Hey there, I'm currently writing an alternative to music theory that is informed by my own self-taught composing. In the western system the 7 note system is used because of the diatonic scale (you may have heard it as the "Major scale", this is usually an inaccurate term and half the time "diatonic scale" is correct). This 7-note system is relied on for almost all the terminology in western theory, which means there is a lot of fudging to make the notes fit, as the diatonic scale is not actually equally spaced apart. That's the reason there is a "minor" and "major" third and not just one "third".
In addition all these terms are one-indexed because zero was not invented yet, so "unison" in western theory, which refers to two of the same note being played, gets the number 1 (uni-). The same goes for the minor/major second, and so on. This is what causes all the terrible addition problems.
The diatonic scale's strong relevance in music theory is not completely unjustified because almost all consonant (or "good sounding") music is made in it, but it's not very helpful to have to deconvert these terms to any other scale.
I visualize all scales as 12-note equally spaced scales and strongly recommend anyone else to do the same. It's known as the chromatic scale. In this system a unison is just 0, a minor second is 1, major second is 2... and so on. You'll see this system used in "music set theory" https://en.wikipedia.org/wiki/Interval_(music)#Generic_and_s... - look at the semitone number to see the amount of equally-spaced spaces between the notes. Although, the word "semitone" is also a poorly thought out choice due to the diatonic scale (it implies a base unit of "2" instead of "1" since semitone corresponds to 1). Music set theory terminology is much better than western theory IMO, but I think a lot of music set theory buys into too many mathematics-based hypotheses (when it tries to draw equivocations between scales), so I find it has its own issues.