Metronome Intervals

[Nachin TheSelf-TaughtGuy]

If the time interval between 2 beats on a metronome set at 60bpm is 1 second,
what is the time interval between 2 beats when the metronome is set at 61bpm? at 62bpm? at 63 bpm? at n bpm?
Thank you!

Edit: What I can deduce for sure is that:
1) The more beats there are in a minute, the shorter the time interval and
2) the fewer beats there are, the longer the time interval

 

[Cubist]

If you're beginning algebra, then why not define two variables for this problem and then try to write an equation? I'll start you off...

Let t=the time interval between two beats measured in seconds
Let ...
continue, and then post back with your work so that we can discuss (and check it's correct)

 

[Nachin TheSelf-TaughtGuy]

Hi! I've taken your advice to heart and came up with the following...

Let t = the time interval between two beats measured in seconds (from your post).
Let n = the number of beats in a minute.

Since we are solving for the time interval, we can model the equation to be:
t = 60/n (this is the only equation I can think of to solve this)

if n = 60 (i.e. 60 beats in a minute [60]) then t = 60/60 = 1
if n = 61 then t = 60/61 = 0.9836 s
if n = 62 then t = 60/62 = 0.9677 s
if n = 63 then t = 60/63 = 0.95238 s

Please, if I've made any mistakes, let me know!
Also, are there any books on mathematical modelling, mathematical logic, reasoning, and abstract mathematical thinking I should read / buy?

 

[Cubist]

t = 60/n (this is the only equation I can think of to solve this)

Good, this is correct. I'd get there by thinking...

"number of beats" times "time between two beats" = "total time"
n*t = 60
t = 60/n after dividing both sides by n

Also, are there any books on mathematical modelling, mathematical logic, reasoning, and abstract mathematical thinking I should read / buy?

Personally I always found my school's recommended textbooks to be enough. Before an important exam (weeks before), I'd sometimes search out extra past papers if my teacher hadn't supplied enough. Are you a student at school?

 

[Nachin TheSelf-TaughtGuy]

Good, this is correct. I'd get there by thinking...

"number of beats" times "time between two beats" = "total time"
n*t = 60
t = 60/n after dividing both sides by n


Personally I always found my school's recommended textbooks to be enough. Before an important exam (weeks before), I'd sometimes search out extra past papers if my teacher hadn't supplied enough. Are you a student at school?

Sweet! Thank you!

No I'm not in school right now. I am practicing math as a hobby.