Music for Conworlders: Polyphony

Polyphony is the texture in which you have melodies simultaneously. The interest is created by their rhythmic and melodic independence.

Several styles of polyphony exist in western music. Out of these, some are fairly obscure local folk styles (e.g. Outer Hebrides choral singing, various folk song styles in the Balkans, etc), but there is one that is not all that obscure – in fact, fairly prominently known. It has the additional benefit of being well formalized, well studied, and material on it is easily available - I am of course speaking of baroque counterpoint.

Baroque polyphony developed out of renaissance polyphony, which developed out of medieval polyphony. Each of these nodes in the family tree of western counterpoint has branches that did not contribute much to the descendants.

The formalizations that exist may be a bit too strict in the sense that they do in fact forbid things that were common. In part, it seems these formalizations might have been more like guidelines or even good things to practice, because doing so made one more aware of the possibilities and problems that various things brought with them.

The rules of counterpoint operate on several levels: there's rules that govern how melodies are to be written. In part, these seem to favour for single melodies that they be identified as "a single voice". There is probably some form of biological reason why we tend to hear things with very similar pitches as coming from the same source if they have the same timbre, but large differences in pitch even on the same timbre is easily parsed as multiple separate sources of sound. This, in fact, is an easy way of "faking" polyphony: make multiple big jumps. The brain will parse distant melodical snippets as part of different melodies, and those that are close together in pitch, but separated by intervening notes in other registers will still be heard as something akin to a melody.

For pairs (or larger sets) of melodies, the rules seem to favour designing them in ways that keep them distinct, so that they not merge into single "supertone melodies" – i.e. if you do a lot of, say, parallel movement, the brain will soon merge the separate melodies that are moving in parallel.

However, only when melodies are very consonant does the risk for that seem to be very high - and this is why parallel fifths and octaves were quite vigorously avoided in baroque music (except as a timbral effect!). Thirds and sixths are slightly less consonant, so some amount of parallel movement on those is not forbidden. With a different tuning or different timbre, the consonance profiles of our different intervals might make the ban on parallel movement less important, or maybe even more important - parallel movement in just intonation might make consonant intervals almost vanish into each other, conversely, 19 tone equal temperament might make parallel fifths unbearably badly tuned?

So, counterpoint favours melodies that move in different directions a lot. Of course, as soon as you have more than two melodies, you'll have to compromise on that at least some of the time. (If you have more than three, it's even impossible not to compromise on it). You have to end up deciding which voices to move similarly or parallelly, etc.

It pays off to read up on the rules of counterpoint, and consider their role in the musical context, and then consider to what extent they can be applied in your conculture's music.

In western music, an important aspect has been development. Development is reusing melodical elements in new combinations with other material - either material you already presented earlier in the piece, or new material. Development seems rather uncommon globally – variations are a much more popular thing worldwide. A variation is simply a melody with some elements changed – a sequence turns down instead of going up, a tone is substituted for another, the order of some tones is reversed, etc.

Microtonal Theorizing: A roadmap to my ideas

So, while I am writing these posts I am also kind of developing my own take on the ideas I present – this is why it takes the better part of forever to make new posts. In large parts, this is stuff based on things other xenharmonists and theorists have worked out, but it probably bears some undeniable traces of my own mind as well: I might have misunderstood other theorists' ideas, or maybe I have even introduced some ideas of my own.

So, a roadmap:

• overtone series and JI to approximations of finite subsets thereof in an equal temperament
• subsets of the overtone series, esp. partially overlapping ones given different starting points in the equal temperament
•  from temperaments and JI to chords as subsets of an ET
• from temperaments and JI to MOSes and MODMOSes as subsets of an ET
• chords as subsets of MOSes and MODMOSes
• movements by restricted paths /by step-size or step-type combinations) within and between group-structures of chords within a temperament; the subset of movements that is within a MOS/MODMOS is of special interest
• movements by restricted paths from MOS/MODMOS to rotation of the same MOS/MODMOS as a group operation. movements from one type of MOS/MODMOS to another type as a group operation.
• OTHER thing altogether: Comma pumps. Making comma pumps and the above come together. Using the inter-MOS/MODMOS modulation or extra-MOS/MODMOS modulation to create compelling chord progressions
• embedding MOSes/MODMOSes in larger MOSes/MODMOSes and relating this to the previous set of ideas (i.e. melodies moving in chords moving in scales^{moving in scalesmoving in scales...})
• Question: is there anything analogous to the comma pump in higher-level modulation?
• Question: does any other weird phenomenon happen in modulation that involves multiple levels of modulation, where weird things start happening?