Here’s a heretical suggestion.
āyataka also occurs in the context of the recitation of dhamma in this fashion -
pañcime, bhikkhave, ādīnavā āyatakena gītassarena dhammaṃ gāyantassa. Attanāpi tasmiṃ sare sārajjati, parepi tasmiṃ sare sārajjanti, gahapatikāpi ujjhāyanti, sarakuttimpi nikāmayamānassa samādhissa bhaṅgo hoti, pacchimā janatā diṭṭhānugatiṃ āpajjati—ime kho, bhikkhave, pañca ādīnavā āyatakena gītassarena dhammaṃ gāyantassa. Na, bhikkhave, āyatakena gītassarena dhammo gāyitabbo. Yo gāyeyya, āpatti dukkaṭassā”ti.
Monks, there are these five disadvantages to one singing dhamma with a long-drawn plain-song sound: he is pleased with himself in regard to that sound, and others are pleased in regard to that sound, and housepeople look down upon, and while he is himself striving after accuracy in the sound there is an interruption in his concentration, and people coming after fall into the way of (wrong) views. These, monks, are the five disadvantages to one singing dhamma with a long-drawn plain-song sound. Monks, dhamma should not be sung with a long-drawn plain-song sound. Whoever should (so) sing it, there is an offence of wrong-doing. : Vin ii 108”
This Vinaya passage is also found in part in AN 5.209.
Although the CPD offers that āyataka means “long, prolonged, long-drawn (of a tone)”, we might perhaps get a better sense of what this entails in chanting by looking at one of the 5 drawbacks of such chanting. It is said that -
sarakuttimpi nikāmayamānassa samādhissa bhaṅgo hoti
while he is himself striving after accuracy in the sound there is an interruption in his concentration,
Could the sarakutti simply mean “melody”, taking sara as “flow” and kutti as the musical arrangement? Instead of the individual words, or clauses, or stock phrases being rendered clearly, these are forced artificially into rhythms in service of the melody or harmony. If so, the criticism of āyataka chanting is that intelligible language propositions are lost for the sake of the syllables and linguistic units conforming to a melodic structure, instead of retaining its linguistic comprehensibility. One of the first casualties would of course be the loss of distinction between short and long vowels (something that is attested to in verse); the other casualty would be the breaking up of a word, with parts being distributed to different parts of the musical structure.
If I’m correct in this, then perhaps āyataka means “un-punctuated”, not in a grammatical sense, but in a musical sense, in that the melody is not disturbed by the inconvenience of word forms taking precedence over the musical form.
Now, let’s see if we can interpret Ud 5.5’s na āyatakena as meaning “not unpunctuated”. Firstly, the anupubbas in the preceding section can all be equally read as “successive”, instead of gradual. This gives us -
Seyyathāpi, bhikkhave, mahāsamuddo anupubbaninno anupubbapoṇo anupubbapabbhāro, na āyatakeneva papāto
Monks, just as the ocean is of a successive inclination, is of a successive sloping, is of a successive slant, certainly without an āyataka drop
evamevaṃ kho, bhikkhave, imasmiṃ dhammavinaye anupubbasikkhā anupubbakiriyā anupubbapaṭipadā, na āyatakeneva aññāpaṭivedho.
So too in this Dhamma and Vinaya, there is a graduated training, a graduated doing, a graduated practice, with penetration to knowledge that is not āyataka.
I’ve chosen to translate the 3 anupubbas as such, as they appear to have been part of the existing Indian lexicon, being applied to the study of the Vedas, archery and accountancy : MN 107. See especially the illustration of this step-by-step education of an accountant in that sutta.
In light of the overall structure of the simile and the 3 anupubbas meaning “graduated” (instead of gradual), it looks to me that Ud 5.5 is saying that āyataka must mean the very opposite of anupubba. This comes closest to the reading of āyataka as “un-punctuated” in the musical sense.
What could the graduated training in the Dhamma-Vinaya be punctuated by? Stream Entry, Once-Return and Non-Return.
Alternatively, MN 107 suggests that the graduated training is the DN 2 model.