Most music is written in 4/4 time, and in today’s world it seems to be the accepted norm. Now, that doesn’t mean mainstream music doesn’t use alternate meters, but it’s just less common than I imagined.
What made 4/4 time stand out and become the norm versus alternatives like 2/4 or even off signatures like 6/8?
Marches are generally in 4/4 (or 2/4 or 6/8, some binary division.) Likewise, most ballroom dances are in 4 (actually, dancers count to 8 but that's more technical that is called for here). Waltz and Viennese waltz are in 3/4 (maybe a few notated in 3/8 but not commonly.) Jigs (6/8 or 12/8) and tarantellas are not so common. Foxtrot, tango, rumba, mambo, bolero (American), quickstep, swing, western swing, cha-cha-cha, Texas two-step, Lindy-hop, salsa, paso doble, jive, nightclub two-step, etc. are all generally notated in 4/4. Some were in the late 1800s and early 1900s notated in 2/4 with an eighth note as pulse.
For some reason (which I will now have to research to satisfy my own curiosity), the breve isn't fast and the longa is really long. Since the 1500s or so, it seems that the quarter note has been the basic pulse indicator. I don't know why yet.
In modern notation, the time signature just carries relative rhythmic information, not basic tempo. Thus older tangos (see Todotango.com) and older rags (Library of Congress) and the like were notated in 2/4. One can re-write them in 4/4 and double the note lengths with no change. I like 4/4 as it's a nice compromise between too many flagged notes and too many open notes. Perhaps that's just because most things I read are in 4/4.
Others have already addressed the aspects of dance and symmetry, so I'll take a slightly different approach.
The term "common time" refers to the use of "C" as a time signature. It looks like a C, and stands for 4/4, which happens to be the most common time signature, so people often explain it as "C stands for common time".
But it's not a C. It's an incomplete circle.
Early on, music was monophonic (think Gregorian chant), and we didn't really need time signatures. It wasn't until about 900 years ago that we started playing around with a second voice, and maybe 100 years later a second voice in a different rhythm. That's when we first realized we need to indicate meter.
At the time, most people were illiterate. The only folks who could read in the 11th and 12th centuries were clergy... so they put a lot of religious significance into everything they did. They considered 3 a perfect number (because it represented the idea of the Trinity), and a circle was a perfect shape - so a circle indicated a triple meter. A broken circle indicated "tempus imperfectus" (imperfect time) - anything that wasn't in 3.
As more complex meters developed, the circle thing became more elaborate. A circle within a circle was a compound triple meter - today we'd probably use 9/8 for that. A vertical line through the circle showed that it was triple meter, but the unit of the beat was a shorter note (the brevis) than the usual one (the 'longa').
Two of those early time signatures survive today, the tempus imperfectus: C for 4/4, and the alla breve (literally, "according to the brevis") for "cut time".
I do not believe there is a single comprehensive, sourced, and easily-falsifiable answer to this question, what you're asking is to some extent a question of psychoacoustics.
In light of this non-answerability, some observations:
* I'm contradicting myself here, but I think this comment can be meaningfully understood with the caveat "if we are to take intuition and personal experience as a valid metric, which some framings of the question logically must, then I would personally say that..."
I don't have enough for a complete answer here (and I missed the bounty anyway) but I have seen some historical documents that might help narrow this down. To be clear: I don't claim any of the sources I cite here were revolutionary in their terminology (quite the contrary); they just happen to be things I was looking at recently that may be relevant.
Early 18th Century Italian term - tempo perfetto
There's some information which may be of relevance in Francesco Gasparini's thoroughbass manual, L'Armonico Pratico al Cimbalo (The Parctical Harmonist at the Harpsichord) of 1708 -- there's an English translation on IMSLP, which I recently started skimming through (like one does). Gasparini, an Italian composer who trained in Rome under Corelli and Pasquini, moved to Venice and became the director of music at the Pieta girls orphanage, where he is best-known for hiring a violin teacher named Antionio Vivaldi.
There's a translator's note which points out that twice, Gasparini uses the term "tempo perfetto" to refer to what we would call "common time". Note that this is contrary to the much earlier use of tempus perfectus to refer to triple time, as documented in @TomSerb's answer. In fact, the translator acknowledges this difference in terminology, and points out that the older sense of "perfect time" (triple time) hadn't been used for about two centuries by that point (emphasis mine):
On two occasions Gasparini speaks of "tempo perfetto" ("perfect time"), but means thereby common time. In the first case (at Ex.31), which deals with quarter-note motion, Gasparini's words "in tempo perfetto, o binario" could mean "in perfect (triple) time, or in duple time," or "in perfect, that is, duple time"; the quarter-note progressions he describes, however, would be too complex for the fast pace of \ the only triple time that could be involved. The second case (at Ex.62) al- lows only the second interpretation, in which "tempo perfetto" is taken as another name for duple, or common time. In any case, the triple measures of the seventeenth century are—properly speaking—not in "perfect time" (this not having been in common use since the early sixteenth century), but are proportions, as Gasparini elsewhere calls them.
