Music Theory for Conworlders: How to Test These Scales

If you happen to play a fretless instrument such as the violin or cello, playing unfamiliar intervals is possible, but may take some practice. With woodwinds, I hear it is possible, but challenging. With brass, the overtone series comes naturally, but is of course slightly challenging once you get sufficiently high up. The slide trombone is of course a very convenient instrument insofar as that goes.

Several synths support .scl files these days. .scl files are a convenient format for storing tunings, and for using them with hardware and software that supports them. Midi keyboards can of course be retuned on the fly - try Manuel op de Coul's Scala.

For people lacking instruments, but who want to try out microtonal music, most freeware trackers permit pitch bends. The small tunes I've made here I've made using sunvox - which can do a lot more than just sound like ass the way those tunes do. Pitch bends upward have the code '11' in the effect column. However, pitch bends in sunvox require some maths - sunvox doesn't use cents, but 64th:s of semitones. Thus, the pitch bend necessary for an interval P (given as a ratio), is rendered as 768*log₂P mod 64 rewritten in hexadecimal, and the number of semitones is naturally (768*log₂P - (768*log₂P mod 64)) / 64. I have made a gnumeric file that calculates this stuff for any equal temperament (I will explain what those are soon enough), and used this to compose, among other things, these compositions. It is basically very much a cheap hack, so no guarantees. I might improve a bit on it in the near future. In order to get overtone scales and other ratio-based tunings, you basically have to set the period to be that ratio, and the number of subdivisions to be one (well, you can set it to anything, but then only every anything:th element will correspond to that ratio or its integer powers, i.e. for 5/4 divided in three steps, you'll get 5/4, 25/16, 125/64, etc every few steps.)

The temperament names given below the pieces are in a way for future reference, as I will get into the kinds of structures I've used in these pieces and what other structures exist that can give equally weird or weirder results:

11-tone equal temperament attempt at Arabic-sounding stuff.


11-tone equal temperament attempt at I dunno, some kind of electronic thingy.

19-tone equal temperament thingy in a somewhat out-there temperament.

An octave-less thingy in "88 cent equal temperament".

A thingy in Bohlen-Pierce temperament.


A fanfare that attempts to do some weird things.