"Organ descant" is a misnomer which I hear or read all too often, but I think you mean an alternate harmonization or accompaniment that is more florid or elaborate than the hymnal harmonization.
The term "descant" specifically (in the context of hymns as well as other compositions) refers to a countermelody to the main melody, usually (although not always) pitched higher than the main melody.
The descant notes on "All glo-ry, laud, and ho-nor to thee, Re-" are just the alto part transposed up an octave in a standard harmonization. After that, the part skips up to an elaboration of the tenor part, up two octaves. This is a pretty standard way of forging (fakebooking?) a descant from inner voices. Hancock's choir does not sing a descant on the verses.
Yes, I just put this together to avoid explaining to the choir how to do that and how to mark it in their scores...the hymn has already caused me enough grief due to the need to Xerox parts from one hymnal and edit the text edits in there to agree with the pew hymnals, whose choral book lacks several verses &c.
Transposing inner parts into a descant may be a common practice where a composed one is not available, but I have always shunned doing this because of the all-to-transparent irritance of doubled voices and objectionable parallel octaves and such. It is easy enough to compose one's own if one isn't at hand. The difficulty here is in composing one that is not overly elaborate! I always end up with something really challenging - like those of Willcocks or Ledger. Choirs love the result, though. There are many published booklets of descants for a variety of hymn tunes available from Oxford and others.
I definitely prefer descants that act as rhythmic counterpoint: ties over measure bars, discreet syncopation and what have you. Because most strophic harmonizations that are commonly used lack that*, I find doubling an inner voice to be weak tea, in addition to the reasons MJO cites. (Doubling of voices is, however, canonical practice for American shape-note hymnody.)
* Unless you're using, say, one of JS Bach's more interesting chorale harmonizations... A particularly choice descant can be found at the 2:21 mark here (used by a trumpet, but illustrative of a more spectacular descant genre):
I didn't actually mean doubling another's part, octaves above. I meant singing that part as a descant, while the voice from which it was taken sings either the melody or another voice part.
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