There was and still is quite an amount of speculation as to what the seer of Asya Vamiya Sukta (diirghatamas. His name itself is interesting!) meant by the levels of speech. There are Vedic classifications and Tantric classifications about levels of Vak. Since Shri T.V. Kapali Sastry is a direct disciple of Shri Aurobindo, who is considered to be one of the modern day seers who could decipher some of the meaning of Rig Veda mantras, the interpretation by Shri T.V. Kapali Sastry becomes significant. I am quoting the who appendix for reference.
As a side note Prof. Abinash Chandra Bose notes in chapter 5 titled "Raja Yoga" of his book the following
But in describing these profound experiences, the Vedic sage expresses his sense of the inadequacy of language. The Veda speaks of four grades of speech known to wise men of divine knowledge: "three of these kept in secret make no motion; people speak only the fourth grade of speech" [RV 1.164.45]. So language as popularly spoken can give utterance only to a part of what the sage has realized; the rest has to be in silence. "For the finite the eloquent man, for the infinite, the mute", says the Yajurveda [YV. VS. 30.19]. The silence is broken symbolic language which expresses a little and suggests much more. Symbolic language does not yield to simple logical meaning, it goes beyond logic to hint at transcendental significance.
Further, in p.297, he does the following translation for 1.164.45
RV 1.164.45 Rishi Diirghatamas, the son of Ucatthya, Metre Trishtubh.
Four are the grades of speech that have been measured;
men of divine knowledge who are wise know them.
Three of these kept in secret make no motion,
people speak only the fourth grade of speech.
RV 4.3.16 Rishi Vamadeva, the son of Gothama, Metre Trishtubh.
To thee who knowest, to thee. O Disposer!
all these musical and secret words,
these speeches of a seer for a seer
I, a poet, have uttered in hymns and praises.
Here is the translation from Shri Kapali Sastry's book.
Rig Veda 1.164.46 Catvari vak parimita padani tani vidur brahmana ye manishinah
Guha trini nihita nengayanti turiyam vaco manusha vadanti
Vak (1st case for 6th case)
vacah krtsayah = of the entire speech
padani = steps
catwari = four
parimita padani = are measured out. (Tr. Speech in its entirety is measured out in four steps.)
Loke = in the world
ya vak asti = whatever speech is there
sa = that
caturvidha = into four kinds
vibhakta = divided
iti arthah = this is the meaning (Tr. whatever speech there is in this world is divided into four classes)
tani padani = these steps
brahmanah vedavidah = Brahmanas who know the Veda
ye manishinah = manas inishinah = who are the movers of the mind
medhavinah = men of understanding
viduh janati = know (Tr. these steps Brahmanas who know the Veda and have understanding know).
tesham madhye = of them (the aforesaid division of steps),
trini = three
guha (seventh case is dropped)
guhyam = in the secrecy
nihita sthapitani = established
na ingayanti na cestante = do not move
na prakasante = do not come to light
iti arthah = this is the meaning (Tr. Three of the four divisions of steps, established in the secrecy, are not manifested.)
Vacah = of the speech
turiyam = the fourth
padam = step
manushah = men
ajnah those = who do not know
tad-jnah ca = those who know that
vadanti = speak
vyaktam uccarati = distinctly pronounce
vyavaharanti use (in their dealings) (Tr. The unlearned as well as the wise speak the fourth step of the speech in their dealings).
kani tani catwari ityatra bahavah svasvamantanurodhena bahudha varnayanti in regard to the question what are these four, many (schools) describe in many ways each according the view of the school.
sarvavaidikavagjalasaya of the collection of all the Vedic words
sangrahrupa comprehensive or inclusive or summary forms
bhuradayah Bhuh etc.
tisro vyavratayah the 3 vyahritis (sacred utterances) (pranavah eka = one Om, iti = thus vedatrayasaratvattasam those Vyahritis being the essence of the three Vedas)
vyahrtinameva sarasamggrahbhutatvat (Pranava being)
the summary substance of those Vyahritis, containing the letter A etc. (AUM) - for this reason
sapranavasuvyahritisu = in the Vyahritis along with the Pranava
sarva vak = all speech
parimita = is measured out
iti = thus
kecana vadavadino = some Vedists
vadanti = say (Tr. Some Vedists say that all speech is measured out in the Vyahritis which Pranava is constituted of the letter A etc. and which itself is the summary substance of the three Vyahritis which again are the Bhuh. etc. the comprehensive and all inclusive forms of all the collections of the Vedic words. This the three Vyahritis and one Pranava make up the four in which all speech is measured out).
apare vyakaranamatanusarino namakhyatopasarganipata-bhedena Others, followers of the school of grammarians say (that the four consist of) the division of naama, akhyata, uparasga and nipata.
kriyapradhanamakhyatam That is the verb akhyata in which action is prevalent.
Dravyapradhanam nama Nama (noun) is that in which substance is predominant.
Pragupasrjyata akhyatapadasyetyuparasargah pradih
The Upasaraga pra etc. is so called because it is placed before a verbal word.
Uccavavesvartheshu niparanannipatah api tu ca ityadih
Nipata, a particle
api tu ca etc. is it so called because it falls down upon (words of) uneven meanings.
Etesveva sarva vakparimita iti (vadanti) In these four alone all speech is measured out -- so they say:
akhandayah krtsnaya vacah caturvidha vyakrtattvat because the all speech which is indivisible is separated or analyzed into four divisions.
