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In choral hymn music, there is usually an "Amen" at the end that is conventionally written as a plagal IV-I cadence. Is there any historical reason of why it is written this way?

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    I think it's because the melody of the "amen" is traditionally to sing the tonic note on both syllables. This is also the last note of the hymn melody. So the hymn closes on the tonic chord with the tonic note in the melody, then the "A-" of "amen" is on that same note. You can't have a V-I cadence under those conditions, and IV-I is the only other candidate that is traditionally a common cadential formula. If someone wants to reopen this question, I'll post that as an answer. – phoog Aug 15 '20 at 23:37
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This answer is more on the "balance of probability" basis.Hard to answer this other than in a subjective way, but backed up with references.

Two parts to this

First, finality. A "perfect" cadence (V - I) sounds more final. A plagal cadence has a sense of finality but is gentler and not as strong, so more appropriate for signing off a psalm - but see later.

The finality aspect comes down again to further subjective associations for the dominant and subdominant keys related to the key you are in now (the "tonic").

Again, very subjective, and simplified, but the dominant key (so, for example G in relation to C) : if you move to that key there are suggestions of an increase of energy, drama, tension. A perfect cadence, has some of the sense of resolving back from the dominant key to the tonic, when you resolve back to the original key, there is a bigger sense of finality. Reference - Earlham College of Music, music theory course as an example of this "Dominant is the chord of dynamic stress"

Similarly - the subdominant key (F, for example in relation to C) : if you move to that, the suggestions are of a decrease in energy, tension etc - so when you resolve back from IV to I, there is also a sense of resolving back to where you started, but not as strong.

Reference - Earlham College of Music, music theory course "This gives the entire realm ruled over by the subdominant a more inward and mysterious quality."

Examples of cadences : BBC bitesize revision

Second - Context - traditions of psalm singing, and also, the tradition of "intoning" - if you imagine that the preceding psalm has been intoned, then a plagal cadence seems a more appropriate ending - a perfect cadence would sound too emphatic.

Reference for more on the practice of intoning, in various Christian traditions - see Religious music - one note for extended period

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