Reginald Bain, A Mathematical Offering, for oboe and bassoon, in ten movements

A Mathematical Offering (2010) is a set of ten contrapuntal miniatures for oboe and bassoon. Written for oboist Rebecca Nagel and bassoonist Peter Kolkay, each movement is a musical manifestation of a musico-mathematical idea. The work was inspired by Douglas Hofstadter's 1979 Pulitzer-prize winning book Gödel, Escher, Bach (GEB), especially its well known reference to J.S. Bach’s The Musical Offering, BWV 1079 (1747) in the introductory chapter. The sixth and ninth movements are musical analogues of lithographs by the Dutch graphic artist M.C. Escher: Waterfall (1961), and Ascending and Descending (1960), respectively. The fifth movement (V. Strange Loop) is a self-referential musical interplay of one of the central themes of GEB. The fourth movement (IV. Partitions) explores an even partition of a twelve-tone series that creates a self-referential hierarchy. The final movement (X. Ladder Canon) is inspired by Bach’s rarefied canonic art – as exemplified in his ten canons of the Musical Offering. The remaining movements – I. Minimal Perturbation, II. The Stepping Stone Analogy, III. Cube Dance, VII. Hyper-Hexatonic Blues, and VIII. Splitting and Fusing – refer to specific concepts in mathematical music theory that relate to themes explored by Hofstadter in GEB, an attempt by the composer to extend Hofstadter’s “Eternal Golden Braid.”

Nagel and Kolkay gave the world premiere at Shandon Presbyterian Church in Columbia, SC on January 28, 2011 and introduced the work at the International Double Reed Society conference in Tempe, AZ later that same year.

I. Minimal Perterbation 0:36

II. The Stepping Stone Analogy 1:21

III. Cube Dance 1:24

IV. Partitions 1:35

V. Strange Loops 1:00

VI. Waterfall 1:13

VII. Hyper-Hexatonic Blues 1:22

VIII. Splitting and Fusing 1:09

IX. Ascending and Descending 1:16

X. Ladder Canon 0:56

D U R A T I O N : 11:52

I.	Minimal Perterbation	0:36
II.	The Stepping Stone Analogy	1:21
III.	Cube Dance	1:24
IV.	Partitions	1:35
V.	Strange Loops	1:00
VI.	Waterfall	1:13
VII.	Hyper-Hexatonic Blues	1:22
VIII.	Splitting and Fusing	1:09
IX.	Ascending and Descending	1:16
X.	Ladder Canon	0:56
D U R A T I O N :		11:52

A MATHEMATICAL OFFERING