We have heard the Te Deum sung on many occasions. The Liber usualis contains a solemn tone (begins on p. 1832 in № 801) and a simple tone (begins on p. 1834 in № 801), and these lift our soul to give thanks to God. There is, however, a Roman tone for the Te Deum, which we fondly call its ‘more solemn tone’. (It is actually listed as iuxta morem Romanum, and its placement in the 1908 Vatican edition of the Graduale Romanum, right after the tonus sollemnis, suggests that it is to be understood as the tonus sollemnis iuxta morem Romanum.) For many of us who had heard this tone first, prior to hearing the solemn tone or the simple tone, the latter tones understandably sounded like a reduction of the Roman tone, quoting bits and pieces of its surprisingly more tuneful melody.
Today is another occasion to hear or sing the Te Deum. If a blessing of Epiphany water is happening somewhere near you, that is. The notation for the Roman tone of the Te Deum is buried in the latter part of the Graduale Romanum. Check it (begins on p. 147* in № 696; p. 118* in the 1908 Vatican edition), and, if you are a chorister or cantor, sing it today. (For us Filipinos, this is rather opportune, considering that an alternating chant and fauxbourdon version of the Te Deum appearing in a collection of sacred music from colonial Intramuros uses the Roman tone for the chant.) Here (the original website carrying this recording is inaccessible as of this posting) is how it was sung by the Benedictine monks of São Paulo. For comparison, listen to the solemn tone and to the simple tone.
Ut in omnibus laudetur Dominus.