McMaster Music Analysis Colloquium



A Schenkerian Approach to Ternary Form


Antonella Bilich


Giovanni Pierluigi da Palestrina (ca. 1525-1594) wrote a great number of masses, many based on preexisting plainchant. One such example is the Missa Aeterna Christi munera (1590) which is a paraphrase mass using the melody of the Gregorian hymn after which it received its name.  The original hymn was used for the Feast of the Martyrs and Apostles.  In this article I will be basing my discussion specifically on the "Kyrie" of this mass setting, analyzing it through a discussion of ternary form as well as through the voice-leading theories of Heinrich Schenker.

Schenker's theory deals specifically with tonal pieces, namely those which are considered 'masterworks.'  Therefore including a piece of imitative polyphony from the 16th century poses certain problems and issues. As the 16th century sees composition through modes, not yet specifically in tonality, there are special nuances that must be considered which are different from regular Schenkerian analysis.  As well, when dealing with a polyphonic work, various specific issues arise regarding the analysis, such as which voice actually contains the melody at any given moment.


Palestrina's entire mass setting, as I stated earlier, is based on the Gregorian hymn Aeterna Christi munera. The three sections of the "Kyrie" are based on the first three phrases of the hymn.  The hymn contains a fourth phrase that Palestrina does not set in his "Kyrie." Interestingly, however, this fourth phrase is identical to the first one.

Some issues arise among Palestrina scholars as to the origins of this hymn. In my own research of this piece, I found contradictory evidence regarding the original Gregorian hymn. In the 1909 English book Hymns Ancient and Modern(1), the hymn is shown in square notation, with modern notation appearing underneath. The square notation is named by the editors as being in mode vii, the mixolydian mode, with the final g. The hymn in modern, four-part notation, however, shows the piece with a final of f, in the key of two flats. The integrity of the intervals is maintained by the key signature; however, there is some discrepancy on the issue of the original hymn from other Palestrina scholars.

Figure 1a. Aeterna Christi munera according to Hymns ancient and modern.

Robert Marshall, in his article on the "Paraphrase Technique of Palestrina"(2) writes out the hymn melody, in modern notation, beginning on c with no key signature.(3)

Figure 1b. Aeterna Christi munera according to Marshall.

In a later example in the paper, he shows a square notation version of the hymn, taken from Guidetti's Directorium. This version also has the final as g in the mixolydian mode.

Figure 1c. Aeterna Christi munera according to Guidetti as cited in Marshall.

The problem with these versions is that Palestrina uses the hymn in his composition beginning and ending on f. With both these source examples, the issue also arises that Palestrina's setting of the third phrase from the original hymn, in his final section of the Kyrie (the form of this mass part will be discussed shortly), begins with a repeated note which then ascends. The note is c, the fifth note above the final f. In both Gregorian examples, the third phrase begins with the leap of a third, up to the fifth above the final, and then this ascends further to the repeated note, a sixth above the final. The rest of the phrase basically maintains its shape.

I was able to come across one other source example,(4) from Songs of Praise in which the hymn has the final f, and where the third phrase of the hymn actually does open with this repeated c going up to the d. This modern version cites Guidetti's Directorium chori (1582) as its source. At any rate, this source most closely matches what we find in Palestrina's paraphrase mass, therefore becoming what could be considered the 'best' possible version of the hymn tune as Palestrina's source.

Figure 1d. Aeterna Christi munera according to Songs of Praise.

This brief look at the source of the plainchant calls various issues to question and gives us a snapshot look at one possibility of the transmission of chant through the centuries. We do not actually know where Palestrina got this hymn, whether it was something in the oral realm of the 16th century, or if he actually had a written source for his version of the hymn.  If Palestrina did have a written source, we are intrigued to try and discover this lost source. However, using the version that seems to most closely match the tune that Palestrina may have used, it seems appropriate at this time to take a closer look at the hymn, through the lens of a Schenkerian foreground graph.

