Logica Universalis

, Volume 12, Issue 1–2, pp 239–269 | Cite as

A Molecular Logic of Chords and Their Internal Harmony

  • Ingolf MaxEmail author


Chords are not pure sets of tones or notes. They are mainly characterized by their matrices. A chord matrix is the pattern of all the lengths of intervals given without further context. Chords are well-structured invariants. They show their inner logical form. This opens up the possibility to develop a molecular logic of chords. Chords are our primitive, but, nevertheless, already interrelated expressions. The logical space of internal harmony is our well-known chromatic scale represented by an infinite line of integers. Internal harmony is nothing more than the pure interrelatedness of two or more chords. We consider three cases: (a) chords inferentially related to subchords, (b) pairs of chords in the space of major–minor tonality and (c) arbitrary chords as arguments of unary chord operators in relation to their outputs. One interesting result is that chord negation transforms any pure major chord into its pure minor chord and vice versa. Another one is the fact that the negation of chords with symmetric matrices does not change anything. A molecular logic of chords is mainly characterized by combining general rules for chord operators with the inner logical form of their arguments.


Molecular logic chord chord operator internal harmony formal music theory 

Mathematics Subject Classification

Primary 03B99 Secondary 00A65 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Philosophy Section of Logic and Theory of ScienceUniversity of LeipzigLeipzigGermany

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