I have this far developed theory that is suitable for harmony and counterpoint, but I have not really talked much about the concepts of harmony and counterpoint - in fact, I've remained quite silent as to why those would be of any interest whatsoever.
In many human cultures, the usual texture has been one of monophony.
Monophonic version of the familiar tune. The slight change in rhythm has nothing to do with the change in texture, but I felt like it added some slight interest. Note that the file has the wrong name.
Monophony simply consists of one pitch played at a time. The pitch can be played by multiple instruments - and in fact lots of middle east music basically consists of a whole ensemble playing the same melodies at the same pitch, and the combinations of instruments simply create different complex timbres. Timbral variation can be obtained by, say, having some instruments be silent in some parts. Whether octaves are to be considered separate pitches for this classification differs between authorities, but if the only simultaneous interval that is permitted is octaves, you probably won't go wrong by calling it monophony.
Examples of monophony include the various plainchants, Chinese art music and Arabic traditional music. Apparently also several African vocal traditions. You've also probably produced monophony yourself - singing unaccompanied is a form of monophony.
A slightly extended monophony can be achieved by including a drone - a tone that basically is sustained throughout the piece. Examples of this style can be found in many places - most bagpipe traditions, the hurdy gurdy and related instruments, and lots of Indian music. Continuing on this, we can again listen to the same tune:
Monophonic tune with C as its drone.
The same tune can be turned into a somewhat different tune simply by changing the drone - and by that realization, we're getting quite close to homophony instead.
Same monophonic tune with A as its drone instead of C.
As a final comment on drones, they need of course not be bass notes - they could be higher in pitch than the melody stuff as well.
Homophony has more voices than just the melody - however, the other voices mainly serve to create a harmonic background, and not to provide all that much in ways of harmonic interest. Therefore, their rhythmic behaviour tends to be pretty similar. The versions of my tune with chords basically all have been pretty simple homophony.
One further type of texture is called heterophony.
A rather fantastic tradition of art music that is replete with heterophony is the Indonesian gamelan. It is well worth familiarizing yourself with it - there's hundreds of records, and of course youtube videos. Basically, heterophony consists of multiple voices playing the same melody - but they occasionally deviate in ways peculiar to their own style. Imagine that two people who have learned the same song, but slightly differently, come together and try singing it in unison - but occasionally, they deviate from each other's lines - their rhythm differs or their pitch selection differs, or both.
Finally, there's polyphony. Polyphony is famously present in Baroque music, but also appears in lots of African styles, Georgian folk music, various musics of the Balkans. Polyphony.ge has a map over different forms of polyphony over the world, and a variety of interesting information in general.
Polyphony as a texture has a lot of variation. Generally, there's more than one melody simultaneously, and they both provide some interest. The interactions between the two or more melodies should be the central idea. Polyphony is quite complicated, however, and I will probably deal more with that in a separate post.
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