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Published online by Cambridge University Press: 01 January 2020
Mr. Chairman, Ladies and Gentlemen,—My object in reading to you a paper on “The Dual Theory in Harmony” is not only to draw attention to a subject which is very little known in this country, but also thereby to stimulate the spirit of comparison, and to induce the study of the various theories which have been put forward as a rational basis for all harmonic phenomena.
∗ Dr. Pole's “Philosophy of Music” (Trübner, 1879).CrossRefGoogle Scholar
∗ Letters of a Leipzig Cantor, 2 vols. (Novello and Co.).Google Scholar
∗ Duplicate values are of course recognised in melodic passages—but not, I would say, in Harmony as a whole. The conscious or unconscious standard in the unaccompanied singing of Ex. 6 would, nowadays at least, be that of equal temperament, and any deviation would be felt as such.Google Scholar
∗ “The Nature of Harmony and Metre,” translated by W. E. Heatbcote, M.A. (Swan Sonnenscbem & Co.)Google Scholar
∗ In Ex. 39, where the f # | a ♭ is given as Augmented Sixth, the reference is to two different G's, ana hence the derivation is now not simultaneous, but “we hear the progression from the G which first was fifth and then became root.”Google Scholar
∗ The Sixth itself, in the Contrapuntal Form, cannot be consistently analysed as third of a Dominant Root, &c., because that would imply the absurdity of a double root, but can be reasonably described as a chromatic auxiliary note which has become harmonically crystallized in connection with certain intervals or chords.Google Scholar
∗ Riemann's “Dictionary of Music,” Augener. (See Articles on Harmony System, Clang, Clang Succession, Consonance, Tone Relationship, Scale, Minor Chord; Minor Key, Dissonance); Riemann's “Catechism of Musical History,” Part I., chap. VII. See also “Die ‘musikalische Akustik’ als Grondlage der Harmonik und Melodik” (by Georg Capellen, Leipzig, C. F. Kahnt Nachfolgen, 1903), in which the author purposes a reform of Musical Theory leading up to Monism as opposed to the Dualism of Riemann and Oettingen.Google Scholar