So speculating heavily, it seems that somewhere between the beginning of the 16th and the beginning of the 18th century, duple time became known as "perfect" (or perhaps "complete"?) time, which could possibly be the origin of it becoming common time in English. One passage in which Gasparini uses this term is while discussing cadences. He is discussing what he calls a "greater compound cadence" and describes it as: "The greater cadence is formed in tempo perfetto, using four counts, in the following way." He then lists a shows of bass figures that essentially correspond to the progression V - I6/4 - Vsus4 - V7 all over scale degree 5 (before resolving to I). So maybe this tempo was "perfect" (i.e. "complete") in that it had enough counts in a bar to complete this entire cadential progression?
English term 'Common Time' is at least as old as mid-18th century
As far as the English side of things, I just happen to have also recently been looking at "A New Musical Grammar" published in London, 1746, by William Tan'sur (imslp link). In this book, the term "Common Time" is used as a synonym for all duple or binary time.
Common time is then broken into further "moods", indicated by various time signatures. Note that this usage of time signatures isn't quite the same as either today's usage, or as the mensural signatures mentioned by Tom Serb, and the modern system of notation.
This description of various "moods" of common time, although it does not match classical practice, matches very closely to the description of time in early American Shape Note Hymnals, such as one from 1800 listed on this page (search for the first occurrence of "common time" on that page).
So like I said, this doesn't completely answer the question of why, but hopefully it at least narrows down the search parameters a bit as to when.
I suppose the origin of rhythm is the movement of our body, and as we have 2 legs and 2 arms all repetitiv movements of mobility and working as walking, rowing, shaking etc. are in a binary rhythm. This would explain that march music, work songs and many folksongs for wandering are in 2/4 and 4/4.
In a slower tempo you can also feel triplets or alternately notate them in 6/8 or 12/8. Thus there isn’t abig difference between these 2 alternatives.
But there are also dance music in Bulgarian or Romanian dances as 5/8, 6/8 etc. that are derived from the dances: e.g. 4 steps left and turn (change the direction of dancing in a half circle. And then the 3/4 of the menuets and the waltz, of course, also giving time to turn around.
I try to give some evidence why 4/4 is more established than 3/4, 3/8, 5/8, 7/8 etc. short said broader than 3 or odd rhythm music and dances.
Edit:
As already mentioned the moving of our body is not ternary but binary. Also the movements of a horse and dromedary which have been the vehicles and modes for transport during thousands of years across the desert, wandering nomads could hear the rhythm and stamping of their legs and feet. Many dances and songs are imitating this stamping (stampede), marching (march).
The force of gravity leads to noises of a pendulum (this could be a chain, a rope on a ship, the ship, the waves of the water, a wheel turning round with a certain effect that gives a rhythmic noise inspiring a binary rhythm.
The spoken language is in majority binary: already the rhythms of the Greek (Iambus, Anapaest etc.) have been in a binary rhythm. I've never heard a ternary RAP.
Mind that the early church rhythm and note lengths of longa, brevis, semibrevis etc. have been ternary (because of the Trinity of God) and I wouldn't wonder if it was not a kind of heresy when the first monks broke this rules.
May be you have seen some horses dancing a Waltz in 3/4. This must have been in the Circus or in the Reitschule in Vienna. But I have in my ear the rhythm of Bonanza: Dam-daba Dam-daba Dam-daba Dam-Bonanza!
Short answer : "most music is in 4/4" only if you don't look much outside western/european music and its derivatives. Indian folk/classical music for instance is replete with time signatures that warrant a life of study just by themselves. To these guys, playing in 4/4 all the time is a bit like playing everything in C major with 1/4/5 harmony would be to a jazz musician.
A better question to ask would be "why is most western music in 4/4". As other have suggested, perhaps this is to do with the relationship to walking and marching rhythms. We could also suggest that different musical cultures developed complexity along different "axes". In Europe we stayed mostly with binary and trinary rhythms, but really went for it in terms of harmony and form. Other cultures stayed with a less sophisticated harmonic concept, but embraced rhythmic and polyrhythmic variation much more deeply. (Then of course the various streams have merged in various ways since the early 20th century.)
Probably the levelness of it. We like things to even up. That, maybe, puts 3/4 lower on the list. And a lot of people find the other odd ones, 5/4 and 7/4, well, odd. But that doesn't exclude 2/4 or even 6/8 - a derivative of 2/4.
There's a possibility that the basic drum rhythm has something to do with it. 2/4 repeats the pattern every two beats, or every bar. Too much of a good thing. But with 4/4 there's an opportunity to kick on beat one, then snare on beat three, giving balance, but spread out more.
Another possibility is that a lot of music was/is used for dancing, and 4 worked out to be the most suitable for lots of dance steps.
I feel that this will be dv'd - please try to qualify the reason!
It came from Valmiki, the composer of the Ramayana.
All Sanskrit shlokas are recited in a 4/4 time signature, which were composed in ancient India even before writing originated.
https://en.m.wikipedia.org/wiki/Valmiki
The time metre is called an Anustubh https://en.m.wikipedia.org/wiki/Anu%E1%B9%A3%E1%B9%ADubh
I think it’s because that’s all most rock drummers can play!
I am a percussion drummer. We know how ghost notes, and 7/4 time signatures, etc. can make things sound a bit groovier.
