This demo illustrates the Moment of Symmetry (MOS) concept in musical scale creation. Moments of Symmetry were first defined and formalized by theorist Erv Wilson, but have existed in some sense long before, as these patterns seem to emerge naturally in world musics for as long as we have record of music history.
The underlying idea of MOS scale creation is that an interval of equivalence, commonly the octave, is represented as a circle, such that similar pitch classes, for example 'C' occupy the same angle, or 'hour' along the perimeter of the circle. Another interval, called the 'generator' is a repeated angle that represents another pitch interval (usually smaller) that takes as its starting point the last generated pitch, resulting in a scale based on 'stacking' the generator. MOS scales are formed at those places along this process where no more than 2 distinct sized 'slices' happen along each ring, a 'large' and a 'small' interval. For instance, we are familiar with the C-major scale, where we have a pattern of whole and half steps like so: LLsLLLs. This pattern is one of many generated by the 3/2 Perfect 5th as a generator, folded within the 2/1 octave, but there are many more interesting and beautiful, and often exotic scales to be explored by experimenting with different sizes of generator.
The default values presented illustrate the musical interval of a 'Perfect 5th' (3/2 or 1.5 in frequency ratio) being used to seed a scale. One can specify another ratio in the 'linear factor' box by typing a ratio (e.g. 5/4), which will be instantly replaced with its decimal equivalent. A similar thing will happen in the octaves box, so one can specify for instance 18/31 octaves and all the other boxes will be corrected automagically upon the user hitting 'Enter' or 'Return' on their keyboard.
Finally, one can feel free to edit or erase some of the suggested MOS scale sizes in the 3rd box from the top. The applet will generate rings only for the listed MOS sizes, which are guaranteed to be theoretically correct MOS points, where there will be 2 sizes of interval in the resultant ring level. The user also can choose the speed of rendering the actual MOS ring diagram; it's a lot of hypnotic fun to watch at the 2 slowest settings, but the impatient will choose a radio button value towards the right...