Figure 2. Schenkerian foreground graph of Aeterna Christi munera.

I feel that this graph provokes the discussion of a few issues which it conveys. The three sections of the piece are differentiated by the use of the double bar line.  The shape of the filled-in interval of a third, as seen in mm. 1-2, is notable, as it recurs in mm. 5, 6-7, 10, and 11-12. This would seem to have some importance on the shape of the melody, and will obviously have its effect on Palestrina's setting of it. From mm. 6-9 we can see the prolongation of the note c, (with a few upper neighbour notes) and this is important because in much of Palestrina's setting of the melody, that section is set in the tonal area of C. In other words, this prolongation of c is important structurally as well as harmonically. The descent 5^- 4^- 3^- 2^- 1^ is present in the last six measures of the hymn, beginning with the aforementioned prolonged c, or 5^.

Regarding the individual cadential gestures of each of the four phrases, I would briefly draw your attention to my discussion of Cristle Collins Judd's concept of modal types in sacred vocal polyphony, which appears later in this article.


Contributing to a discussion of ternary form in which our class is presently engaged (specifically in regards to the writings of Douglass Green, Ernst Levy and Siegmund Levarie) I would like to present my analysis of the "Kyrie."  Firstly, the text of all "Kyrie" mass parts is as follows:

Kyrie eleison, Kyrie eleison, Kyrie eleison
Christe eleison, Christe eleison, Christe eleison
Kyrie eleison, Kyrie eleison, Kyrie eleison

It is interesting to note that the 'typical' Kyrie, setting has three repetitions of each invocation (Kyrie eleison, Kyrie eleison, Kyrie eleison)(5) while Palestrina's setting is different: the first Kyrie has only two repetitions, while the Christe and the final Kyrie have three. This apparent peculiarity has not been mentioned in my own readings, and I can not hazard a guess as to why this might be. In any case, the triple division of the whole text (Kyrie, Christe, Kyrie) immediately suggests a three-part musical structure, and throughout history, the "Kyrie" mass part has been set in three sections. However, this is not the only reason to consider this "Kyrie" as ternary in form.

Dr. Renwick, discussing Green's theory on ternary form, writes:

Douglass Green states that the division into three parts that marks ternary form is brought about entirely by design. The first division is normally due to a strong cadence marking the end of part one, and the second due to the contrasting nature of the material. Green's definition can be further reduced: the division into three parts is due to the contrasting material of the middle section.(6)

This concept is clear in the Palestrina "Kyrie" in that the A section has a strong cadence on the tonic note f. The B section ends with a strong cadence on c. The A' is like the A in that it cadences on f. However, the material of the A' section is not motivically linked to the opening A section. More importantly, the musical material of the B section is not significantly different than anything else in the piece.

However, continuing to look at other arguments within Green's theory, Dr. Renwick summarizes that full sectional ternary [A-B-A(')](7) occurs where there is a formal division at the end of each section, consisting in a perfect authentic cadence in the key of the given section. This is evident in the "Kyrie" where a perfect authentic cadence ends each of the three formal sections. We can see that Palestrina employs the usual cadential figure of Renaissance polyphony in treating his final cadences.

Figure 3. Final cadences of the A, B and A' sections respectively.

At this point, I think it is useful to discuss Cristle Collins Judd's article, in which she discusses modal types and tonalities in 16th century polyphony.(8)  Through Judd's ideas, we can better understand what occurs in polyphonic pieces, and this will inform the discussion surrounding the issues, specifically to pre-tonal works, already alluded to at the beginning of my article. In her article, Judd classifies three types of tonal systems within the polyphonic repertoire of the time, as suggested by her title, being Ut modes, Re modes and Mi modes. She hypothesizes:

