The Architecture of Music

Scales

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The Five Perfect/Semi-Symmetrical Scales

While exploring scales, a class of scales became evident which were asymmetrical but had symmetrical scale properties. I classified these scales as semi-symmetrical because their modes inverse within them just as symmetrical scales but are asymmetrical. If you study the diagram below you will see that semi-symmetrical scales are modes of each other across the central mirror line. What this means is while there are two semi-symmetrical modes depicted, they are modes of a single scale hence there are only five perfect/semi-symmetrical scales in existence. While the most central or symmetrical modes were used to identify the semi-symmetrical scales below, all the modes of these scales are considered semi-symmetrical and will have an inverse within the scale.

The Five Perfect/Semi-Symmetrical Scales