Between two realms: a study of the superhexatonic scales

This paper investigates the superhexatonic (hexatonic-plus-one) spelled heptachords. It aims to situate the superhexatonics (set class 7-21) among families of symmetrical and asymmetrical scales. The article is divided into four parts. Part one presents the structure of the superhexatonics and compares them with symmetrical scales. This comparison involves a new concept that I call “heptatonic symmetrical hybridization”, by which a heptatonic asymmetrical hybrid is generated from two symmetrical scales. The second part begins by proposing a way of normalising the relationship between spelled heptachords and modes, using solfège syllables and the line of fifths. In the third part, I examine the superhexatonics in light of set theory and show how they can be generated by the same interval cycle as the double harmonic (or <i>verbunkos</i>) minor scale. I illustrate this by addressing two musical excerpts, one by Bartók and the other by Liszt. I finish the article with an extensive analysis of a piece by Rosemary Brown, which, in my view, shows a highly rational and sophisticated use of a superhexatonic scale.