Pseudo-diatonic scales

Abstract

The generalization of diatonic scales in a given tone system has been investigated by Eytan Agmon (see Agmon 1989, Agmon 1991), John Clough (see Clough 1979, Clough and Myerson 1985), and in relation with microtonality by Gerald Balzano and Mark Gould (see Gould 2000). Recently, (2006) gave a new synthetic approach of pseudo-diatonic scales (Model A). From our first essay (Jedrzejewski 2002) until the last article (Jedrzejewski 2008), we developed a new model of generalized diatonic scales based on a new arrangement of the Stern-Brocot tree (Model B). With our new definition of diatonicism, we recover Wyschnegradsky' diatonic scales in the quarter tone universe, a concept that he called diatonicized chromatism (Wyschnegradsky 1979), studied in (Jedrzejewski 1996) and (Jedrzejewski 2003). In the present article, we point out the differences of the two models (A and B). © 2009 Springer-Verlag.