Imperfect/symmetrical scales are also symmetrical about the central note of the LCOF. In rare cases, an imperfect/symmetrical scale (such as the Van der Horst Octatonic and Genus Chromaticum) will have multiple mirror lines, modes that inverse multiple times, multiple symmetrical modes, and the original scale will repeat in the modes. The Genus Chromaticum has three mirror lines and has three sets of three identical modes. And even though it has 9 modes, it only has 3 unique modes total. The Van der Horst Octatonic has eight modes, two mirror lines, four symmetrical modes, two pairs of identical modes, and only represents 4 unique modes total. More research needs to be done on symmetrical and semi-symmetrical scales, and scales really need to be diagrammed out using the COF diagram of the scales to understand where the mirror lines lie, how many there are, and how many unique modes each represents. Symmetrical and semi-symmetrical scales makes calculating the total number of scales that generates the 2,048 mathematically possible unique modes difficult because a single scale like the Symmetrical Decatonic (a 10-note scale) only represents five unique modes. But symmetry and semi-symmetry in scales is interesting because of the negative chord and inverse mode relationship and the possibilities for creating negative composition with negative chords using a single scale. Though not included in the scale encyclopedia in this book, some symmetrical and semi-symmetrical scales have been diagrammed on pages 6-9 for your perusal. |