Oscilloscope
An oscilloscope is one of the most powerful diagnostic tools available for electronics. It allows you to view electrical signals as they change over time, making it possible to diagnose problems that cannot be detected with a voltmeter alone. By observing signal shape, voltage, timing, and noise, an oscilloscope can quickly reveal many electrical faults. It measures electronic signals and displays them graphically as waveforms. Various wave patterns mean different things, and by reviewing the wave pattern you can discern specific issues when things aren't working.
Oscilloscopes allow you to measure signal voltage, frequency, pulse width, rise and fall times, timing relationships between signals, and unwanted electrical noise. These characteristics are often critical to the proper operation of digital communications and controller electronics.
You can determining the frequency and amplitude ("height") of a signal, measured in volts or millivolts. These are critical elements to the successful operation of many electronic circuits and certainly those inside light controllers. If a signal isn't there, is too strong or isn't strong enough, or isn't operating at the right frequency it can easily cause a circuit to fail. An oscilloscope can help you uncover electrical noise in your circuit. When there's a lot of noise present, the noise sometimes covers the desired signal so it can't be understood by the electronics.
Oscilloscopes are measured by their speed, and the faster the oscilloscope, the more exact it can analyze signals. But a 10mhz scope would obviously have difficulty measuring a crystal that's running at 18.432mhz. A scope should generally have significantly greater bandwidth than the highest frequency you intend to analyze accurately. Oscilloscopes are specified by their analog bandwidth and sampling rate. For most DIY Christmas electronics, a 50 MHz to 100 MHz digital oscilloscope is more than adequate. Modern entry-level digital oscilloscopes from manufacturers such as Rigol, Siglent, and OWON are available at prices that make them practical for serious hobbyists, while used laboratory instruments remain an excellent value. Much faster scopes are certainly available but the price skyrockets rather quickly. You can sometimes find good buys on used oscilloscopes, too.
Oscilloscopes are also extremely useful when troubleshooting modern pixel controllers. They can verify pixel data timing, examine UART and RS-485 communication signals, observe clock signals, detect power supply ripple, and identify electrical noise that may interfere with reliable operation.
An example of how an oscilloscope can help in this hobby is by detecting the "zero cross signal" which is so important to being able to dim lights effectively using A/C current. The ZC is happens 120 times per second with normal 60hz electricity, and if the controller can't recognize it, dimming A/C lights gets very inconsistent. Here's what the ZC signal looks like on a 'scope:
