MOLT identity 

a systematic analytical framework for each mode, designed to delineate its pitch-class content, interval-class vector, tonal permeability, internal structure, color features, complemented by examples drawn from Messiaen’s compositional practice.

for each mode:

– intervallic Identity:
a complete intervallic profiling, including the full interval-class vector, enumeration of all ordered and unordered intervallic possibilities, and identification of structurally privileged intervals resulting from the mode’s transpositional limitations.

– tonal presence:
basic mapping of all potentially emergent tonal or quasi-tonal centers

– disjoint tonal subsets:
A presentation of several disjoint tonal subsets, including triadic, seventh-chord, or extended sonorities. These function as pitch-class partitions that reveal the mode’s harmonic features.

– modal signatures:
Identification of unique subsets—invariant under a restricted number of transpositions—that distinguish the mode from its internal transpositional forms and from the transpositional arrays of other modes.

– structures:
a complete list of rotational permutations of the mode within its pitch-class cycle (cyclic permutations), highlighting the structural invariants and revealing how each rotation sculpts the modal intervallic profile. This includes the enumeration of internal subset lattices (cf. MOLTexplorer 2.3: subsets of notes).

– characteristics:
a selection of the mode’s unique colors