Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

On the level of tones⁷

⁷
Chew speaks of ’pitches’ instead of tones or note names. We keep close to Chew’s notation but avoid the term pitch.
there corresponds a tone $p(k)$ to each note name $k (- F$ (c.f. Subsection 2.4).
On the level of triads there corresponds a major triad $tMaj(k)$ and a minor triad $tmin(k)$ to each note name $k (- F$
On the level of keys there corresponds a major key $kMaj(k)$ and minor key $kmin(k)$ to each note name $k (- F$ . These are encoded as lists of triads $kMaj(k) = (tMaj(k),tMaj(k+ 1),tMaj(k - 1)) kmin(k) = (tmin(k),tMaj(k + 1),tmin(k+ 1),tmin(k - 1),tMaj(k- 1))$

In this section re-interpet Chew’s definitions in terms of harmonic configuration space and propose natural candidates for a Riemann Logic $RL$ .