Elements that were essentially distinct in the minds of fifteenth- and sixteenth-century theorists, but that were intimately related in polyphonic composition, can resolve the incongruities evident in modal classification. These elements include the hexachordal position and pitch of the final; melodic characteristics, particularly in the superius, that correspond with modal markers; contrapuntal procedures; and the registral conventions of a vocal ensemble. Consideration of these elements leads to a theory of three basic tonal systems, distinguished by hexachordal nomenclature as Ut, Re, and Mi tonalities.(9)

Judd goes on to discuss Glarean's position on this subject: "Every song ends either on re or on mi or on ut."(10) Basically, the Ut tonality has the full hexachord available to it, with an emphasis on the first five notes: ut, re, mi, fa, sol. In the Re tonality the final and upper boundary of the hexachord emphasize the fifth: re, mi, fa, sol, la. Finally, in the Mi tonality the final and the boundary of the hexachord emphasize the fourth: mi, fa, sol, la. These show the differences, which occur in modality, regarding the relationship of the intervals within the various notes of the hexachord.  Using this as her basis, Judd then shows a chart of modal cadence types in relation to these three tonalities, reflecting "Schenkerian principles in the use of reductive representations of a structural voice-leading framework and hierarchical notation."(11)

This chart is of interest to the discussion at hand and is useful as a basis for comparison with the Palestrina "Kyrie."  We can note that our A section cadence is summed up by Judd's first and second cadences in the Ut type.  We see, in the cadence of the A section of the "Kyrie", the soprano descending to the leading tone and then rising to the tonic, while the tenor voice descends directly to the tonic.  The same cadence occurs at the end of the A' section.  The final cadence of the B section is also similar, in that a combination of both the first and second Ut cadence types form the cadence.  We see the soprano voice again landing on the leading tone then rising to the tonic, while the tenor descends to it.

Returning now to Green's discussion, we can see that the "Kyrie" seems to be divided into three separate pieces, by virtue of the final cadences.  There is a complete piece, followed by another contrasting complete piece, ending with a restatement of the first piece.(12) The construction of Palestrina's "Kyrie" is in keeping with the concept of each section constituting what could be an individual piece in the given key. However, this may be considered somewhat problematic in that Green considers the A and A' sections to be exact or at least highly similar. This is not the case with Palestrina's "Kyrie" where the A and A' sections are different melodically and motivically. This is obvious and expected seeing that the sections are based on two different phrases of the original hymn. Therefore, we could say that the formal divisions do occur in Palestrina's "Kyrie" through strong cadences. Even though the A and A' are not similar, they are in the same key and the difference in the B section allows us to consider it full sectional ternary. As well, the end of the B section, with its cadence on c (the dominant of the key of the entire piece), requires fulfillment and resolution back to the home key of F.  In other words, Green's basic idea of full sectional ternary, A-B-A', as being home-away-home, is exemplified by the "Kyrie." This idea is furthered by the fact that the A' section sees a return to the text of the A section.

Ernst Levy and Siegmund Levarie situate their discussions on ternary form within the context of what they term Ontic and Gignetic elements.(13) Using this as the basis for my discussion of the "Kyrie", I will discuss the piece in light of the questions raised there. As noted earlier, there is some form of contrast between the A and B sections, namely the key. The A and A' sections are clearly in the key, or tonal area, of F, while the B section is in the area of C. Although we are never clearly in C major, we get the modal hints of many b-naturals, many g dominant-function type chords. Also, right from the beginning of the B section we feel as though we are 'somewhere else' harmonically: we begin on an unstable b-flat under an f, certainly jarring after that solid f cadence that ended the A section. On the other hand, the three sections are based upon a different phrase from the original Gregorian hymn, so their respective melodic and motivic material varies. This includes the comparison of the A section with the A':  although both are in the key of F, they are not comprised of the same material. One could argue perhaps that a remote possibility exists of labeling the piece A B C, but especially because the key of F returns, I think this is not feasible.

