Automorphism selection

1. Choose a mapping of the generators:

U	L	P

2. Choose a permutation of the augmented chords:

3. Choose an image for each chord.
(The mapping of the remaining chords is automatically determined.)

C_M	E_M	G♯_M
C_m	E_m	G♯_m

G_M	B_M	E♭_M
G_m	B_m	E♭_m

D_M	F♯_M	B♭_M
D_m	F♯_m	B♭_m

F_M	A_M	C♯_M
F_m	A_m	C♯_m

Transformation of chords

Help: part 1 - part 2 - part 3

	The central part shows the Colored Cube Dance. It is an extension of the Cube Dance of Douthett and Steinbach in which the unique parsimonious relation relating major, minor, and augmented chords is refined using three different binary relations notated U, P, and L. The binary relations P and L are similar to the corresponding neo-Riemannian transformations, while the U binary relation relates major and minor chords to augmented chords.
	If an automorphism has been completely selected (see next part), hovering over a chord will highlight its corresponding image in blue. Clicking on the chord will play it.
	If the Option key is pressed down, hovering over a chord will highlight it in orange and clicking on it will add it to the current chord progression.

	An automorphism of the Colored Cube Dance is completely determined by three pieces of information:
	1. The mapping of the generators U,P, and L of the Colored Cube Dance, i.e. the binary relations that relate the major, minor, and augmented chords.
	2. The mapping of the augmented chords. Eight possible permutations are allowed, which can be chosen using the left and right arrows.
	3. A mapping of the major and minor chords. Only the image of one chord in each quadrant is required, as the rest of the mapping will be automatically determined from the selected mapping of the generators and of the augmented chords. The chord in each quadrant can be selected in the corresponding dropdown menu, and a choice of three allowed images will be displayed correspondingly.
	When an automorphism has been completely determined, its internal index will appear and you can add it to the list of automorphism that transform the chord progression on the right.