How to exactly find the correct tempo of a song?
I'm still a student learning music so I pretty much don't know all the fundamentals in music (though I learned 9 years, it could because my teacher's just giving the essentials and doesn't bother with other details..).
Based on what I know, a tempo shouldn't be over 250 or so.. Let's say a song is in the time signature of 4/4. The grouping should be 4 crotchet beats in a bar, FOUR of the 4 crotchet beats in a bar as well, and it "probably" keeps stacking for each section (verse, chorus, etc.). This is just based on my HYPOTHESIS after all.
I've arranged some songs and I've concluded that there are a number kinds of tempo.
*All sheets will be in the description of the YouTube video
- Granbelm OP Piano - Tsuki wo Ou Mayonaka - https://www.youtube.com/watch?v=iiqlQKuYA3A
This song I arranged has a fixed tempo of 187. Which can't be divided because that would be 93.5. Having a decimal.
- Tejina-senpai OP Piano - FANTASTIC ILLUSION - https://www.youtube.com/watch?v=e6aUeRQkKvA
Even though most of my arrangements are in TV Size (a full song made into a 120/90 second song), this arrangement with its Time Signature change proves that its a tempo of 140.
- Love Live! School Idol Festival Piano - Niko puri♥Joshi dou - https://www.youtube.com/watch?v=p4CMX1wJa-c
Since the grouping/syncopation of this song contradicts to my hypothesis.
Love Live! School Idol Festival Piano - soldier game - https://www.youtube.com/watch?v=rMiJSmmfs7k
Since the tempo is 132, it can be divided to 66. But if it's 66, the Time Signature has to be 4/2 instead of 4/4. So this brings up my question.
This is just a reference and it's not my arrangement. Animenz made an arrangement on Love Live's Snow Halation - https://www.youtube.com/watch?v=Z4KmL4KI0cQ
He used the tempo 87 instead of 174. Since he's a professional, I thought this could just be an arrangement technique.
How do we correctly find a song's exact tempo? Could this just be an arrangement technique? How would the Time Signature be affected if so/even if it isn't?
P.S. : I didn't realize I used a lot of Love Live! songs as references before I was done typing this...