This article concerns the singing of the Ordinary Form of the Mass, but its main point pertains also to the desirability of sung Masses in the Extraordinary Form.
The Second Vatican Council expressly linked its teaching to that of St. Pius X when it taught: “Liturgical worship is given a more noble form when the divine offices are celebrated solemnly in song, with the assistance of sacred ministers and the active participation of the people” (SC 113). The implication is that Catholics should aspire to give worship a more noble form by celebrating it in song — in other words, that the sung Mass should once more attain prominence. This implication was drawn out clearly by the Sacred Congregation of Rites just a few years later, in the Instruction Musicam Sacram (March 5, 1967), which had its 50th anniversary last week:
Liturgical worship is given a more noble form when it is celebrated in song, with the ministers of each degree fulfilling their ministry and the people participating in it. Indeed, through this form, prayer is expressed in a more attractive way, the mystery of the liturgy, with its hierarchical and community nature, is more openly shown, the unity of hearts is more profoundly achieved by the union of voices, minds are more easily raised to heavenly things by the beauty of the sacred rites, and the whole celebration more clearly prefigures that heavenly liturgy which is enacted in the holy city of Jerusalem. Pastors of souls will therefore do all they can to achieve this form of celebration. (MS 5)
In other words, the chanted celebration of Mass should be a rule, not an exception. The same document, which is still the most authoritative Vatican document on music since the time of the Council, states: “For the celebration of the Eucharist with the people, especially on Sundays and feast days, a form of sung Mass (Missa in cantu) is to be preferred as much as possible, even several times on the same day” (MS 27).
As if to underline that singing is not an add-on but part of the inherent structure of the Mass, the Instruction Musicam Sacram goes on to establish, perhaps surprisingly, three degrees of musical participation for Mass (see nn. 28-31), such that one should begin by singing what pertains to the first degree, then add that which pertains to the second, and finally, move on to the third, according to the capabilities of the congregation and choir.
One can see that the first degree depends on the priest’s chanting his parts given in the Missal, which, in the Church’s tradition, have always been in a simple form of chant, involving a few notes of melody, and may even be sung recto tono in a case of necessity. These prayers and dialogues are the most fundamental elements of the liturgy to be chanted. The second degree adds beauty and solemnity by giving the choir and faithful more scope for singing the Ordinary of the Mass, which brings out the full richness of the prayers themselves. The third degree completes the musical elevation of the liturgy by ensuring that its meditative texts (antiphons and lessons) are sung.
The singing of the Mass is not something rare, only to be done on feasts, but something normal, flowing from the very nature of liturgy. We can see this in the fact that the Church’s tradition provides chants for every day of the year, every occasion. As Dom Mark Kirby explains:
It is too obvious to be denied that a celebration sung in the Gregorian manner is more solemn than a celebration which is merely recited; but this statement is especially true in the modern perspective of a celebration which is habitually recited. The ancients had provided melodies for the most modest celebrations of the liturgical year, and these melodies were no less carefully worked out than those of the great feasts. For them the chant was, before all else, a means of giving to liturgical prayer a fullness of religious and contemplative value, whatever might be the solemnity of the day. Such should also be our sole preoccupation in singing. As long as people look upon the Gregorian chant solely as a means of solemnising the celebration, there will be the danger of making it deviate from its true path, which is more interior.
Dr. Jennifer Donelson begins her classes on liturgical chant with “Top Ten Reasons to Sing the Mass”:
These points are borne out in the section of the General Instruction of the Roman Missal (2nd ed., 2011) devoted to “The Importance of Singing”:
39. The Christian faithful who come together as one in expectation of the Lord’s coming are instructed by the Apostle Paul to sing together psalms, hymns, and spiritual canticles (cf. Col 3:16). Singing is the sign of the heart’s joy (cf. Acts 2:46). Thus St. Augustine says rightly, “Singing is for one who loves,” and there is also an ancient proverb: “Whoever sings well prays twice over.”
40. Great importance should therefore be attached to the use of singing in the celebration of the Mass, with due consideration for the culture of peoples and abilities of each liturgical assembly. Although it is not always necessary (e.g., in weekday Masses) to sing all the texts that are in principle meant to be sung, every care should be taken that singing by the ministers and the people not be absent in celebrations that occur on Sundays and on Holydays of Obligation.
However, in the choosing of the parts actually to be sung, preference is to be given to those that are of greater importance and especially to those which are to be sung by the Priest or the Deacon or a reader, with the people replying, or by the Priest and people together.
41. The main place should be given, all things being equal, to Gregorian chant, as being proper to the Roman Liturgy. Other kinds of sacred music, in particular polyphony, are in no way excluded, provided that they correspond to the spirit of the liturgical action and that they foster the participation of all the faithful. Since the faithful from different countries come together ever more frequently, it is desirable that they know how to sing together at least some parts of the Ordinary of the Mass in Latin, especially the Profession of Faith and the Lord’s Prayer, according to the simpler settings.
It is noteworthy that numerous magisterial documents, following the directive of Vatican II, specify that the people should be able to chant in Latin the parts of the Mass that pertain to them. We have always joyfully implemented that policy at Wyoming Catholic College. This has included the chanting of the Creed, as is provided for by GIRM 55, 68, and 137.
These are some of the reasons why we ought to sing the Mass — not merely sing at Mass. The beauty of doing this on a regular basis is something that I have experienced at Wyoming Catholic College, where the following has often taken place since 2007:
With a celebrant and congregation who know their chants from repeated experience, and provided there is a brief homily as recommended by the Church for daily Mass, it is possible to do most of these things within a 35-minute daily Mass, and all of them within an hour or a little more on Sundays and Holy Days. Moreover, there is no question that the congregation participates more fully when singing their parts than when merely reciting the spoken text. From the vantage of the pew-sitter, it is the difference between the uplifting unison of simple chant and a scattered muttering of words.
In conclusion: chanting the Mass is more in accord with Catholic tradition. It is in harmony with what anthropology, sociology, and psychology tell us about how ritual activity is best done if it is to be satisfying, renewing, and connecting. It is more in keeping with Vatican II and subsequent magisterial teaching. Lastly, it is crucial for the evangelization of modern and post-modern man through “the way of beauty.” This is the step we must take if we wish to get past the doldrums of excessive verbosity to the heights of prayerful engagement with the sacred mysteries.
 See here for more.
 The GIRM cites here Musicam Sacram, nn. 7 and 16 — clear proof, if any were needed, that the 1967 Instruction is still considered to be pertinent to the Pauline missal, which appeared a couple of years later.