- In
musical tuning and harmony, the
Tonnetz (German for 'tone net') is a
conceptual lattice diagram representing tonal space first described by Leonhard...
-
modeled with
several interrelated geometric structures. The
Riemannian Tonnetz ("tonal grid,"
shown on the right) is a
planar array of
pitches along three...
- Vogel's
Tonnetz is a
graphical and
mathematical representation of the
scale range of just intonation,
introduced by
German music theorist Martin Vogel [de]...
- The
Tonnetz is an
example of a
torus in
music theory. The
Tonnetz is only
truly a
torus if
enharmonic equivalence is ****umed, so that the (F♯-A♯) segment...
-
Leonhard Euler's
Tonnetz, with the
horizontal axis
showing the
perfect fifths and the
vertical axis the
perfect major thirds. In the
Tonnetz, the diatonic...
-
Bridges of Königsberg (see above). The
device drew
renewed interest as the
Tonnetz in Neo-Riemannian
theory (see also
Lattice (music)).
Euler further used...
-
shapes from a
larger lattice).
Examples of
musical lattices include the
Tonnetz of
Euler (1739) and Hugo
Riemann and the
tuning systems of composer-theorists...
-
using two-dimensional (or higher-dimensional) lattices,
under the name of
Tonnetz. In
these models, one
dimension typically corresponds to
acoustically pure...
- sets in the Tn/TnI
equivalence class.
Identity (music)
Pitch interval Tonnetz Transformational theory Sc****jer 2008, 99.
Hanson 1960.
Forte 1973. Rahn...
- (harmonic
resonance based on
equal string divisions)
Tonality diamond Tonnetz Utonality and
otonality Music portal Reginald Smith Brindle, The New Music...
