D = A220

DD115438

D = A220 is what we call an unidentified piece of music by Delia for which there is an unconventional mathematical score in her papers.

Analysis

The piece consists of six bars called A to F, each of which is contructed from three or four of eight musical phrases, [1] to [8], which are played on six notes, bottom C, D, Eb, A, Bb and top C, transposed so that the D is a 220Hz, the A below middle C. The phrases are:

[1] A
[2] A D
[3] A Bb A D
[4] A Bb A Eb
[5] A Bb A Eb D
[6] A Bb A Eb D C,
[7] A Bb A C' A
[8] A Bb A C' A Eb D C,

where "C," means the bottom C and "C'" the top one, and the bars are composed of the phrases:

A: [1] [2] [3] [5]
B: [2] [4] [6]
C: [2] [3] [7] [2]
D: [2] [3] [4] [3]
E: [2] [5] [3]
F: [2] [7] [8]

The note lengths within each phrase, written in a circle above each note, are different each time the phrase is used, hence so is the length of each phrase, written in a circle above each phrase's bracket. The cumulative running time of the piece is written under the stave, for a total of 6 minutes and 50 seconds.

The table in the bottom right corner gives all the multiples of 2.6 seconds from 1 to 42, so presumably that is the length of a note of duration (1).

The matrix above left of it gives the duration of each phrase when it is used in a particular bar and is derived from the score, adding no extra information.

This information is sufficient to reconstruct the piece.

Score

Here is the typeset score in four formats:

• the LilyPond source file
• the typeset score as a PDF (right)
• a MIDI file that you can listen to
• An audio file of the MIDI file played on a cheesy electric piano