The texture remains quite stable within the three sections, as does the metre and the tempo. Looking at the rhythm of the B section, it is evident that it begins to speed up, with more prevalence given to the eighth notes than in the A section. However, the A' section continues with this acceleration and we see even more emphasis on the eighth notes -- they are now within the counter subject itself. This accelerating of the rhythm is not uncommon, in my opinion, in Renaissance and even Baroque music, where there is often a sort of propulsion occurring towards the final cadence. In regards to the phrasing of the piece, as is typical of imitative counterpoint, the internal cadences (those other than the ones ending each of the sections) are always somehow elided. The phrases are overlapping: while some voices are cadencing, another voice is just beginning its statement of the subject. I would also say that there are no drastic changes in register throughout this piece. Being composed for a four-part choir, the register is limited to the vocal ranges of the respective parts.  (See my discussion of register later in this article.)

There is no obvious linking or bridging passage between the three sections. Each section comes to a complete stop with the end of the main cadences. However, there is a different type of link between sections: the notes that carry over from the cadence.  The B section begins with a b-flat, in the altus, a whole tone below the c just sung in the final cadence of the A section, and instantly the cantus reiterates the f that ended their line in the A section. A stronger instance of a formal link is found at the opening of the A' section, where the altus picks up with the c (even though the tonal area of this section is F) that ended the B section final cadence. Therefore, the tonal area 'feeling' of C is continued on into the new section.

Within the individual sections, there are often elided cadences. This is exemplified quite dramatically in the B section, especially in mm. 21-25. These elisions contribute in the forward moving feel of the piece in its entirety, but especially of the B section, where we are 'away from home' so to speak, and never quite feel the comfort of being anywhere completely stable.

Figure 4. Elided cadences, mm. 21-25.



Saul Novack, in his "Analysis of Pre-Baroque Music,"(14) discusses many issues that are fruitful for this study. In a summary of thirteen basic points regarding the analysis, specifically Schenkerian, of pre-Baroque music, Novack presents various observations, some of which are particularly illuminating for this analysis of Palestrina's "Kyrie". Novack sees these points, which apply to pre-Baroque musical compositions, as having the function of making the Schenkerian analysis of the works that fulfill these requirements more feasible.  I will discuss the arguments which are more critically important to my discussion of the "Kyrie".

Firstly, Novack sees the presence of tonal prolongations right from the beginning of polyphony. Prolongations abound in the "Kyrie".  A specific instance of prolongation is seen at the beginning of the A' section, (as discussed earlier) in relation to how the B section ends with a tonic chord in C, and the A' section has the altus beginning a counter subject on c, while the tonal area of the section is actually F. This type of prolongation occurs in order to link the sections together. However, there are many obvious prolongations, especially of the tonic chord, that can be observed in many moments of the piece. The fact that these prolongations do occur allows for a feasible application of Schenkerian analysis to this piece of Renaissance polyphony.

Figure 5. Middleground graph of the "Kyrie" showing tonal areas and prolongations.

In his second argument, Novack posits that there is much evidence of the triad functioning as an organizing force. This is evident in the "Kyrie" which, although being based on a modal hymn, exhibits much reliance on the triad, specifically on the tonic triad. This is linked with the first point of prolongations. However, the contrary argument to this is that in two of the three final cadences of the pieces, we see cadences that omit the third of the chord.  It is important to note that throughout the phrases, there is the presence of the third of the chords. It is only within the final cadences of the A and A' sections that we see these open fifth type cadences, which, of course, are the typical cadential patterns of the Renaissance period. This is further affirmed by Novack's third point, in which he states that modality and tonality are not opposites, but rather that they work in conjunction, their relationship appearing in varying degrees in different moments of the pre-Baroque periods.

Novack's fourth point discusses the leap of a fifth in the bass as a property of tonal relationships. This is seen especially at the main cadential points within the work. The leap always constitutes a V - I relationship. In the case of 16th century polyphony, the third in the V chord is always present, which differs from what Novack exemplifies from the 14th and 15th centuries. This is evident in all the final cadences of the "Kyrie."  In his sixth point, Novack argues that the technique of melodic and rhythmic repetition in the form of motive are present and add to the sense of a tonal function. This is explicit within the style of imitative counterpoint where everything stems from the subject, in this case based on a preexisting Gregorian hymn.

Novack's next two points (7 and 8) deal specifically with the Urlinie.  Therefore before discussing them, I will present my analysis of the background graph of the piece.

Figure 6. A background graph of the "Kyrie".

In his seventh point, Novack states that "the Urlinie of the top voice makes itself clearly felt early on [in history]"(15) We can see the descent 3^ - 2^ - 1^ in the "Kyrie" in Figure 6. In the eighth point, Novack argues that often the motion of the Urlinie is to the leading note, moving then to the tonic. He writes that "the leading tone acts as an inner voice below the second degree"(16) and this is evident in the background of the "Kyrie". For example, in the final cadence of the piece (see Figure 7), we see the cantus with the motion 7^ - 1^, while the tenor fulfills the regular tenor cadential function of 2^ - 1^. This is typical of Renaissance cadential practices, as I have discussed earlier.

Figure 7. Final cadence of the piece.

Novack's tenth point is in regard to prolongations of chords other than the tonic, which are harmonic and function in the background. Evidence of this can be seen throughout the piece. Some examples of this can be seen in Figure 5, with the various prolongations of c and of the dominant chords of C.

An interesting issue that Novack raises in his twelfth point is that there tends to be a general absence of registral shifts in the music prior to the 17th century. This is evident in the "Kyrie" in that the various voices are limited by their range. However, one could possibly see registral shifts in looking at which voice has the melody at any given moment, the shift between tenor and cantus, for example. This idea promulgates the need for further thought, and although it is beyond the scope of my article, I think it would be an interesting endeavor to argue registral shifts in imitative counterpoint of the 16th century.

Palestrina's "Kyrie" from the Missa Aeterna Christi munera is an interesting catalyst for the discussion of ternary form within the basis of the original hymn tune and its structure, through Schenkerian analysis and the evidence of modal types within pre-Baroque music.


1. Hymns ancient and modern for use in the services of the church with accompanying tunes, Historical edition, (London: Printed for the Proprietors [by] W. Cloves and sons, 1909), 202.

2. Robert L. Marshall, "The Paraphrase Technique of Palestrina in His Masses Based on Hymns," The Journal of the American Musicological Society, XVI/3 (1963): 347-372.

3. Marshall, "The Paraphrase Technique," 350.

4. Many thanks to Dr. Renwick for pointing me to two of the sources -- both the Hymns Ancient and Modern mentioned above, as well as this source Songs of Praise, words ed. Percy Dearmer, music eds. Ralph Vaughan Williams and Martin Shaw, (London: Oxford University Press, 1931), 37.

5. As suggested to me by Dr. Renwick via LearnLink.

6. See Dr. Renwick's Appendix, 4.

7. See Appendix, 12.

8. Cristle Collins Judd, "Modal Types and Ut, Re, Mi Tonalities: Tonal Coherence in Sacred Vocal Polyphony from about 1500," The Journal of the American Musicological Society XLV/3 (Fall 1992), 428-467.

9. Judd, "Modal Types," 437.

10. Judd, quoting Glarean's Dodecachordon, "Modal Types," 437.

11. Judd, "Modal Types," 441.

12. See Appendix, 12.

13. See the discussion in Appendix, 7.

14. Saul Novack, "The Analysis of Pre-Baroque Music," Aspects of Schenkerian Theory, ed. David Beach (New Haven: Yale University Press, 1983), 113-133.

15. Novack, "The Analysis of Pre-Baroque Music," 130.

16. Novack, "The Analysis of Pre-Baroque Music," 130.

Copyright 1999 by Antonella Bilich.