Music

Degrees of Accuracy (2002)
for trombone and electronic string sounds

Download: ( mp3, up to Reh. Letter J, 4.1 MB, 4:29 )
Format: mp3, 128 kbs, 44.1kHz, joint-stereo

Degrees of Accuracy (2002) was inspired by the number pi (3.14...). That is to say, its pitches, durations, tempos, and so forth were derived from pi in various ways. Mathematicians have proved that pi, the ratio of every circle's circumference to its diameter is an irrational number, that is, it is a number that cannot be represented as a ratio of two whole numbers. When expressed in decimal form, such numbers take the form of an infinately long sequence of digits to the right of the decimal place. As far as we know, this sequence never repeats itself. Somewhat paradoxically, statistical studies have unveiled that the digits of pi appear to be random in their distribution. Nevertheless, mathematicians (and musicians!) continue to study pi, having recently calculated it to a precision of over 51 billion digits. Despite this race toward greater accuracy, there is still no end in sight to this endless sequence of digits.

The work's title derives from the notion that pi can never be exactly expressed, it can only be approximated. This notion has many parallels in music. For example, pitches and durations are never "exactly" expressed by human performers. Unlike a human performer, a computer can accurately encode a pitch interval or note duration such as 3.14:1, however, even a computer cannot encode the exact value of the irrational number pi.

Degrees of Accuracy was commissioned by and is dedicated to trombonist Brad Edwards who gave the premiere on January 27, 2003 at the USC School of Music Rectial Hall in Columbia, SC.

More about Degrees of Accuracy

Degrees of Accuracy is a traditional theme and variations form. The pi-inspired theme, notated below in Fig. 1, was carved out of the first 26 digits of the decimal expansion of pi (3.14159265358979323846264338...).

Fig. 1. The pi-inspired theme from Degrees of Accuracy (2002).

Download: ( mp3, pi-theme from Degrees of Accuracy, 520 KB, 0:33 )
Format: mp3, 128 kbs, 44.1kHz, joint-stere

Petr Beckmann, A History of Pi, (New York: Barnes & Noble Books, 1993).