Imperfect/symmetrical scales are also symmetrical about the central note of the circle of fifths and will also have at least two mirror lines about which the modes inverse. Imperfect/symmetrical scales will also have at least one other mode that is also symmetrical. This can be seen as the diminished mode in the diminshed pentatonic scale on the previous page. In rare cases, an imperfect/symmetrical scale such as the Van Der Horst Octatonic and Genus Chromaticum will have even more 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, four mirror lines, four symmetrical modes, four pairs of identical modes, and only represents 4 unique modes total. More research needs to be done on scales and scales really need to be diagrammed out to understand where the mirror lines lie and how many there are. But symmetries like this are interesting because of the negative chord and inverse mode relationship and the possibilities for creating negative composition within a scale. |