Abstract
In the work PRISM the sonification of atoms is reimagined through my current research in live coding, algorithmic composition and generative sound. Atoms are instantiated live through code and their corresponding emission spectra of visible light are used as overtone series for sound synthesis. This is done by translating the wavelengths of the light spectrum to an audible range by dropping the frequency by many octaves. The interference patterns that emerge by combining all the the frequencies (in most cases tens to hundreds) result in various rhythmical and harmonic/disharmonic sounds. During the performance different emission spectra are explored and used in a live coded manner. The rhythmic and harmonic structures are combined with an experimental mix of electronic music. The visuals complement the performance by displaying the spectra of visible light as a barcode of the elements in the universe, with their intensities reacting in realtime to their own sound.
This piece was selected and commissioned by the Beyond Quantum Music project and performed at Center for Cultural Decontamination (CZKD) in Belgrade, Serbia.
Method
The research for this performance started with the sonification of the absorption and emission spectra [1] of a Hydrogen-like atom. When an electron is excited by absorbing a photon upon collision the electron moves to a higher energy level in the orbital shell [2]. When the electron falls back to a lower orbital the energy-difference between the two orbitals is released in the form a photon particle/wave. The color that appears is determined by the photon’s wavelength (and therefore frequency). This frequency is determined by the energy calculated with the formula:
Ephoton = hv
where Ephoton is the energy, v is the frequency and h is Planck’s constant [3]. The wavelength is determined by
λ = c / v
where c is the speed of light [4] in vacuum. Therefore we can write the relationship between the wavelength and the energy as
λ = hc / E
The energy needed to separate an electron from its current orbit in a Hydrogen-like atom is defined as
E = 13.6eV / n2
where n is the orbital number [5][6][7]. We can see that an electron in a higher orbit is therefore less bounded to the nucleus (the core of the atom). When an electron falls back the difference in energy between the orbits results in the amount of energy that can be observed as light. For example an electron dropping from orbit n = 3 to n = 2 gives of a photon with energy
En = 13.6eV / 22 – 13.6eV / 32 = 1.89eV
Only the absorption of these specific differences in energy to excite an electron to a whole orbital number is possible. Therefore also only the emission of these specific amounts of energy is possible, resulting in specific colors of light emitted for every atom differently. We can convert this emitted energy to a wavelength by
λphoton = hc / 1.89eV = 656nm
This wavelength of 656nm corresponds with the color red [8][9] and can be observed with spectroscopy.
Alternatively we can convert the wavelength of the visible light to the corresponding frequency. This is calculated by dividing the speed of light c by the wavelength in meters:
fphoton = c / 656×10-9 = 457×10-12Hz
is about 457 THz (TeraHertz). Even though the wavelength of light is an electromagnetic wave – which is not at all the same as air pressure waves that we can perceive as sound – with a bit of artistic freedom and creativity we can still approach it as if. In that case we drop the THz lightwave about 39 to 43 octaves, meaning we half the frequency over and over, in a total of about 40 times, or
faudible = fphoton / 240
to get frequencies of the same pitchclass in the audible range [10]. So even tho the frequency is not the exact frequency of the lightwave, the (dis)harmonic relationship between the frequencies remains intact, resulting in a chord of a few (or sometimes hundreds) of audible frequencies. For example the 656 nm wavelength of red could be an audible frequency in the following three octaves:
c / 656×10-9 • 2-40 = 415.6Hz
c / 656×10-9 • 2-41 = 207.8Hz
c / 656×10-9 • 2-42 = 103.9Hz
In order to use the emission spectra for all of the atoms in the Periodic Table [11] the Atomic Spectra Database was used from the NIST (National Institute of Standards and Technology) [12]. This database provides access and search capability for evaluated data on atomic energy levels, wavelengths, and transition probabilities. Via custom code it was possible to scrape the website for the spectral lines (filtered in the range of the visible light spectrum, 380nm to 780nm) and intensities of all the atoms in the Periodic Table and store those in a json database for quick acces in live performance situations.
The intensities were normalized on a per atom basis by dividing all the intensities of the emission spectrum by the highest intensity, resulting in a list of intensities between 0 and 1. These normalized values were considered as the amplitude value for the frequency of every line. A threshold of -24dB (converted to an amplitude value with the formula a = 10(dB/20)) was applied to remove all lines with a lower intensity. The threshold was chosen in a way that preserved most of the harmonic relationships between frequencies, but also reduced computing drastically, because by removing the less intense lines most atoms stayed below 200 lines (which would result in 200 sinewave oscillators).
For the visual representation in the piece the actual emission spectra were used. Creating a direct connection between the audible frequencies and the perceived colors.
Composition
During the process of making the composition for the live performance I’ve listened to all the emission spectra of the atoms 0 – 86 and described their spectral qualities both visually and sonically. A few atoms already caught my attention during the first listening session and during a second pass I marked all the atoms that I’ve found specifically interesting. Interesting can mean many things, for example the frequencies combined into an interesting beating pattern, or the frequencies combined harmonically pleasing. Or they were spread very evenly, or very focussed on one specific range of the spectrum. From the selected list of atoms I created a composition where the atoms can complement eachother by for example combining an atom that predominantly has lines in the lower wavelengths (towards red) with an atom that has a higher characteristic (towards blue/violet). Below you can find a list of short captures of the sound of the spectra of atoms during the listening process. The video initially shows a white line that depicts the overall amplitude in time of the composite sound, then the line expands into the spectrum depicting the individual lines with their corresponding color and amplitude.
Bibliography
[1] https://en.wikipedia.org/wiki/Emission_spectrum
[2] https://en.wikipedia.org/wiki/Atomic_orbital
[3] https://en.wikipedia.org/wiki/Planck_constant
[4] https://en.wikipedia.org/wiki/Speed_of_light
[5] https://www.ifa.hawaii.edu/~barnes/ASTR110L_F05/spectralab.html
[6] https://en.wikipedia.org/wiki/Energy_level
[7] https://en.wikipedia.org/wiki/Principal_quantum_number
[8] https://en.wikipedia.org/wiki/Light
[9] https://en.wikipedia.org/wiki/Frequency
[10] https://en.wikipedia.org/wiki/Octave
[11] https://en.wikipedia.org/wiki/Periodic_table
[12] https://www.nist.gov/pml/atomic-spectra-database
[13] https://en.wikipedia.org/wiki/Balmer_series