Vagvaiparacyavyakrtavadat tamindromadhyatovakramya vyakarot tasmadiyam vyakrta vagudyata iti sruteh (This is the passage from Taittiriya Samhita quoted by Sayana to support the statement of fourfold differentiation of the Speech which was beyond and undifferentiated.)
Speech verily was beyond and undifferentiated. Indra stepped down into her and spoke, therefore she became differentiated, and this speech is spoken (This is quoted part of Shruti).
Anye tu yajnikah mantrah kalpo brahmanam caturthi laukiki Others, votaries of Sacrifice (say) Mantra, Kalpa, Brahman and the fourth ordinary speech in the world.
Yajnikaih samamnatonustheyathaprakasako vedabhago mantrah The Mantras are that division of the Veda that is recited which illumines the meaning of what is performed or observed.
Mantravidhanapratipadako vedabhaga iti mantrah kalpotah urdhvamityadinoktah kalpah (this is a quotation of Sayana from the Kalpa Literature.) The division of the Veda which teaches the use of mantras, the Kalpas etc. has been declared (in the Sashtra)
Mantratatparyarthaprakasako vedabhago brahmanam The Brahmana is the portion of the Veda which throws light on the meaning of the purport of the mantras.
Bhogavishaya gamanayetyadirupa vyvahariki The speech of which worldly enjoyment such as 'bring the cow' etc. is the object is
vyavahariki the speech of the common dealings in the world.
Esveva sarva vak niyamiteti yajnikah The votaries of Sacrifice hold that in these (four) all speech is (contained), 'measured out'.
Rgyajuhsamanicaturdhi vyavharikiti nairuktah Those of Nirukta school say that the rik. yajus, saman and the fourth is the common speech for dealings in the world.
Sarpanam vagvayasam ksudrasarispasya ca caturthi vyavaharikityaitihasikah The followers of legendary tradition hold the speech of serpents, of birds, of vile reptiles, and the fourth is the speech in dealings of the world.
pasusu tunavesu mrgesu atmani ca iti atmavadinah The atmavadins (votaries of Atman) say: in the animals, in musical instruments such a flute, in the beasts and in the soul, the four fold speech is contained.
Apare mantrkah parkarantarena pratipadanti para pasyanti madhyama vaikhariti catvariti Others of school of Mantra (Tantra) teach in a different way: the four are Para, Pashyanti, Madhyama, Vaikhari according to them.
Ekaiva nadatmika vak muladharadudita sati para ityucyate The speech, only one in the form of sound, rising from the centre of the solar plexus is called Para. Being subtle and not demonstrable, the same sound entering the heart is called Pashyanti because of Yogins being able to perceive it.
Saiva buddhim gata vivaksam prapta madhyama ityucyate The same entering the buddhi, understanding, and desiring to express (to speak) is called Madhyama.
Madhye hradayakhya udiyamanatvat madhamayahSame in the centre or middle called Hridaya the Madhyama rises.
Atha yada saiva vaktre sthita talvosthadivyaparena bahirnirgacchati tada vaikhari ityuchyate Then when the same Nada comes out for expression through the exertion of the lips, teeth etc., it is called Vaikhari.
Evam catvari vacah padani parimitaniThus are the four steps of Speech measured out.
Manisinah manasah svaminah svadhinamanaska brahmana vacyasya sabdabrahmani dhigantaro yoginah paradicatvari padani viduh jananti Wise men, masters of mind, with mind under their own control, Brahmans, knowers of Shabdabrahman to be expressed, yogins, know the steps to be four, Para etc.
Tesu madnye trini paradini guha nihitani hrdayatarvartittvat Of these, three steps Para etc. are placed in the secrecy because of their being inside the heart.
Turiyam tu padam vaikharisanjanakam manusyah sarve vadantiBut the fourth step, Vaikhari by name, all men speak.
Vyakaranaprasiddhanamakhyatadipakse manishino brahmanh prakrtipratyayadivibhagajna vagyogavidastani padani jananti On the side of Nama, Akhyata etc., celebrated in Grammar, the wise Brahmans, knowers of the divisions of base suffix etc., knowers of word arrangement (speech set-up) know those steps.
Avgyogavidah pamara vaco vangmayasya turiyam caturvidham bhagam vadanti, vyavaharanti Those who do not know the arrangement of speech i.e., the unlearned, speak the fourth part of speech in their dealings.
Arthaprakasanaya prayunjate They apply it (knowledge) for making the meaning clear.
Ayam mantro nirukte vyakhyatah This mantra is explained in Nirukha.
So'trapranusandheyah Here also that must be calmly considered.
[Quotation from Nirukta 13.9.]
Athapi brahmanam bhavatiThen there is the brahmana text (in this context),
sa vai vak srsta caturdha vyabhavatthat very speech released became manifested into four,
esveva lokesu trini pasusu turiyam in these (three worlds) there are three steps of speech and the fourth is in the creatures.
yo prthivyam sagnau sa rathantare That which is in the Earth that is in Agni that is in Rathanthara (name of a Saman).
Yantarikshe sa vayau sa vamadevyaThat which is in the mid-air region, that is in the Vayu, that is in the Vamadevya (Saman).
Ya divi saditye sa brhati sa stanayitnauWhat is in the Heaven, that is in the Aditya, that is in Brihat (Saman), that is in the Lightning.
Atha pasusuThen in the creatures,
then what ever speech remains transcended that was placed in the Brahmanas.
Tasyamadbrahmana ubhayim vacam vadanti ya ca devanam ya ca manishayanamiti Therefore the Brahmanas speak the twofold speech -- that which is the speech of Devas and that which is the speech of the men.
[Transliteration errors: mine.]