Chemistry for Everyone
Musical Chemistry: Integrating Chemistry and Music
W
A Nine-Part Series on Generating Music from Chemical Processes Mahadev Kumbar Department of Chemistry, Nassau Community College, Garden City, NY 11530;
[email protected] We live in a world that is not only tantalizingly beautiful, it is also filled with spine-tingling mysteries, pleasant surprises, and mind-boggling intrigues. Human nature includes curiosity and the impulse to understand the world around us: experts use the tools of their fields to explore the natural world. For example, chemists investigate the world in terms of atoms, molecules, and chemical reactions. One (perhaps surprising) aspect of the natural world is that each and every process in nature—chemical or otherwise—produces some kind of sound, whether audible (20 Hz–20 kHz) or nonaudible (20 kHz), characteristic of that process. Those sounds, I believe, are the music that is the universal language of the natural world. Music and chemistry—being integral parts of the natural world—have shared commonalities: they both use fundamental units as building blocks (chemical elements in chemistry and musical notes in music); they both have time dimensions that are meaningful; and both find expression in the language of mathematics. Few attempts have been made in the past to understand the relationship between music and macroscopic and microscopic processes, including atoms and elementary particles (1–3). No studies, as far as I know, relate music to chemical reactions, although the problem is of considerable interest to both chemists and musicians. Such investigations may lead to discovery of new classes of chemical reactions not yet seen. Therefore, in a ninepart series, I have explored the musical aspects of a variety of chemical reactions and also a few other chemical processes. Their titles are shown in List 1; detailed explanations for each, as well as sound files, are provided in the Supplemental Material.w Overview Music is an art; yet it is based on the science of mathematics. Chemistry is a science that is also describable in the language of mathematics. Hence, it is possible to express chemistry in the language of music. In part I, I have tried to answer this fundamental question: do chemical reactions make music?
List 1. Titles for Each in a Nine-Part Series Developed To Integrate Chemistry and Music
I: Can Chemical Reactions Make Music?
II: Fourier Analysis of First-Order Reaction Kinetics
III: Ordinary Chemical Reactions IV: Oscillating Chemical Reactions
V: Nuclear Decay Reactions
VI: Pharmacokinetic Reactions VII: Enzyme Kinetic Reactions VIII: Musical Properties of Electron Transition IX: Musical Properties of the Periodic Table
Techniques for Using Chemistry To Produce Sound To answer this question, I designed a process that starts with a chemical reaction and progresses through several steps that ultimately lead to a musical piece playable either on a computer or with a musical instrument. The steps include: describing the nature of the sounds; establishing a correspondence between the perceptual attributes and physical attributes of the sounds; and transforming the sounds via mathematics and principles of music theory into music that humans can play on musical instruments or computers with appropriate software. The various steps involved are shown in the following flow diagram: chemical reaction Fourier transform
frequency amplitude spectrum phase music theory music (computer music or instrumental music)
sound
The main quest here is to transform the time domain (chemical reaction) to the frequency domain (music) using the Fourier transformation. Once the physical attributes are extracted through this technique, they are then converted into perpetual attributes using music theory so that music can be produced. In that respect, this article describes a strategy to transform aspects of chemical reactions into music. Mathematics under It All Before music can be derived from chemical reactions (part I), the essential mathematical techniques and the methodology need to be developed. This is achieved in part II using the firstorder reaction as a model function: (1) A B The reaction rate can be measured either in terms of rate of disappearance of reactant (A) or rate of formation of product (B). The equation for the first kind is
Ct C0 e k1t
(2)
where Ct is the concentration of A at time t, C0 is the concentration of A at time zero, and k1 is the first-order rate constant. Similarly, the equation for the second kind can also be written.
www.JCE.DivCHED.org • Vol. 84 No. 12 December 2007 • Journal of Chemical Education 1933
Chemistry for Everyone
Our aim here is to extract the frequency content of eq 2. If a given function satisfies Dirichlet’s condition (4), it is guaranteed that it will have frequency content. However, except for oscillating chemical reactions, all chemical reactions are not periodic in nature and go to completion in a finite time. Therefore, a methodology is developed to make the first-order reaction equation periodic using Fourier series techniques as well as a protracting method. Furthermore, discrete Fourier transformation (DFT) is applied to selected model functions to extract frequency, amplitude, and phase values. The results are summarized in the form of spectral analysis. Transforming Chemical Characteristics To Produce Specific Aspects of Sound It is important to understand how C0 and k1 influence the music. It appears that C0 simply manipulates the amplitude (loudness) without altering the quality of music (timbre), although k1 seems to influence the timbre. The frequencies produced by these model functions fall in the mHz range, which is well below the threshold frequency of human hearing (20 Hz). In addition, the amplitudes are smaller in magnitudes than audible ones. For that reason, the frequency and amplitude are magnified to hear the sounds. Sound files generated using the Csound (5) computer program are included in the Supplemental Material.w Magnified frequencies are further transformed into musical notes using principles of music theory (6, 7) based on an equal-tempered scale. Observe that the derived musical notes are dependent upon the way the magnification is carried out; magnification using the factor of 10n (where n is an integer) is applied in such a way as to bring the lowest frequency just above the frequency of the lowest musical note (27.5 Hz) in an equal-tempered scale. Then the same magnification factor is applied to the remaining frequencies. The grand staff playable 250
Amplitude
200 150 100 50 0 0
5
10
15
Frequency Index, k Figure 1. Plot of amplitude values versus the frequency index for decomposition of N2O5 (g).
on the piano is generated with the help of Mozart software (8). (This software application and the Csound computer program are used, respectively, to build musical staves and sound files in all parts of these tutorials. See the Supplemental Material for further details.w) From Reaction to Spectra to Sound In part III of this series, 25 real ordinary first-order reactions (12 reactions for the rate of disappearance of reactants and 13 for the rate of formation of products) are examined using the methodology presented in part II. The experimental data are first fitted to first-order rate equations, and subsequently used in carrying out the DFT analysis. For example, the spectral analysis for the decomposition of N2O5 (g) is shown in Figure 1. The deduced frequencies for the reactions considered here also fall in the infrasound region (
