In connection with this argument I introduce the idea of modal pitch-class sums and show that a mapping exists between these sums and a scale's structure upon the line of fifths. In chapter three, I discuss the placement of "tendency tones"-minor seconds that resolve to a member of the tonic triad-in various scales and modes, and how this placement affects the tonal implications of a given mode. I discuss the implications of these properties when modes of these scales are realized in actual music. In chapter two, I review the theoretical literature on various relevant scale properties, such as transpositional asymmetry and intervallic content. This account is based on Hook's (2011) use of the line of fifths, but generalized to any eligible generating interval. In chapter one, I develop a systematic account of how to describe a large set of musically useful scales by using a generated line of intervals. The topic of this thesis is the properties of scales and modes other than the familiar major and minor, and the possibilities these afford for extended tonality and alternative functional harmony.
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