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The Viennese theory on the other hand, the "Theory of the degrees" (Stufentheorie), represented by Simon Sechter, Heinrich Schenker and Arnold Schoenberg among others, considers that each degree has its own function and refers to the tonal center through the cycle of fifths; it stresses harmonic progressions above chord quality. [19]
In keeping with Westergaard's characteristic "concern with fundamental methodological questions", [1] ITT begins with a discussion of what it is that a theory of tonal music consists of. The conclusion reached is that it is a "logical framework in terms of which we understand tonal music"– [ 2 ] the operative words being "we understand".
"All harmonic idioms in popular music are tonal, and none is without function." [4] [vague] Tonality is an organized system of tones (e.g., the tones of a major or minor scale) in which one tone (the tonic) becomes the central point for the remaining tones. The other tones in a tonal piece are all defined in terms of their relationship to the ...
Russell posited that tonal gravity emanates from the first seven tones of the Lydian mode. As the player ventures further from the Lydian tonic however (and further up the circle of fifths), the tonal gravity shifts. For example, if notes further up the circle of fifths (e.g. ♯ 2/ ♭ 3) are used, the tonal gravity is probably shifting. [5]
Depiction of Curwen's Solfege hand signs. This version includes the tonal tendencies and interesting titles for each tone. Hand signs, also borrowed from the teachings of Curwen, are performed during singing exercises to provide a visual aid. [2]: 156 This technique assigns to each scale degree a hand sign that shows its particular tonal function.
Here there is an unexpected link between Schenkerian theory and Riemann's theory of tonal functions, a fact that might explain Schenker's reluctance to be more explicit about it. In modern Schenkerian analysis, the chord of IV or II is often dubbed the "predominant" chord, as the chord that prepares the dominant one, and the progression may be ...
The axis system is "concerned with harmonic and tonal substitution", [1] and posits a novel type of functional relationship between tones and chords. Lendvai's analyses aim to show how chords and tones related by the intervals of a minor third and tritone can function as tonal substitutes for one another, and do so in many of Bartók's ...
Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...