In the MONASTIC ANTIPHONAL, two psalm-tones are given for mode III, one with TI as the dominant, the other with DO, though it has been my experience that most monastic houses employ the TI dominant psalm-tone. It is so much more lovely and haunting. Too, one can see in many mode III pieces in both the ANTIPHONALE and the GRADUALE the tension between TI and DO, both sometimes fighting for "dominance" in the same piece. Of course mode VIII is the same, the TI dominant has pushed up to DO over the centuries, though one can clearly see in the mode VIII tracts, for example, sung at the Easter Vigil, that the melody rises to the TI and not the DO as it appears in the modern editions of Chant. There were interesting discussion at the time of the Vatican Commission as to whether the "modern" ear would accept the TI dominant, perhaps it is a pity that they thought it wouldn't.
With the advent of polyphony TIs were often raised to DOs and MIs were often raised to FAs to forestall the incidence augmented fourths between voices.
Because polyphony arrived late in southern Europe, the Beneventan and Aquitanian manuscripts usually retain the TIs and DOs that were replaced in other manuscripts.
The St. Gall and Laon neumes, which do not show exact pitches, do show the direction of melodic movement; and these often confirm the correctness of the Beneventan and/or Aquitanian readings.
The form of the third psalm tone employing TI as the tenor is clearly the older and is to be preferred, I think, because it reflects the essential character of the mode.
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