but cannot belinked by particularly efficient voice leading; the same holds for {C, G, Af} and {G,Af, Df}
Showing that the voice leadings that the Tonnetz represents are not always efficient.
6 Matching Annotations
- Jan 2026
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dmitri.mycpanel.princeton.edu dmitri.mycpanel.princeton.edu
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nversionallyrelated chords are close when they share common tones
This does not depend on the structure of the lattice.
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tuning lattices are only an approximate model ofcontrapuntal relationships, and only for certain chords
These specifically-defined tuning lattices only work for a restricted number of chords and voice leadings.
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- Nov 2025
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dmitri.mycpanel.princeton.edu dmitri.mycpanel.princeton.edu
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the voice leading (C, Df)(Df, C) reflects off the orbifold’s uppermirror boundary
C-Db --> Db-C as a reflection off the boundary of the orbifold represents the encoding of note-swapping equivalence.
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To model an ordered sequence of n pitch classes, form the quotient space(R/12Z)n, also known as the n-torus Tn. To model unordered n-note chords of pitchclasses, identify all points (x1 , x2 , ... xn) and (x(1) , x(2) , ... x(n) ), where is anypermutation. The result is the global-quotient orbifold Tn/Sn (17–18), the n-torus Tnmodulo the symmetric group Sn. It contains singularities at which the local topology is notthat of Rn.
\(T^n/S_n\) represents \(T^n\) if the corresponding similar chords identified by \(\sigma\) were divided out.
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www.r-5.org www.r-5.org
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certain kinds of scales sound good with some timbres and not with others
timbre affects consonance
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