Hydrogen Balmer series.
When hydrogen glows, it emits exactly four bright lines in the visible spectrum — and a handful more in the near-ultraviolet. Each line is a single electron falling from a higher orbit down to the second one. The wavelengths are fixed by quantum mechanics; we use them to identify hydrogen in stars billions of light-years away. Eigentone takes those same wavelengths and divides them by 240, dropping them into the audible band.
An electron falls. A photon leaves. A note plays.
Pick a transition. The energy-level diagram shows the electron dropping from level n to n=2; the photon released has a wavelength set by the gap. The strip below is the real visible-light spectrum at that wavelength, and the readout is the audio frequency Eigentone produces.
Why hydrogen has stripes.
An electron orbiting a hydrogen nucleus can only sit in certain energy levels — labelled n = 1, 2, 3, …. It cannot exist between them. When an electron drops from a higher level to a lower one, the energy difference leaves the atom as a single photon, and the photon's color is set entirely by that energy gap.
The Balmer series is the family of transitions that all end on n = 2. The first four — 3→2, 4→2, 5→2, 6→2 — sit in the visible spectrum. They are the four bright lines you see when you put a hydrogen-discharge tube in front of a diffraction grating, and the ones astronomers measure to figure out what stars are made of.
A fingerprint, everywhere.
Hydrogen makes up about three-quarters of the visible matter in the universe. Wherever there's enough of it, glowing hot, you see exactly these wavelengths — Hα at 656 nm in the red, Hβ at 486 nm in the cyan, then Hγ, Hδ in the violet.
Plug those four numbers into the Rydberg formula and you can predict every other hydrogen line in any other series — Lyman in the UV, Paschen in the infrared. Same constant, same physics, whether the source is a discharge tube on a lab bench or a galaxy at high redshift.
The Rydberg formula.
Every Balmer wavelength comes from a single equation, written by Johannes Rydberg in 1888:
1 / λ = RH · ( 1/2² − 1/n² )
Here RH = 1.0967758 × 107 m−1 is the Rydberg constant for hydrogen — measured to fifteen decimal places, one of the most precisely-known numbers in physics. The integer n is the level the electron starts on (3, 4, 5…). The number 2 is fixed: every Balmer line ends on n = 2.
Convert wavelength to frequency with f = c/λ, and you have a frequency in hertz — but it's a hertz of visible light, hundreds of terahertz.
Light frequencies are absurd — Hα sits at 456 THz. Halve it forty times and you land in the audible band, with every ratio between lines preserved exactly.
= 2991.4 Hz · ( 1/4 − 1/n² )
Constants: c = 299 792 458 m/s, RH = 1.0967758 × 107 m−1. Audio Rydberg = c · RH ÷ 240.
What each white key plays.
Eigentone uses a linear ladder: each successive white key climbs to the next transition, instead of repeating the same notes per octave. Seven keys, seven Greek letters, seven photons.
Above Hη the higher transitions converge toward the series limit at 2991.4 / 4 = 747.85 Hz — the frequency a fully ionized hydrogen atom would emit on capture into n = 2.
Hear it played.
Hydrogen Balmer is in the free tier — load the demo, switch the frequency-set selector to "Hydrogen Balmer", and play the bottom seven white keys.