From Circle to Hyperspheres

Episode III :
Graphs Embedding,
Polarized Tonnetz,
Spinnen Tonnetz,

Chapters

16 Hyper ChickenWire
17 Analogies / Cohn Regions 2D
18 Analogies / Cohn Regions 4D
19 Embedding 2D Graphs in 4D
20 Polarized Tonnetz
21 Harmonic Paths : Vertical
22 Harmonic Paths : Horizontal
23 Spinnen Tonnetz

-> ChickenWire Hypersphere is an Embeding of Jack Douthett’ Chicken Wire in 4D.
-> By morphing, we show the Analogies beetwen Planet Graph and different well known 2D graphs (Cohn Hexatonic Cycles, , Weitzmann’s Region, and Douthett’s Dancing Cubes (2000)”
-> Same process in 4D
-> Ability tp project any 2D musical graph on the -> Polarized Tonnetz is an extension developped w. H.Seress, to the Tonnetz
-> Construction : 1 PLR Direction, 2 Modal Orientation, 3 Polarity (#/b)
-> Demonstration of Vertical/Horizontal Path in Tonal Music
-> Spinnen Tonnetz, based on above ; Due to tonal attraction, the Spider will come back home, using parcimonious voice leading (w.H. Seress)

Premiered at Queen Mary University of London , 2015