Science of Music - Physics / 60
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Violin and viola – Dominic Sterland
Voices – Max Catmur, Zhuo Yu and Rudolf Römer
Composition, synthesis and other instruments – Gavin Bell
The 5-minute piece of music celebrates the 60th anniversary of the Physics Department at Warwick. It is inspired by the number 60 and the idea of symmetry, a notion of central importance to physicists. It also draws heavily on ideas explored in the Science of Music interdisciplinary module. This undergraduate module is taught in Warwick’s Institute for Advanced Teaching and Learning (IATL) and was developed by Gavin and colleagues in Physics. The structure is quite symmetrical, comprising five one-minute sections proceeding at a consistent120 beats per minute.
Sections 1 and 2 focus on violin, viola and bass guitar. They use a symmetrical scale, where the intervals between notes follow the pattern whole tone / semitone / whole tone / semitone / etc. This is called the “diminished scale” or “Messiaen’s second mode of limited transposition”. Phrases containing numbers of beats equal to factors of 60 are overlapped.
Section 3 continues with time-stretched violin and viola drones and bass guitar. Physicists strive for simplicity, and here the tonality reverts to an even simpler symmetrical scale, where every interval is a whole tone. This is called the “whole-tone scale” or “Messiaen’s first mode”.
Section 4 uses treated voices. The Department’s favourite equations are inscribed in the floor beneath the Foucault Pendulum at the main entrance, and these were recited in English (Max, undergraduate), German (Rudo, staff) and Mandarin (Zhuo, postgraduate), reflecting the international nature of the Department.
The American composer Alvin Lucier developed a method of sound treatment in the 1960s, close to the founding date of the Department, which we used here. This involves playing back recorded speech in a room and recording it. This recording is the played back in the same room, and recorded again. By making recordings-of-recordings, the original speech patterns devolve into resonances associated with the room. We used the Physics Teaching Laboratories, which have a nice bright echo and some bass resonances (coming from cavities formed by the lab benches, we think). Fragments of the original voices are mixed into the room resonance along with some vocoder, a voice treatment gaining popularity in the same decade.
Section 5 abandons conventional tuning and scales. The Western standard is 12-tone equal temperament, 12-TET, where an octave is spanned by semitone frequencies in multiples of the twelfth root of 2. This means that after 12 semitones, we have increased in frequency by a factor of 2, which is called an octave in the Western system or a “diapason” more generally. This is only a convention, though it does approximate well the key harmonic series intervals such as the fifth (1.5 times frequency) while allowing transposition between all keys. In this section, I use four-octave 60-TET tuning, where the diapason is four octaves (times 16 in frequency) and we have 60 intervals, so the nth scale frequency is given by
We have 15 rather than 12 intervals per octave, and a plot of the first octave is shown here:
The scale is chosen to start at A0 = 27.5 Hz. In this lowest octave, the alignment to 12-TET is good, except Western fourth and sixth notes of the major scale are “split” in 60-TET. Which scale degrees are split varies over the four octaves of the 60-TET. The octaves themselves agree exactly.
Tones for section 5 were synthesised using pure sine waves in MATLAB, and also approximated on (fretless) bass guitar. Three-note chords are built with notes close to those of the 12-TET C whole-half scale used in sections 1 and 2. I think they sound rather pleasant.
Spontaneous symmetry breaking is an important idea in physics, and so right at the end of section 5 the symmetrical scale and 60-TET rules are abandoned in favour of a nice ordinary chord!