The Architecture of Music


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Visualizing Symmetrical Scales Using the Circle of Fifths

Some of the symmetrical scales from the previous page have been diagrammed below using their COF diagrams to better depict where the mirror lines lie and how many there are. If the LCOF diagrams are turned back into circles, we have half as many mirror lines as it appears on the previous page. For instance, the Raga Kalahamsa, which appears to have two mirror lines in its LCOF diagram, actually only has a single mirror line running down the center of its COF diagram (below).

Depicting symmetrical scales using COF diagrams is useful as it makes the symmetry and how the mirror lines work very clear. However, due to the size and shape of the COF diagrams it is obvious using the LCOF has its advantages as many scales can be explored and organized in much less space and the symmetry of the scales is still obvious. But looking at scales in this way is useful and has its advantages as well. With more complex symmetrical scales with multiple mirror lines, depicting the scales in this manner is useful in better understanding how they work. Ultimately, to understand and explore symmetrical scales to their fullest, diagramming them using the COF is the best way.