Ts-tonnetz NPM

TypeScript Tonnetz

TypeScript Tonnetz is a set of functions and operations from Mathematical Music Theory (transformational approach). Specifically, it deals with Tonnetz spaces and functions related to the topic. The objective is not musicological analysis itself, but the application of these tools born from analysis for algorithmic composition and live coding.

It emerged as a development branch to contribute to Miika Alonen's phenomenal ZifferJS project.

Features Implemented

Transformations and functions follow the edge flip between triangles and their geometries (so far), so they maintain two common notes (not necessarily voice-leading considerations). In other words, diferent Tonnetz Spaces follow the voice-leading space geometry of the conventional Tonnetz.

PRL functions and compositions of any length, cardinal transformations
Film music transformations: f(), n(), s(), h(), t6()
HexaCycles, OctaCycles, EnneaCycles, Hamiltonian Cycles
Weitzmann Regions, Boretz Regions, OctaTowers
Cube Dance, Power Towers

Mathematical inspiration (Trajectoires) in the Doctoral thesis written by Louis Bigo:

Représentations symboliques musicales et calcul spatial (2013).

Dual geometry of the Tonnetz

We have implemented all the Neo-Riemannian functions developed in the Doctoral thesis written by Sonia Cannas:

GEOMETRIC REPRESENTATION AND
ALGEBRAIC FORMALIZATION OF
MUSICAL STRUCTURES (2018)

Each of these new transformations from the generalized transformational theory for seventh chords is enabled for the Tonnetz you want to explore.

PLRQ-group

p12, p14, p23, p35
r12, r23, r42, r35, r53
l13, l15, l42
q43, q15, rr35, qq51, n51

PLRQ-group extended

Includes more types of seventh chords and their transformations between them.

p18, p19, p26, p39, p47, p64, p87, p98
r63, r76, r86, l71, l89, q62, q76
rr19, rr39, rr98, qq38, qq98

PLR*-group

Transformations with augmented and diminished triads.

p, r, l, p32, p41, lt13, l41, l14, rt23, rt42, q13, q42, n42

ST-group

Transformations between triad chords and different types of seventh chords. The groups PLRQ and PLR* must be included.

p1M, l1d, p2m, r2M, p3d, r3m, p4M, l4m, p5d, r5d, rr5d, z5d

Mathematical inspiration in the paper:

A Generalized Dual of the Tonnetz for Seventh Chords:
Mathematical, Computational and Compositional Aspects
(Sonia Cannas and Moreno Andreatta, 2018).

Extensions of the Axis System in Béla Bartók

Generalized implementation on any Tonnetz of the harmonic groups of axis system ideaded by Ernő Lendvai: Tonic (8 chords), Subdominant (8 chords), and Dominant (8 chords). The parameters specify two directions, sought emotion (based on the ideas of Mauro de Maria), cross or diagonal movement. Major-minor and minor-major alternation available for cross path.

The manipulation can be done using a single function:

genCardinalPoints()

Groups with chord roots separated by major thirds (which we will call triangular) are also added.

genTriangularPoints()

We added six new graphs generalized inspired by the idea of cardinal points (extension of the axial system) for film music by Mauro de Maria. These graphs link the groups of cardinal points with the groups of three chords.

Each graph can be manipulated from a single function: