How much of the Mass we sing varies drastically from parish to parish, even from Mass to Mass. We should sing as much as possible, since in singing we unite ourselves to the "primordial song of the liturgy," which is that of Christ's "victory over sin and death". (Sing to the Lord: Music in Divine Worship, 7). We usually do not see the average Mass entirely sung though, because it can be difficult for priests and congregations to know and fully participate in singing everything. So if we don't sing everything, what should we sing? In other words, what parts of the Mass have a priority for us to sing over other parts of the Mass? "Instruction on Music in the Sacred Liturgy" (Musicam Sacram, 28) answers this by separating the parts of the Mass into three "degrees." The first degree contains the most important parts of the Mass to be sung. If you sing at all, it should be the first degree. If you sing the parts of the Mass in the third degree, you should be singing the first and second degrees as well. So what is the most important part of the Mass to sing?
The First Degree: The Order of the Mass
The following belong to the first degree:
(a) In the entrance rites: the greeting of the priest together with the reply of the people; the prayer.
(b) In the Liturgy of the Word: the acclamations at the Gospel.
(c) In the Eucharistic Liturgy: the prayer over the offerings; the preface with its dialogue and the Sanctus; the final doxology of the Canon, the Lord's prayer with its introduction and embolism; the Pax Domini; the prayer after the Communion; the formulas of dismissal.
This is called the Order of the Mass, which consist of dialogues between the priest and the congregation. The first example given above is the simplest, which we know as, "The Lord be with you." "And with your spirit." These chants can be found in the Roman Missal and on the ICEL website, and if your congregation isn't used to singing them, it's something that can be addressed with your pastor, since the priest/deacon leads these chants during the Mass.
Why are they so important? Love needs to be expressed. On a human level, love is communicated through our bodies and our voices. It's difficult to maintain a relationship when love is not communicated. When we participate in the dialogues at Mass, we enter into unity with the Church, who communicates with the priest standing in persona Christi (in the person of Christ). The purpose of the Mass is for us to enter into Christ's work of redemption through the Cross and Resurrection, and the dialogues communicate our desire to enter into this relationship. A great example of this is the Preface Dialogue:
The Second Degree: The Ordinary of the Mass
The following belong to the second degree:
(a) the Kyrie, Gloria and Agnus Dei;
(b) the Creed;
(c) the prayer of the faithful.
These texts are called the Ordinary of the Mass, since we use them every Mass (depending on the liturgical season, such as the Gloria). What is most surprising on first glance is the Creed. It is very rare to find a parish who sings the Creed, and although it might be difficult and take a long time to teach and master a sung arrangement of the Creed, it should be in the long term vision for music directors to introduce it in a pastoral manner.
The Third Degree: The Propers of the Mass
The following belong to the third degree:
(a) the songs at the Entrance and Communion processions;
(b) the songs after the Lesson or Epistle;
(c) the Alleluia before the Gospel;
(d) the song at the Offertory;
(e) the readings of Sacred Scripture, unless it seems more suitable to proclaim them without singing.
As you can see, musicians preparing for the Liturgy typically spend the most time and energy on what's actually the least important to sing, which are called the Propers of the Mass. Many times this leads us to only singing the parts of the Mass that are in the third degree. If we understand the purpose of singing the Mass, and what parts of the Mass are most important, we can see how this demonstrates a disordered view of the Mass.
Musicians should still put in the time and energy in leading music that is excellent, beautiful, and most of all prayerful for the Entrance, Offertory, Communion, etc., but we should also be sure to sing the dialogues (Order of the Mass) and the Ordinary. The more we can sing at Mass, the more we can express the nature of the Mass, where Christ calls us to enter into the song of His sacrifice to the Father, in anticipation of full communion with God in heaven.
For more on what we sing for Entrance, Offertory, and Communion, check out my post on Singing the Antiphons.
For further reading, check out Bishop Olmsted's article on "Singing the Mass"