H\"arpfer's Extended Indispensability Algorithm in Z

TL;DR

The paper presents a formal specification of H"arpfer's Extended Indispensability Algorithm in Z, which generalizes Barlow's original metric tree approach for analyzing musical meter importance, allowing arbitrary groupings.

Contribution

It provides a formal Z specification of H"arpfer's extended algorithm and proposes a generalization to arbitrary metric trees, enhancing the original method's flexibility.

Findings

Formal Z specification of the extended algorithm

Generalization to arbitrary metric trees proposed

Enhanced flexibility in meter importance analysis

Abstract

Since 1978, Clarence Barlow developed the ``Indispensability Function''. It operates on a metric tree that is bound to the same prime number of branches for all subtrees of each particular level. It assigns to all leaf postions of this tree a numeric value which indicates how important the acoustic presence of an event at this position is for the meter to be recognized as such. Bernd H\"arpfer extended this concept in 2015 to deal with meters which have arbitrary groupings into two or three at any position of the tree hierarchy. This is called ``Extended Indispensability Algorithm''. This article gives a specification of the Extended Algorithm in a slightly extended version of the Z specification language, and a possible generalization to arbitrary metric trees.