Nick Vuci's Fundamentals of Xen: Difference between revisions

Moments of Symmetry (MOS) are special scales based on a simple principle. Take some generator and reduce in some period (usually the octave). Stack the generator over and over. When you get some collection of notes by doing this that have only two step sizes, you have a moment of symmetry. Another way to think of it is to consider you have some number of large (L) and small (s) steps, say 5L and 2s. Make it so that the 2s are as evenly distributed amongst the 5L as possible. This looks like LLsLLLs or sLLsLLL. This is called maximal evenness.

The largness or smallness of the steps is called the step size ratio. The quality of the step ratio, whether it’s hard or soft or equalized is categorized according to the Temperament Agonstic Mos NAMing System (TAMNAMS). The ways to modify mosses are documented on the page “Operations on MOSes”. Things like chromatic alterations, subdividing scales (muddling), or neutralizing the scale are all documented. There’s a lot you can do with MOS. Things like splitting the scale into a hexachord or a tetrachord allows you to transpose the same melodic segment. You can morph between scales, say between hard diatonic and soft diatonic. It’s worth looking at the MOS family tree as well for reference, illustrating MOS’s recursive structure. The Math behind MOS is actually quite simple, but that’s not what we’re hear to cover.