I've never heard the terms before:
Antecedent and consequent phrases
they seem to be elements of a period. It seems to be evident that I am not the only one ...
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This answer repeats a lot of what I wrote in... Where is the antecedent and consequent phrase in this melody?
My understanding is antecedent and consequent are the two parts of a period.
The two parts are defined by cadences.
The antecedent can end with a variety of cadences but not a perfect cadence in the main key/tonic. The typical thing is some kind of cadence on the dominant chord of the main key.
The consequent ends on a perfect cadence in the main key.
My understanding of the theory is a period sets up tension in the antecedent by cadencing somewhere that isn't the tonic then later resolves that tension in the consequent by a cadence confirming the tonic. The idea is to create structural dissonance.
In the case of a simple period the structural dissonance is resolved quickly because the second phrase - the consequent - goes to a cadence in the tonic. You can compare that to a sonata structure which also starts with a kind of antecedent, a cadence on the dominant, but then the structural dissonance is hugely elaborated with other phrases cadencing in other keys before finally recapitulating with a final cadence on the tonic.
Periods are found through out classical music. Here is one (Mozart K.331)...
...mm. 1-4 are the antecedent and end on a half cadence
I6/4 V while mm. 5-8 are the consequent and end on a perfect cadence
I6/4 V7 I.
This particular melody exhibits parallel properties meaning that the antecedent and consequent use the same basic melody with slight variation. While many periods are parallel in shape the parallel shape should not be confused with period structure. The two-part antecedent/consequent structure of a period is defined by the cadences ending the phrases!
A period is one type of theme, like the sentence, common to the Classical style.
The period is generally eight measures long and contains two four-measure phrases, called antecedent and consequent.
2 fine examples are posted in this link: