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Related is that going four steps around the circle of fifths, for a total of five pitch classes, produces the pentatonic scale (e.g. the black keys). This is th
by osteele 12y ago
Related is that going four steps around the circle of fifths, for a total of five pitch classes, produces the pentatonic scale (e.g. the black keys). This is the longest sequence that doesn't contain any half steps. Continue for a total of seven notes and it's the diatonic scale (e.g. white keys†). This is the longest sequence that doesn't contain consecutive half-steps. Finally, continue for a total of twelve notes, as the article describes; the resulting chromatic scale is either (in just temperament) the longest sequence where every step is at least a half step, or (in even temperament) the longest sequence before the pitch classes repeat.
† Annoyingly, the tonic (tonal center) of the diatonic scale is the second note in the sequence of fifths (e.g. C in FCGDAEB). I believe this is so you depart the tonic by a fifth in either direction, since fifths sound so good.
- acjohnson55 12y agoYep. In other words, the common scales are the number of consecutive perfect 5ths to "almost" land back on the first note, with "almost" defined progressively stricter. This exercise could be extended to make longer scales, but the additional notes would be close enough to the first 12 to just sound to human ears more like knockoffs of notes in the first 12 than new notes in their own right. Instead, the standard of modifying the 11 notes after the first in various ways to make instruments sound good in more keys proved to be more worthwhile.