I don't think you really grasped the point of this whole thread. I've NEVER said that intervals are not important. It surely is. And I would gladly discuss them in another forum where I (and you) are not responding to a direct question. This is a thread totally devoted to what we as outsiders (as I guess you're not either Shellback, Savan or any of the Wolf Cousins...) know about the melodic math. I'm sorry that you see me as some sort of evil mr. know it all, but given that I've studied Max's songwriting to unhealthy levels, and I circulate amongst the people either working with him now or have done so frequently in the past, I gladly share what I know to those who doesn't have the time or opportunity to take the time themselves. I'm no Billboard songwriter, and I spend time here because of my fascination with Max and that type of songwriting. I'm guessing the same goes for you?
There are only a select few that now all the ins and outs of the "Melodic Math". As I said before, some are public some are not as public and some I (and many of us in here) would give our left foot to know. But at least I can prove that time and time again, Max and his fellow companions have reused the same rhythmic structures, they continue to hit the chorus (amost exclusively) within 50 seconds, so on and so forth.
You sir on the other side, who are exactly as stubborn as you seem to think that I am, have not yet given any Max-related evidence of intervals that can be seen as a part of what they call "Melodic Math".
"Melodic Math" are helpful guidelines toward optimizing your song. If you have a cool chorus hook starting on the downbeat, then maybe it's a good idea not to start the verse and pre chorus on the downbeat as well. Same goes with rhythm. If the start of the chorus is chopped upp and syncopated, then a straight line to follow is the way to go to balance it out. If you havn't hit the chorus at 55 seconds, then maybe you should look at scrapping the pre chorus or whatever. There is a long list of things that are consequent in Max's songs, some 101'ish, some not, but listning to other writers, they are not nearly as consequent in using them. There seem to not be a silver lining in the use of certain intervals though, which is what we're looking for here. Maybe Elton John or some other really great writers have awesome theories on intervals, and I would love to hear them, but in this forum, we are focused on what can be purely pin pointed to Max's craft of songwriting.
If you can prove in any way that there is a certain set of intervals that Max uses (and that others fail to notice) then please prove me wrong and let me bow my head in shame, which I will. To me, intervals are incidental and it takes ear and gut feeling to write good ones. This is what Max has, Dr Luke has, and some others as well, and with their sense of melody and with help of the statistics involved in the "math" helps them become the world dominating writers they are.
I will point out though that you are absolutely right in what you said about Max's strenght being subtractive producing and what not. With all the mathematics in the world, he could not have been as succesful as he his without knowing when to remove stuff, when to let spaces be spaces, and when something is good or not. In later days, I'd say that DJ Mustard is a good example of the same principles, even if the music is entirely different. He may be the most talentless producer to ever have 7 songs on the Billboard Hot 100 at the same time, but he KNOWS what'll work and what is a hit or not. Max does as well. Most of us will never have that ability. And that can never be written down in a formula as such.