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I'm a programmer and I'm developing some software for use in combination with music. Part of the software will include a sequencer that can show / start certain tasks that match the music's tempo.

I also performed as a DJ for several years, but all of the music I played always contained the most common (in my world) beat: counting 1, 2, 3, 4 and starting over again, varying in BPM from anywhere from 80 through 200.

Because I want to make the software I'm writing as flexible as possible, I'm trying to figure out what I should reasonably support, to include as much as possible.

When working with simple 4-beat songs, the math is simple. If you want a pulse between the 1 and 2 (for example), you end up with a 1/8th pulse, or a 1/16th if we go even further. How does this translate to other formats?

I'm sorry if the question is unclear as I've never had any music theory, so I don't know the right place to start to ask the question.

For displaying purposes, software like Rekordbox shows timings such as this: 1.1, or 36.3, where the first number translates to the 'n-th time you counted 1, 2, 3, 4' (which is named?) and the second number to the beat within that same measurement. How would this work with a non-4-beat scheme?

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    Have you considered getting familiar with existing sequencer software?
    – piiperi Reinstate Monica
    May 25, 2021 at 10:13
  • @piiperiReinstateMonica are there any you can recommend?
    – Ruben Rutten
    May 25, 2021 at 10:14
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    One way to approach the problem is to implement MIDI Clock sync support. For example, if your software had to synchronize to an external hardware MIDI sequencer or, say, a looper pedal which outputs MIDI Clock. When you look at how different existing MIDI Clock sync capable programs and devices do it, you'll see what sort of problems there are and what sort of solutions others have come up with.
    – piiperi Reinstate Monica
    May 25, 2021 at 10:48

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1-2-3-4, 1-2-3-4 is actually called common time - it's the most common!

Other often-used times are 1-2-3,1-2-3 - waltz time, and 1-2,1-2 - march time, as it equates to left-right,left-right.

You're correct that each beat can be sub-divided, making for example 1&2&3&4&, 1&2&3&4&. Or sub-divided again so each beat has four sub-beats. 1e&a-2e&a-3e&a-4e&a

There is another sub-division that gets used, too - triplets, where each beat becomes three. 1-trip-let 2-trip-let 3-trip-let 4-trip-let. That effectively splits 4/4 time into 12/8, or 2/4 into 6/8, or the less used 3/4 into 9/8.

It's essential that you have more than just a background knowledge of this if you're going to incorporate it into your program! And each 'box' of, say, 1-2-3-4 is called a bar (or measure on the left of the Atlantic).

EDIT: the time signature numbers are a bit like fractions, in that the top number denotes how many 'beats' per bar, the bottom what sort of beats they are. As in 3/4, there are 3 beats, each one being a crotchet (quarter note). In 12/8, there will be 12 'beats' per bar, each being a quaver (eighth note). But beware - the feel of compound time signatures is somewhat awkward to understand, especially for non-players. Like I said - more than background knowledge needed. 'Theory' only helps a bit - practical works far better!

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  • There are some terms that I can definitely work with to read into more of what I need. To see if I understand it correctly, there's 4 beats in a bar when working with a track uses common time? If I have a waltz-time, can you note that as 3/3? Does that mean there's 3 beats in a bar? When you have 12/8, does that means a bar is 8 beats, but you chain multiple bars so that songs match up correctly again?
    – Ruben Rutten
    May 25, 2021 at 10:18
  • I think that for the purpose of my software, I'll allow the user to input the numerator, denominator, and BPM, then display a bar with the same amount of blocks as the numerator. Thanks for the help!
    – Ruben Rutten
    May 25, 2021 at 10:29
  • In time signatures, the top number refers to the number of beats in each bar/measure, the bottom number tells you the value of those beats. So 4/4 time is "four crotchet (or quarter notes in US) beats in a bar. 3/4 is "three crotchet beats in a bar. 12/8 time means "12 quaver (eight-notes US) beats in a bar". The bottom number of a time signature is almost always 2, 4 or 8, denoting minims, crotchets or quavers (half-note, quarter-note or eighth-note).
    – Greg Kaighin
    May 25, 2021 at 14:31
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The basic beat of all music (with the exception of Gregorian chant and some modern experimental music) consists of quarter notes, eighth notes or half notes. Sixteenths or whole notes as the basic beat are possible and "permitted" in principle, but are hardly ever used - for reasons of readability, one would notate a 3/16 bar as 3/8 and add a corresponding tempo indication.

You probably already recognise the pattern: the denominator is a power of two. There are no "third notes"; a triple time like in the waltz, for example, would be notated as 3/4, it consists of three quarter notes in one bar.

For your software, this means that the denominator must be a power of two, the numerator an integer in the range from 1 to something (I would put a cap at 16). The most common values are 4, 3, 2 and 6; 5 is occasionally found in jazz, rock and pop, 7 and higher practically only in songs by Tool or Dream Theater. :)

There is another aspect you should consider: Time signatures can change within a song. A prime example is "Golden Brown" by the Stranglers, which changes cheerfully between 3/4 and 4/4.

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  • What? Yanni's "Santorini" and "Keys to Imagination" are in septuple meter for lengthy portions (probably 7/8 time). I've also had to play music for piano lessons in 7/8 time ("Crimson" by Robert Starer).
    – Dekkadeci
    May 25, 2021 at 13:50
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    Try Unsquare Dance, Dave Brubeck.
    – Tim
    May 25, 2021 at 15:26
  • This answer almost entirely ignores the existence of relatively common compound metres 9/8 and 12/8; but also, even Green Day play in sevens, it's really not that unusual. Anyone wanting to program non-triplet swing in a sequencer will definitely want larger numbers to simulate simpler metres, too. I'd also point out that irrational time signatures using things like "third notes" are occasionally used as an alternative to metric modulation, but that's less important given that, yeah, it's just an alternative to metric modulation.
    – Esther
    May 26, 2021 at 1:56

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