# Musical Universe: selected research notes

Prepared 22 October 2026. This is a selected explanation of the documented work, with sources and numerical details for readers who want to look further.

## Listening to a relationship

Musical Universe uses sound and visual models to explore relationships in astronomical data. In the Uranus and Neptune study, orbital rates become tones. Their relationship comes close to an octave, but does not land exactly on it. Selected harmonics make that small difference audible as a slow pulse. The instrument generates these sounds from model values; they are not microphone recordings of planets.

The artistic work lies in making a relationship available to perception: choosing a listening range, building the instrument, designing the visual explanation and arranging the comparison. Scientific data and those creative choices can both remain visible.

## Music and physical pattern across scales

David Byrne's “Harmonia Mundi” chapter in *How Music Works* follows the history of connecting musical relationships to cosmic order and extends it toward hearing, culture and music as environment. It provides questions and historical context. The studies here use the physical model and sources relevant to each example.

On a stretched string, [resonant modes form a harmonic series](https://openstax.org/books/university-physics-volume-1/pages/16-6-standing-waves-and-resonance). In TRAPPIST-1, [observations and dynamical modelling support linked orbital resonances](https://arxiv.org/html/2010.01074v2). These give concrete relationships to compare across scales, with different physical mechanisms. Turning their cycles into sound makes some of those relationships available to listening. The choice of audible range, tone and visual form belongs to the instrument's design.

## What the Uranus and Neptune study does

The production uses a retained Solar System model and fixed reference rates. It applies the same multiplier to both orbital rates. This changes their pitch range while preserving the ratio between them. The demonstration then compares the original relationship with a deliberately adjusted, exact octave.

| Quantity | Retained production value |
| --- | ---: |
| Uranus orbital period | 84.016846 Julian years |
| Neptune orbital period | 164.79132 Julian years |
| Orbital-rate ratio, Uranus to Neptune | 1.9614080728524372 to 1 |
| Shared multiplier | 3,000,000 Hz per cycle/day |
| Uranus generated fundamental | 97.76077956314028 Hz |
| Neptune generated fundamental | 49.8421419368223 Hz |
| Neptune generated second harmonic | 99.6842838736446 Hz |
| Gap between that harmonic and the Uranus fundamental | 1.9235043105043275 Hz |
| Uranus adjustment in the authored comparison | +33.732334966833555 cents |
| Adjusted Uranus comparison tone | 99.6842838736446 Hz |

These are retained model and rendering values, not a statement of measurement accuracy to every displayed decimal. One Julian year is 365.25 days. The calculation takes the reciprocal of each period in days, then multiplies it by the shared scale. Equivalently, the mapping multiplies the physical rates in cycles per second by 259,200,000,000. The exact comparison changes the generated tone; it does not change the orbital data.

The sound includes eight synthesized harmonics, with coefficients proportional to harmonic number raised to −1.35, normalized once. Neptune's second harmonic and the Uranus fundamental produce the highlighted beating. Its approximately 1.92 pulses per second arise in this synthesis, rather than from acoustic waves interacting between the planets.

The visual sequence traverses retained positions from 2000–2030 at compressed speed while the audio uses fixed reference rates. The displayed span is not a complete orbit of either planet. Logarithmic radius guides are display guides rather than orbital paths. Headphones or speakers able to reproduce roughly 50–100 Hz make the listening comparison easier.

The model values and processing above come from the retained production report. JPL's [Approximate Positions of the Planets](https://ssd.jpl.nasa.gov/planets/approx_pos.html) explains one established approach to limited-accuracy planetary modeling. That page is background here; its element table is not presented as independent verification of these exact frozen period constants.

## What is established, and what is being explored

**Established orbital physics.** Gravity connects orbital distance, period and motion. NASA's [explanation of Kepler's laws](https://science.nasa.gov/solar-system/orbits-and-keplers-laws/) provides an accessible introduction. Some planetary systems also have dynamically supported resonant relationships. [Agol and colleagues' TRAPPIST-1 study](https://arxiv.org/html/2010.01074v2) derives a dynamical model from transit observations and examines its resonant behavior. A period ratio near simple integers, by itself, is not enough to establish resonance.

**The instrument's choices.** Moving rates into hearing, adding harmonics, assigning visual dimensions and creating an exact-octave reference are authored transformations. They can preserve particular relationships while changing others. In a time-history orbital view, a vertical time axis represents elapsed model time, not a planet's physical height.

**The larger inquiry.** Similar mathematical patterns can invite comparisons across scales. An audible resemblance does not by itself demonstrate a common physical mechanism or a universal musical tuning. Specific claims can be tested while the artistic inquiry remains open.

## A separate test of planetary spacing

A completed project study asked whether a selected exoplanet population was closer to seven fixed just-intonation interval classes than matched synthetic systems. The frozen primary selection contained 24 systems and 66 adjacent pairs, using NASA Exoplanet Archive catalog values. The archive's [PS and PSCompPars documentation](https://exoplanetarchive.ipac.caltech.edu/docs/API_PS_columns.html) explains the underlying table and parameter meanings; the result below belongs to the project's analysis, not to NASA.

The observed mean distance was 56.730999 cents. Its improvement over the matched null was −2.760896 cents, with a 95% host-bootstrap interval of −10.525392 to +4.720886 cents and a one-sided Monte Carlo p-value of 0.743163. In plain terms, the selected planets did not show the proposed closer alignment in this test. An independent implementation reached the same negative decision, with p = 0.747013.

This result did not support the study's specified 20-cent claim at the reported catalog values. Complete measurement-uncertainty propagation was unavailable for the full selected population, and the statistical comparison was not a planet-formation or survey-selection model. The result neither establishes a universal musical law nor rules out every possible musical relationship. It is separate from the Uranus–Neptune listening demonstration and from established orbital resonances.

## Sources and scope

The linked physics textbook and primary astronomy references explain the acoustic foundation, astronomical background and data semantics. The numerical rendering values and the separate negative study result are summarized from retained project reports. No new experiment was performed for these notes. Historical or artistic inspiration is not substituted for scientific evidence.