Other types of periods are defined in music theory books:
Expanded period - A period with three or more phrases. We can find many different combinations of phrases and cadences. What is important is that inconclusive cadences precede conclusive cadences. The double period we have previously described, can be considered an expanded period. But since it is very common, it has received a special name. Some possible combinations are described here (IC = inconclusive cadence, APC = authentic perfect cadence):
Modulating period - Is a period in which the second phrase modulates to a new key. A very common example is found in part A of pieces binary form in which the second phrase modulates to the dominant or relative major key. Some theory books prefer to use parallel or contrasting period terminology even if the period modulates.
Asymmetric period - Is a period in which the phrases have different number of measures.
Phrase group - All periods must have the question (inconclusive cadence) / answer (conclusive cadence) form. If this characteristic is not found we can call the phrases a phrase group.