Music of the Spheres

1: The Science of Sound

In this section, we will examine certain physical characteristics of sound and will consider the ways in which sound is manifested in music. Beginning with the observations of Pythagoras, we will attempt to develop a basic understanding of the properties of sound waves, their use in harmonic and tonal-based systems of music composition, and the ways in which these phenomena are perceived.

This is a complex area, and one which has occupied many theorists over the centuries. There are many (sometimes, very lengthy) tracts on the finer points of tuning and temperament, the details of which lay outside the scope of this session. More importantly, we will attempt to explore the ‘relative’ nature of musical correspondences, questioning the notion that western musical pitch relations are, in essence, a natural construct.

This topic will therefore lay the foundation for a consideration and analysis of music encountered in subsequent sessions.

Class Documents

Lecture 1 – notes
Score Examples
Sound Examples
- Scolica Enchiriadis: Non nobis Domine
- Le Chant des Templiers - Antiphona: Crucem Sanctam
- Louis-François Dauprat: Minuetto
- Benjamin Britten: Prologue from Serenade for Tenor, Horn and Strings
- Kalmoukie: Khöömii
- Tuvan throat singing
- Fujara
- Hej, coze ma je po nom, po poli zelenom
- The following illustrate an auditory illusion known as circularity in pitch judgement, first noted by Roger Shepard, and later by Jean-Claude Risset (see also Diana Deutsch’s Illusions and Research examples.
  - Discrete :[audio:Shephard.mp3 |titles=Discrete Shephard Tone]
  - Continuous :[audio:Shephard-Risset.mp3 |titles=Continuous Shephard Tone]
  - Continuous Descent 2 :[audio:Shepard_Tones.mp3 |titles=Continuous Descent Shephard Tone]
  - Infinite Descent :[audio:DescenteInfinie.mp3 |titles=Infinite Descent Shephard Tone]
Text Examples – A complete translation of Plato’s Timaeus is available from the Internet Classics Archive, and the relevant part, in which the ratios of the Pythagorean scale are described – the Music of the Spheres – is available for download here.
Presentation Examples – A short presentation about Pythagoras and Music given by Paul Jackson and Alison Ainley (Head of Philosophy) at the Cambridge Festival of Ideas in 2008.

Audio

BBC Radio 4: In Our Time – The Music of the Spheres Melvyn Bragg and guests discuss the music of the spheres, the elegant and poetic idea that the revolution of the planets generates a celestial harmony of profound and transcendent beauty.

Video

The Perfect Fifth – from the French TV series Kaamelott, a fund, but probably accurate, depiction of the effect of medieval music making that ‘deviated’ from Pythagorean values,

Articles

Just Intonation Explained – Kyle Gann
Understanding Temperaments – Pierre Lewis
Pythagorean Tuning and Medieval Polyphony – Margo Schulter
Relating Tuning and Timbre – William Sethares

Internet Sites

The Whipple Museum of the History of Science in Cambridge has a significant collection of nineteenth century acoustical apparatus, in particular several examples from the famous Parisian instrument maker Rudolph Koenig.
The Online Interactive Harmonograph allows you to experiment with different ratio settings that produce graphic results.
This very useful Interval Calculator from Dolmetsch Online enables you to convert from pitch to frequency to cents. Here is another one.
The Research on Audiocommunication site, by Ernst Terhardt, contains many useful explanations of various aspects of the Perception of Auditory Pitch, and the Perception of Music Sound. You can download the whole site from here. Look particularly at the sections on Pitch perception, Definition of pitch, Spectral pitch, Virtual pitch, Absolute pitch, Affinity of tones, Octave equivalence, Musical consonance and Harmony.
Ancient Greek Music contains computer-generated examples of extant melodies, together with sound examples from reconstructed instruments.
The Tuning and Temperament Bibliography at the Huygens-Fokker Foundation Centre for Microtonal Music contains a huge list of texts and online articles relating to matters of tuning and temperament.
The Physics Classroom section on Sound Waves and Music, whilst intended for American high school physics students, provides a good introduction to the properties of musical sounds for non-physicists.

Music

Fujara contains information and examples from the Slovakian wind instrument that uses only notes of the Harmonic Series.

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