間隔 and 周期: a gap and a complete repeating cycle
Use a lamp alternating between on and off to distinguish the gap between changes from the time needed to return to the same phase.
Identifying both ends of a gap
A time 間隔, read かんかく, is the gap between specified events. 点灯から消灯までの間隔は一秒です。 says that the gap from switching on to switching off is one second.
点灯と次の点灯の間隔を測ります。 says that the gap from one switch-on to the next will be measured. Identify both endpoints first.
Returning to the same phase
周期, read しゅうき, is the length of a complete repeating cycle. 点灯から次の点灯までが一周期です。 defines one cycle as the time from one switch-on to the next.
In this example the lamp starts on, switches off after one second, and switches on after another second. The complete on-to-on cycle therefore lasts two seconds.
When a gap equals a cycle
一秒ごとに点灯と消灯を切り替えます。 says that the lamp alternates between on and off every second. A single change and a return to the original phase take different lengths of time.
Measuring 次の点灯までの間隔 gives one complete cycle in this example. The word 間隔 does not always identify a shorter duration than 周期.
If an initially lit lamp switches off after one second and on after another second, is its cycle one second?
Show the answer and why
No. In this example returning to the on phase takes two seconds. One second is the gap between successive changes of state.