Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift

The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities

“…In a sense, the emotion of the music is objective. Because the emotion of music mainly reflects the subjective emotional experience of the creator when creating it, this emotional experience has been positioned by the creator for the listener [3]. Different listeners have different emotional experiences of the same music in different mental states, but this difference will not be very different from the emotional state of the original creator.…”

Symbolic dynamical scales: modes, orbitals, and transversals

“…(see [3,30] for more on the Thue-Morse sequence and substitution systems in general). The set of standard (or admisible) Thue-Morse scales in 12-TET tuning system reported in [21], as integer compositions, is M C (m) 12 = ϕ L 12 (m) ⊂ C 12 and consists of the following 18 elements:…”

“…A symbolic sequential scale is a musical scale obtained from a (mathematical) symbolic sequence, according to certain (mathematical) rule. For example, the standard Thue-Morse scales introduced in [21] and defined as certain sets of scales obtained from the renowned Thue-Morse binary sequence, with coding rule the binary representation of scales. This rule can be generalized to sequences over larger alphabets, for example as the distinguished symbol rule, that likewise generates scales on every n-TET tuning system; it consists on coupling a block that occurs in the sequence with a "symbolic chromatic scale" of the same length, that is, a block formed with increasingly ordered elements of a set of "symbolic notes", and then letting the scale defined by the rule be formed with the notes carrying the distinguished initial symbol of the corresponding block.…”