So basically! There are 12 notes in our normal western scale. A, B, C, D, E, F, and G, with flats and sharps except in the case of F being equivalent to E-sharp and B being equivalent to C-flat. Those notes were chosen for a lot of reasons, but, they were chosen, and have limitations. Most of the 'important' intervals between notes are approximated well, but the 3rds and 7ths are really, really not in tune– the 7ths so much so that we basically don't have any true dominant seventh chords in our harmony. Now, all fixed-pitch instruments have to be tempered. Tempering, in a really short definition, refers to the fact that music should logically have an indefinite number of pitches spiraling upward; when you go all the way up the circle of fifths, you don't go from C to C; you go from C to B-sharp, except that B-sharp is now higher in pitch than C by about 23 cents. So, a lot of tuning systems temper out those 23 cents, also called the Pythagorean comma. What some old tunings did is simply concentrate all of that dissonance into one wolf fifth, which is a term you may know, so that they could play beautifully in-tune major and minor chords in most keys. But if you want to avoid the wolf fifth and be able to play equally in-tune in every key, you can just divide the dissonance totally evenly across every octave and every note. That gives us the tuning system we mostly use over here, and have for well over a century. Some select areas of western music drift outside of 12-tone, namely in the orchestra, but practically, western orchestras and choirs tune themselves to pianos, usually, which are equally tempered. Temperaments are not bad; we absolutely need them for our music, but, we don't always have to temper evenly or to 12 tones. Some temperaments have 17 tones, some have 31, and Wendy Carlos made several scales that don't repeat at the octave as is typical in order to search for better harmony.
NOW. GETTING TO THE POINT.
A supermajor third is a really cool interval that can be be written as 9/7. It is worth noting that this is almost as simple as 8/5 or 9/5, which are, respectively, the minor 6th and minor 7th. These aren't as simple of ratios as the octave (2/1), fifth (3/2), or major third (5/4), but, also, almost nothing is. To elucidate on the random numbers: simpler fractions tend to sound more pleasing to the human ear. The wolf fifth, for reference, is usually an interval of 262144/177147. 12-EDO's minor 7th is... 2/5/6:1, whatever that means.
The supermajor third is a little weird to get used to, but as a bass note, it leads nicely down into Em. As the highest voicing, it can give you a way to make C feel less at rest if C is the tonic. As the fifth of A, it gives you a very floaty kind of minor chord; a bit like a consonant tritone. The important thing is that it's one of the easiest microtonal intervals to access and modify chords with. For reasons I have yet to disover, it also allows you to slip a diminished 5th (an actual one; genuinely between F and G) into the key without it sounding jarring. I suspect this is because the relationship between the supermajor third and diminished fifth is more akin to the relationship between a root and a major second, but I'm also an idiot, so I don't know.
I'm not a bonafide expert at any of this so stone me to death if I flubbed anything, but you should consider using microtones. If you can't program your own keyboard full of weird frequencies, then try getting some of those tape-on frets for your guitar. You can use your ear to find pleasant interval combinations. Just listen for the ones that don't sound like the frequencies are clashing. Music is your oyster.
if i post my penis every two hours for the rest of today starting at noon, you guys have to let me talk about the supermajor third and septimal whole tone. what is the supermajor third and septimal whole tone? idk i’ll tell u if i post my cawk enough