CORNELL

THE DUODECUPLE {OR TWELVE-NOTE) SCALE 39Ex.74Allegro.Successions of minor thirds and minor sixths were possibleThe collapse came when a string ofmajor thirds or major sixths was attempted, and°^. '^^'"j the effort made by some of the theorists to explainon the older principles.SuccessionsMajor a succession of diminished seventh chords as in-Sixths.eluding some falsely written major sixths wouldnot be devoid of humour had it not been productive of suchdeplorable results to students of harmony.But the power of giving successions of equal intervals andchords by no means exhausts the possibilities of the " semij., . tonal " scale. Apart from the special Impression-'^Enlarged . . . ^ .^Possibilities istic technique discussed m Chapter X., theof Harmonic boundaries of harmonic colour have been infinitelywidened. The passages in this chapter can onlybe explained satisfactorily on the basis of the duodecuple scalesystem, and it is noteworthy that whilst many composerssecure more coherence by a semitonic melody, quite mild byitself, others repudiate any such assistance to the comprehensionof their harmony or melody.The central point of this system is the complete abandonmentof the Dominant as such, a course which at once bringsThe with it a keenly felt want of some efficient sub-Abandoned stitute for securing cohesion. Consequently, inDominant, ^^acing the gradual extension of the scale possibilities,we find this note is the last to give up its weUestablishedspecial claims. With the duodecuple system,however, if there is any secondary centre in addition to thechief Tonic hold, it is the diminished fifth or the augmentedfourth ; or, in other words, the seventh semitonal degree.Now, the number twelve is not cryptic like three ornine, nor has it the mystic significance of seven, yet there does