# Formula for length of a measure in minutes?

This question is probably a crossover with mathematics.

I'm charting a song into a music game. The song has numerous #/12 time signatures, but the game can only handle power-of-2 signatures (#/4, #/8, etc).

As a workaround, I'm trying to use #/16 and increase the BPM so it takes the same time as if it was in #/12. However I can't figure out how much faster.

What is the formula for how much time a measure takes, given the BPM & time signature?

• May I ask what song is in a #/12 time signature? I wasn't aware that such a thing existed. May 27, 2020 at 23:12
• @meganoob I think that 12/12 is the same as 4/4 played with triplets. I've never heard of any other such time signature. May 27, 2020 at 23:20
• @LemmyX that would actually be 12/8. There can’t be a 12 in the bottom of a time signature because there is no native 1/12th note. dan9er do your numbers refer to the top note of the time signature? May 28, 2020 at 2:29
• @JohnBelzaguy while standard music notation does not support time signatures with a denominator that isn't a power of two, it's fairly trivial to extend the system. (In fact, numeric time signatures were originally nothing more than fractions; they had nothing to do with measure length because measures did not exist when they came into use.) As LemmyX suggests, the note that has 1/12 the duration of a whole note is the eighth note triplet. It's confusing, but possible. Mar 8, 2021 at 17:47
• @JohnBelzaguy I agree with your opinion about anyone who uses an x/12 time signature. I would say though that "triplet" here doesn't necessarily imply anything about grouping; it just means "the note whose duration is 1/3 that of a quarter note." Mar 9, 2021 at 2:38

It is: BPM divided by top number of time signature = number of bars per minute. As long as the BPM corresponds to the bottom number of the time signature you don’t need it. If the BPM corresponds to a group of notes, say 3 notes in 9/8 then divide by the number of groups per measure, in the case of 9/8 it’s 3.

60 seconds divided by number of bars per minute = seconds per measure.

Example 1: 120 BPM 4/4 time

120/4 = 30 measures per minute; 60/30 = 2 seconds per measure

Example 2: 200 BPM 6/8 time

200/6 = 33.33 measures per minute; 60/33.33 = 1.8 seconds per measure

Example 3: 140 BPM 9/8 time, dotted 1/4 = 140 BPM

140/3 = 46.67 measures per minute; 60/46.67 = 1.28 seconds per measure

Please correct me if I’m wrong, I USED to be decent at math years ago.

• You nailed it John. I used to manually calculate times back in the Cakewalk 6 days to be able to have loops to sync properly and completely forgot about it. Mar 8, 2021 at 7:36
• @SaccoBelmonte Thanks, to this day I still like figuring some things out with pencil and paper even if there IS an app that can do it in a split second. Mar 8, 2021 at 16:55

You can figure something like this out. By definition the lower number indicates the type of note that gets ONE beat. I prefer to keep it as a fraction. So common time, 4/4 is the same as 4 quarter notes, 4*(1/4). We have 8th and 16th but we do not have 1/12 notes in standard music notation, unless it's something new. So I am not even sure I can directly answer your question. But I will provide a formula for the other time signatures that make sense to me. If you have the BPM (beats/min) and you know the time signature as N/M then each 1/M note gets ONE beat. In 3/2 time, with a tempo of 120 bpm, each 1/2 note gets 1 beat and a measure in 3/4 would be 3 of these. If one note is one beat then the time for a single beat is 1/120 minutes, or a 1/2 second and a single measure of 3/2 is 3/2 seconds long.

So all you really need is N/BPM. The value of the note does not come into play. You would read this as there are N M-th notes in a measure, each M-th note gets a beat at tempo BPM, hence the measure is N/BPM units of time long.