Why Are There Twenty-Nine Tetrachords? A Tutorial on Combinatorics and Enumeration in Music Theory

Combinatorics on words: a tutorial

Enumeration and construction in music theory

In this paper we describe in a more or less complete way how to apply methods from algebraic combinatorics to the classification of different objects in music theory. Among these objects there are intervals, chords, tone-rows, motives, mosaics etc. The methods we are using can be described in a very general way so that they can be applied for the classification of objects in different sciences....

Why Believe That There Is a God?

This article presents an argument for the existence of God, showing that the evident phenomena are best explained by supposing that a God causes them. The argument is based on the inductive force of four very evident general phenomena: that there is a physical Universe; that it is governed by very simple natural laws; that those laws are such as to lead to the existence of human bodies; and tha...

Combinatorics of cluster enumeration

47 thereby facilitating reduction of polyoxometallates of these types. The concept of binodal orbital aromaticity in reduced early-transition-metal polyoxometallates may be related to their classification as mixed valence compounds. Robin and Day36 classify mixed valence compounds into the following three classes: Class I, fully localized corresponding to an insulator in an infinite system; Cla...

The Combinatorics of Alternating Tangles: from theory to computerized enumeration

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight n is given to each connected component, and in particular the limit n → 0 yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two typ...