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About: Vogel's Tonnetz     Goto   Sponge   NotDistinct   Permalink

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Vogel's Tonnetz is a graphical and mathematical representation of the scale range of just intonation, introduced by German music theorist 1976 in his book Die Lehre von den Tonbeziehungen (English: On the Relations of Tone, 1993). The graphical representation is based on Euler's Tonnetz, adding a third dimension for just sevenths to the two dimensions for just fifths and just thirds. It serves to illustrate and analyze chords and their relations.The four-dimensional mathematical representation including octaves allows the Evaluation of the of chords depending on the tonal material. It can thus also serve to determine the optimal tonal material for a certain chord.