Ok, this might be a noob question, but as I'm looking through the Requiem Mass, I find the Dies Irae, of course. I notice it's listed as being mode I, with corresponding DO clef. However, is this chant not mode II? If the DO clef is changed to a FA clef, which is standard for mode II, the entire chant can still be sung as notated and fits better with the range of the chant, which is from low LA to high DO, with final on RE, as would be expected for mode II (well, the presence of the low LA really clues me in for this, and the fact that the range fits better for a LA to LA description, with a slightly extended upper range). Am I correct in my analysis of this? I suspect not, but I am seeking enlightenment from those of you with more experience with these types of things.
As you noticed, this melody's range is too wide to fit tidily into either the relevant authentic (mode I) or plagal (mode II) mode. In such cases, the melody is typically assigned to the authentic mode of the pair. Of course, since you don't need to choose a psalm tone to go with this chant, it doesn't particularly matter whether it's mode I or II. (Other examples of wide-ranging melodies include the sequences Victimae paschali and Lauda Sion and the Kyries Rex genitor and Cum iubilo.)
Also, the rule of thumb as I remember it is that it is "normal" to exceed the range of the mode by one note; the Dies irae on the other hand, besides hitting Do frequently, reaches high Re in the vs. Judicandus near the end.
Also, it does use "la" a fair bit, as mode 1 should.
A "normal"(?) Mode I chant usually will have an ambitus from Re to Re an octave higher (the Mode I "scale") and not infrequently will descend to the Do below the lower Re (the "subfinal") which is often seen in final cadential formulae. This is also characteristic of Mode 3 & 7 chants, namely to have an ambitus that ranges from one note below the final (the "subfinal" on Re & Fa, respectively) to an octave above the final (Mi & Sol, respectively).
A stanza by stanza examination of the "Dies irae" suggests that, while some stanzas (notably the 1st) have the characteristics of Mode II (ambitus descending to La below Do, with Fa as a "dominant" tone), the majority of stanzas adhere more closely to typical Mode I chat in terms of ambitus (already described above) and "dominant" on La.
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