The Conventional Nomenclatures for Notes and Intervals

If the cognitive octave (a, b) is set to (12, 7) and privileged status is bestowed upon the “natural core”—the set of seven notes (0, 0), (2, 1), (4, 2), (5, 3), (7, 4), (9, 5), and (11, 6)—then the conventional nomenclature for notes (for example, “E double-flat”) may be accounted for. Similarly, if privileged status is bestowed upon the “usual primary intervals”—the set of eleven note intervals (0, 0), (1, 1), (2, 1), (3, 2), (4, 2), (5, 3), (7, 4), (8, 5), (9, 5), (10, 6), and (11, 6)—then the conventional nomenclature for note intervals (for example, “descending triply-augmented fifth”), may be accounted for (Sect. 4.1). Staff-notational idiosyncrasies with regard to relative note height, interval direction, and register, are noted (Sect. 4.2).