edo again, that one that behaves like diatonic but all the intervals are neutral (or perfect), as there is no difference between major and minor
though dicot is considered worse, as the difference between major and minor is actually a pretty nice thing to have functionally for harmony, and a lot of people don't like neutral thirds
anyway, with that out of the way, you can now kinda understand that graph i posted :3
if you wanna go further down the rabbithole feel free to message me and i can like, show you practical applications of this stuff
