Well, first of all, I think we have to define what classical music is to have a decent understanding of its precursors and contemporaries. The most typical answer is "Music written for a somewhat formal setting by white Europeans from roughly 1700 to 1900." In truth, this does not constitute a single genre, though it is consumed as such today. It consists instead of a bunch of subgenres like "opera seria," "opera buffa," "string quartet," "fugue," "lied," etc, each with their own origins, listening habits, precursors, etc.

Second, I think the general prehistory of Classical Music in its common understanding is a bit too broad to summarize in a single post. The answer to this question is what an entire music history course would teach you. It involves pretty much the entire history of western music making from roughly 900 to 1700. It is roughly equivalent in scope to a question like "What are the precursors to modern warfare?" It's an almost impossibly broad question.

Finally, it's hard to know what specifically you are looking for when you talk about non-western traditions. Obviously, the period from 1700-1900 will have a lot of music activity no matter where you are looking, whether it's in Vienna, Tokyo, Accra, or Denpasar. Just because it's 200 years of music! People do a lot in 200 years, but they might not do at all related things depending on where you are. So it's hard to know exactly what you are looking for here.

I hope I understand your question correctly, I think you are looking for evidence of musical style before what is generally lumped in to a musical category as "classical music"?

It is generally considered likely that the earliest forms of music were beat based, percussive types with probably some degree of human voice accompaniment. Gradually wind instruments, like reed flutes and stringed instruments, emerged. We know of simple forms of these from ancient Egypt. Long trumpet like instruments with droning sounds, relying on the blower to make the noise, were used in pre Christian Ireland and Denmark, and the guitar came along, invented by the Hittites, approximately 3500 years ago. The earliest forms of music, then, were likely to be simple instrument accompanied songs, that gradually increased in complexity as more instruments were invented.

The oldest recorded complete song is a first century AD Greek song known as the *Seikilos Epitaph", it was used to mark a grave site.

Music became increasingly complex as more instruments came into use. China had already started the tradition of its very distinctive orchestral music, based at least in part on the fabulous array of tones they could achieve on bamboo pipes. Archaeology also provides evidence of pipes made from bone and clay. Stringed instruments began to develop rapidly too.

Many cultures started out with a pentatonic scale, that is 5 notes per scale instead of our usual 7 today, the heptatonic major and minor scales. It is the scale that gives music its distinctive feel.

A lot of what we know about music comes from what was recorded in documents, and since the Catholic church adopted music throughout, how they recorded it plays a large part in how we know about music now. The church had a system of notation known as modes, the precursor to our present date scales. Because of this we know that a precursor to Classical music was Gregorian Chant, with it's very distinctive, voice based sound.

Following from Gregorian Chant was the early polyphonic style ( 2 unrelated melodies playing at once) These grew more complex over the Medieval period and more and more layers were added, with layers of voice and instruments. Rounds, where a melody is begun at different timed intervals, were very common at this time. This new complexity gave rise to Baroque music, the earliest of the type of music that gets labeled as "classical". In the mean time, of course, people still had simple accompanied melodies and folk songs and sang all the time.

When music could be published (because of the introduction of printing and useful notation) it developed quickly into more complex forms and notations. Instruments were now highly complex and capable of playing chords. The idea of bass harmonies developed. Baroque music is extremely layered and intricate. It features instruments like harpsichords, trumpets and stringed instruments like violins and cellos. It is dense, complex polyphonic music, strongly exploring harmonic progressions and counterpoint. The Baroque period was roughly 1600 - 1750 and famous composers of this style include Handel and Bach.

Classical music - as a definition rather than the catch all modern interpretation - was written between 1730 and 1820. It is different from Baroque as it is homophonic, featuring a single clear melody, and has a much cleaner sound and a sewing machine regular rhythm. The harpsichord is replaced by the piano and the orchestra turns into what we mostly know it as today. Notable composers of this style are Mozart, Schubert and Haydn.

Romantic music was written between 1780 and 1910, it is grander in feel than classical, given to dramatic swells and romantic themes. It is often written in a larger, much longer forms than the classical precusors. Composers tried to incorporate themes and literary components into their music. Beethoven, Chopin and Mendelssohn are composers of this genre.

In non western culture a distinctive difference in the prevalence of heterophony, a very complex textured musical style where many variations - varied by rhythm, embellishments or tempo - of one melodic line are played/sung simultaneously. Arabic, Thai and Indonesian classical music are of this style.