Benjamin Boretz’s Meta-Variations (PNM)

1) positivists divided knowledge into logical and empiric truths

2) Phenomenalists: reality includes nothing more than can be directly observed; thus, theoretical entities (x-rays, neutrons) and the French Revolution are beyond the grasp of direct observation; regard indirectly observable things, such as ‘beauty’ as “metaphysical nonsense”, or as “theoretical constructs.”

3) all scientific statements must be reducible to this phenomenalist basis

Carl Hempel’s D-N model (deductive-nomological)

1) deductive: explanations must entail the explanandum

2) ‘nomos’ = law; D-N requires empiric laws, generalizations:

a. must be true; [often, generalizations are only approximately true, hence law-like]

b. must be empirical [however, can’t be tested]

c. must be universal [not all generalizations are universal, so they can’t be law-like]

d. must be predictive [must have boundaries; must be able to explain why or why not something happened]


1) endorses phenomalism to rid music theory of vague, metaphysical jargon

2) endorses D-N model to give music theory methodological rigor
3) observations are reduced to 3 primitives (x=pitch, y=time point, x matches y), from which he constructs a generalized system of primitive definitions and relationships that apply to all music as well as a serives of “syntaxes” that account for specific repertoires and works
Meta-variations does not succeed in presenting a scientific model of explanation for music theory:
1) most philosophers doubt truth and plausibility of phenomenalism, including Hempel

2) distinction between theoretical and observational languages is arbitrary separation of a continuum; distinction is theory-bound, observational terms are theory-laden

3) 3 primitives:
4) discards many observational terms (i.e., style) on grounds they’re “non-cognitive”; however, untrained listeners have no difficulty distinguishing Medieval from Baroque, Impressionism, etc.

5) fails to account for concept of interval equivalence

6) is inconsistent; basically, after stating insistence on D-N model, he discards it, creating a descriptive system with no empiric or predictive content