What does this have to do with music history? We could look at different forms or genres from both dimensions. For example, the rondo or rondeau form has existed for a very long time so we could look at it vertically through time. In the 13th century it was both a poetic and musical form with a repeated refrain in both the words and music. Here is an example by Adam de la Halle:
In the 15th century we have a different kind of rondeau, but still based on the refrain principle. Here is Craindre vous vueil, a rondeau cinquain form by Guillaume Dufay from around 1430:
The rondeau became purely instrumental in the 17th and 18th centuries and is often spelled "rondo". In this variant, a principal theme alternates with contrasting episodes. The first were often for harpsichord. Here is a famous one by Rameau, Les Tendres Plaintes:
The rondo was a favorite form in the classical period as the final movement in sonatas or concertos. Here is a very well known one, the Rondo alla turca by Mozart:
Another famous rondo is the last movement of the Pathétique sonata by Beethoven:
Of course the genius comes not only in how the principal theme is constructed, but how ingeniously it is led into each time it recurs. The rondo or rondeau is a rare form nowadays, but it has had an interesting history.
But what would a horizontal look at music history consist of? I had a theory teacher once that brought a number of pieces to class for us to analyze, all composed in 1951, which turned out to be the year he was born. In a less-capricious manner, we could pick a year, or decade, and look at what different kinds of things were going on at that time. Just for the heck of it, let's pick the year 1964 and see what was going on. It was a time of immense upheaval in the musical world and if we pick three particularly significant pieces of music, we might get a sense of that. For the first, I choose a string quartet by Dmitri Shostakovich, composed in 1964. Though a uniquely and powerfully individual work, the inspiration is undoubtedly the quartets of Beethoven. Composers in Soviet Russia were, on pain of banishment or worse, encouraged not to be too avant-garde. Shostakovich seems to have not let this make him any less creative. I devoted a whole post to the String Quartet No. 9 here. Here is a performance, in three parts, by the St. Petersburg Quartet:
For my next example, a piece by Karlheinz Stockhausen composed over a number of years, but with a substantial portion complete by 1964. Here is a performance of Momente from 1965:
Everything you hear is part of the performance. That clapping at the beginning is the choir. Here is a description from Wikipedia:
In addition to singing, the choir members clap their hands, snap their fingers, stamp and shuffle their feet, and slap their thighs. They also play small "auxiliary" instruments: choir I has cardboard tubes of various lengths with glued-on covers, played like drums using light mallets; choir II uses twelve pairs of claves—all with different pitches; choir III shakes plastic soap boxes and refrigerator drink canisters filled with buckshot, which sound like maracas with different pitches, according to the number of pellets and the size of the plastic canisters or boxes; choir IV uses twelve pairs of Volkswagen lug-nut spanners (which kept disappearing during rehearsals, because most of the choristers drove Volkswagens). The purpose of these instruments was to create mediating links between the percussion and vocal timbres. Having the choristers play simultaneously with each syllable they sing or speak automatically and easily solves the problem of rhythmic coordination (Stockhausen 2009, 129). However, Stockhausen reported that the WDR choir, which sang for the première, initially objected to these practices (Stockhausen 1964a) and, "because such means of sound and noise production can have a comic effect, . . . one newspaper report talked about a 'cabaret performance' and ridiculed the whole thing" (Stockhausen 1964b, 132).Momente is written in "moment form" an invention of Stockhausen. It is worth reading the Wikipedia article. The basic idea is that the composition is a mosaic of 'moments' set off from one another and with no overall narrative line.
Now, for my third example, I choose a musical event that completely overshadows both of the preceding ones: Beatlemania. You may be too young to have experienced this, but for a few years the Beatles were popular in a way that has never occurred before or since. If you look at the Wikipedia page for "1964 in Music" in Wikipedia, it seems as if half of the entries are about the Beatles. Sales of Beatles records made up 60% of the singles market. For a while the top five on Billboard's Hot 100 were all by the Beatles. When they visited Australia for the first time, 300,000 fans met them at the airport. In a matter of a mere year and a half the Beatles went from an obscure bar band playing in Hamburg, to the most famous people in the world. The biggest release for the Beatles in 1964 was A Hard Day's Night, the soundtrack to the movie, which was also a success. Here are some songs:
So, there were three different kinds of things going on in music in 1964: the continuation of the classical tradition by people like Shostakovich; the invention of entirely new kinds of musical forms by people like Stockhausen and the triumph of popular music, largely at the hands of the Beatles. Sociologically, the Beatles are obviously far more important than either Shostakovich or Stockhausen. But what about aesthetically? There is no denying that the Beatles were extraordinary song-writers, probably the best since Schubert or Schumann. They were also amazingly innovative in their arrangements and use of the studio environment. But what was crucial to their success was the baby boom generation: a host of young people looking for something new and with disposable cash. For them, the Beatles were by far the most interesting music around. One interesting consequence is that since the 1960s, the whole classical field has been dwarfed, economically, by the pop artists. In the case of the Beatles, it is hard to deny their appeal. But now, with Nicki Minaj, Psy, Lady Gaga and their ilk, it just seems like an aesthetic train wreck.
It is Stockhausen that is most difficult to put into perspective. He and many others of the European avant-garde received a great deal of support from the US State Department and CIA as part of their Cold War cultural battles. But it is hard to say that his music was the "music of the future". Instead, it seems, to me at least, to be the most dated of my examples. Shostakovich's quartet sounds better to audiences today than probably at any time since it was written. And the Beatles' music never seems to age. Every single one of their albums has been in issue constantly since they first came out--including the very first one, Please Please Me. But Stockhausen might not be listened to too avidly fifty years from now.