How do you determine what type of interval sound you want?
Is it a note thing? A pitch thing?
I kinda thought the 4 toms were supposed to play that horseracing bugle call song, the 4 note one... know what I mean? That 4 note tune?
Hell, I don't know - trying to learn here.
"First Call" is what you're referring to. Some people call it "Call to the Races."
Re: interval, mine isn't scientific. For gigs, I typically play 2 up, 1 down in a 10" 12" 14" configuration. I tune my 12 first and then the 14 and once I'm satisfied how they sound going from another, I tune the 10 in relation to the 12. If I add my 8" tom and 16" floor tom, then I tune the 8 in relation to the 10 and the 16 in relation to the 14. Keep in mind that the gigs
I'm playing there's a 50% chance I won't have my toms mic'd -just kick, snare, and 2 overheads. Because of that, I do tend to tune a little bit higher than normal.
All that being said, if I'm playing the entire kit (3 up, 2 down) AND I'm going to be mic'd up, I tune the 16" floor tom first and tune it to where I feel it feels natural and then tune all the smaller toms in succession.
If someone is using a 12, 13, 16 configuration, there's usually enough size difference between the 12 & 13 to where good tuning will give you the separation you're looking for. Would I call it a "true interval?" Probably not. If I wanted to make sure there was enough distinction between the drums, I'd look at putting a single ply batter on the 12 and a (overall) thicker batter on the 13.
Regarding the calculated intervals and tuning to specific notes, there are more qualified people on this forum who do that who can guide you there.