Sevish Music

Getting hard with scales

People working with musical scales have found various ways to categorise them. Recently I’ve heard of a new way of sorting scales depending on how big the difference is between the large and small step. This idea, the “step ratio spectrum” applies to moment of symmetry scales.

Reminder about moment of symmetry (MOS) scales: MOS scales have have exactly two step sizes: large and small, usually notated as L and s. One example is the major scale (LLsLLLs).

On the “soft” end of the spectrum, the large and small steps are almost equal in size. The melodic quality of these scales seems smoother to me.

As for the “hard” end, large steps are very exaggerated in how large they are in comparison to the razor-thin small steps. Melodically this sounds quite dramatic to me because of the obvious difference in the step sizes.

In the below video, you’ll hear one piece of music which explores various points on the hard side of this spectrum. The scale used is LsLsLsLsL, tuned to various equal temperaments:

EDO L:s ratio L (cents) s (cents) TAMNAMS name
313 53:12 203.2 46.0 Superhard
24 4:1 200 50 Superhard
19 3:1 189.5 63.2 Hard
14 2:1 171.4 85.7 Basic
9 1:1 133.3 133.3 Equalized

It’s because I only recently heard about scale hardness and found it an interesting perspective that I’m posting about the topic here. Maybe this could be a jumping off point for further reading and study about interesting tuning thingies.

Xenharmonic Wiki


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