We estimate the Kolmogorov complexity of melodies in Irish traditional dance music using Lempel-Ziv compression. The "tunes" of the music are presented in so-called "ABC notation" as simply a sequence of letters from an alphabet: We have no rhythmic variation, with all notes being of equal length. Our estimation of algorithmic complexity can be used to distinguish "simple" or "easy" tunes (with more repetition) from "difficult" ones (with less repetition) which should prove useful for students learning tunes. We further present a comparison of two tune categories (reels and jigs) in terms of their complexity.

We have attempted to discover formal rules for transcribing into musical notation the fugue subjects of the Well-Tempered Clavier, as this might be done by an amanuensis listening to a'dead-pan' performance on the keyboard. In this endeavour two kinds of problem arise: what are the harmonic relations between the notes, and what are the metrical units into which they are grouped? The harmonic problem is that the number of keyboard semitones between two notes does not define-- their harmonic relation, and we further develop an earlier theory of such relations, arriving at an algorithm which assigns every fugue to the right key and correctly notates every accidental in its subject. The metric problem is considered de novo, and a metrical algorithm is described whose failures to generate Bach's notation are as illuminating as its successes. INTRODUCTION The performance of a piece of music involves both the performer and the listener in a problem of interpretation. The performer must discern and express musical relationships which are not fully explicit in the musical score, and the listener must appreciate relationships which are not explicit in the performance. How the performer should convey his interpretation of the piece is an aesthetic question of the utmost delicacy; but the converse process, that of listening to a piece and discerning its structure, is partly amenable to objective investigation. This is because European classical music is written in a notation which conveys to the performer a considerable amount of information about its structure, and this information can be reconstituted by the educated listener from even a mediocre performance. The'correct' annotation of the melody in question is, of course: This gap in musical theory is all the more glaring in view of the considerable effort which has been devoted to much more ambitious undertakings, such as programmed musical composition. We are cynical enough to believe that it is only the prevailing babel in contemporary classical music which saves most of these compositions from being treated with the derision which they merit, and that if any progress is to be made in this direction it will first be essential to formalize the most elementary facts about musical cOmpetence, such as those we have just mentioned.

We have attempted to discover formal rules for transcribing into musical notation the fugue subjects of the Well-Tempered Clavier, as this might be done by an amanuensis listening to a'deadpan' performance on the keyboard. In this endeavour two kinds of problem arise: what are the harmonic relations between the notes, and what are the metrical units into which they are grouped? The harmonic problem is that the number of keyboard semitones between two notes does not define-- their harmonic relation, and we further develop an earlier theory of such relations, arriving at an algorithm which assigns every fugue to the right key and correctly notates every accidental in its subject.