In Tier 0 you compared the Sun, a pendulum, and a household clock by observation and notebook. In Tier 1 you compare electronic oscillators — first by ear, then with software, then with progressively more precise hardware. The comparison is first directly heard, then conditionally inferred beyond direct perception, and finally measured by instrumented conversion. The order is intentional.
Tier 1.0 — Two Speakers, One Beat
This is the acoustic entry point. The student hears the comparison directly — the same beat-note physics that every subsequent exercise measures digitally. Exercise 1.0 requires no laptop. The ear is the measurement instrument.
Tier 1A — Browser Oscillator Lab
Beat Lab runs entirely in the browser. In internal mode, the browser generates two tones and you measure the beat. In microphone mode, the browser analyses audio from your device mic — including the speakers from Exercise 1.0. The software confirms and extends what your ear detected.
Tier 1B / 1C — Hardware Oscillator Comparison
The hardware tier uses two off-the-shelf modules: an XR2206 function generator kit (~€4, the free-running oscillator) and a reference source. In Tier 1B (~€17 total with speakers), the reference is an AD9833 DDS module. In Tier 1C (~€185 total), the reference is a Leo Bodnar LBE-1420 GPS-disciplined oscillator — traceable to atomic time. Both signals drive speakers (heard) and feed into the sound card (measured).
See the hardware specification for the bill of materials and exercise sequence.
Tier 1C Field Deployment Kit
For Tier 1C, a complete field-deployment specification is available: the Starter Kit specifies three devices (GPSDO, breadboard VCXO, oscilloscope with DDS) that form a minimal three-clock network. It includes connector guidance (SMA/BNC), a solar power bank for locations with unreliable mains, and full cost summaries including shipping and customs estimates.
Environmental Characterisation
Before connecting clock instruments, it is valuable to characterise the local environment — temperature, magnetic field, atmospheric pressure — to understand the noise landscape in which the clocks will operate. The Local Data Collection Guide shows how to do this using open-access weather databases (NOAA ISD, ERA5) and smartphone sensors (via the free phyphox app). It includes a worked example translating magnetic field fluctuations into clock frequency shifts, and a noise-budget summary table template.
This step requires no specialised equipment and can run in parallel with theoretical work. It is particularly useful for deployments in locations without established laboratory infrastructure.
Three Frequency Regimes
The same kit supports three frequency regimes, each teaching something the others cannot:
Regime 1 — Acoustic (440 Hz): Both oscillators and the beat are audible. The ear is the detector. This is Exercises 1.0 and 1.1.
Regime 2 — Ultrasonic (25–40 kHz, provisional): The oscillators are above hearing, but the beat may be audible through nonlinear mixing in the speaker or microphone. The comparison separates from the source. Status: prototype-gated.
Regime 3 — RF (10 MHz, Tier 1C advanced): The oscillators require a physical mixer to bring the beat down to audio band. This is how real frequency metrology works. Requires GPSDO + crystal oscillator module.
For the full concept, see the speaker driver and three-regime concept note.
Conceptual Bridge
In Tier 0, the pendulum is free-running, the mechanical clock is regulated, and the Sun is the reference. In Tier 1, the VCO is free-running, the DDS is programmable, and the GPSDO is disciplined to an atomic standard via satellite. Same logic, higher bandwidth, electronic rather than mechanical.
Going Further
After Tier 1, continue to Tier 2: Simulate — numerical clock networks with full statistical analysis.