MODAL HARMONY IN THE

MUSIC OF PALESTRINA

Andrew C. Haigh

THIS paper is about something which, according to R. O.

Morris, has never existed.

"As various text-books express a pious hope that the student is famil
iar with what is called Modal Harmony, it may be as well to explain
in conclusion, that such a thing has never existed.* Modality is prop
erly a term of melodic definition; it is only in a derivative sense that
harmony can be described as modal. In that sense you might say that
modal harmony is harmony formed strictly from the diatonic series
of notes constituting the mode in which the melody of any given piece
is written. . . . Such harmony is to all intents and purposes our diatonic
major and minor harmony in its simplest form, except that tonality in
the modern harmonic sense did not yet exist, whilst modulation . . .
did not mean quite the same thing for Palestrina as it means for us/ 2

Anyone who has perused many student exercises in sixteenth-

century counterpoint exercises which may be technically flaw
less as to contrapuntal procedure must have wondered, as has
the present writer, why they did not sound like sixteenth-century
music. Could the harmonic scheme have anything to do with it?
"Such [sixteenth century] harmony is to all intents and purposes
our diatonic major and minor, harmony in its simplest form . . ."
Can we accept this statement at its face value even with the
exceptions attached?

Morris and Jeppesen, 8 whose contributions to the understanding

of sixteenth-century music merit the gratitude of every student in
the field, are scholars of erudition, painstaking thoroughness, and
caution. Though they treat contrapuntal procedures in detail, they
appear to minimize the importance of harmony as a formative ele-

1 1 2 ESSAYS ON MUSIC

merit in sixteenth-century music. By their reticence on the subject,

they seem to give tacit assent to what I believe to be two widely
held and fundamentally erroneous views.

One of these is the view that the modes are indistinguishable

harmonically, except by the final cadence. If the piece cadences on
G, it is mixolydian; if on D, dorian, and so on. That which precedes
the final cadence is just our diatonic major and minor harmony in
its simplest form.

The other is the view that sixteenth-century harmony "just

happens," as a secondary result of contrapuntal exigencies that
Palestrina s music has no systematic harmonic organization of its
own. 4

The questions raised above prompted the writer to embark on a

research into the harmonic organization of Palestrina s music. 6 It
was his conviction that dependable conclusions could be reached
only on the basis of facts established through a minute statistical
analysis of a fairly large representative sample of Palestrina s com
plete works that intuitions, even though based on a thorough
familiarity with Palestrina s music, might be untrustworthy. He
therefore set about sampling, and collecting facts. The contents of
some 22,000 measures (about 20% of the complete works of Pales-
trina) were scrutinized from about a dozen points of view, and the
results tabulated and percentaged. The present essay summarizes
the conclusions about only one aspect of Palestrina s harmonic style:
that of its relation to the modes. The facts supporting these con
clusions are presented in a series of tables and graphs to which the
interested reader is referred. 6

Morris is right, of course, in saying that modality is properly a

term of melodic definition. I should also accept the statement that
modal harmony is harmony formed strictly from the diatonic series
of notes, if I were permitted to delete the word strictly. In the
sample analyzed, all the chromatic tones were found, excepting
only D flat, G flat, and A sharp. Palestrina s tonal material, then,
consists of the modal tones (white keys of the piano) , plus C sharp,
D sharp, E flat, F sharp, G sharp, A flat, and B flat.

What harmonies does Palestrina form out of this tonal material?

The smallest number of harmonies found in any piece was six: these
being, as might be expected, the triads (with their inversions) on
C, d, e, F, G, and a. 7 This minimal assortment is possible only in the

ANDREW C. HAIGH 113

major modes, and in mixolydian only if it is willing to get along

without authentic cadences.

What we might call the normal assortment of harmonies consists

of the six mentioned above, plus D, E, A, g, and B flat. Almost
exactly a third of the sample contained just these eleven harmonies,
and many more pieces contained ten, or nine harmonies. The har
mony on b (only as chord of the sixth) appeared on rare occasions.

Added to these are six extremely rare harmonies, namely, c, E

flat, f , f sharp, A flat, and B. These harmonies appeared in only five
pieces: three madrigals, Vox dilecti from the Song of Songs, and
one other motet a total of twelve occurrences. The employment
of these unusual harmonies seems to be chiefly a characteristic of
the secular style, in which they are used mostly for expressive
purposes.

In regard to chord forms, it is customary to say that Palestrina

used only triads and chords of the sixth, with possibly a few six-
fours. However, it is not difficult to find other forms, including
most of those used in the classical period. Augmented and dimin
ished triads, sevenths of four types (major seventh with major third,
minor seventh with minor third, minor seventh with major third,
and seventh on the leading tone"), and most of the six-fives, four-
threes, and chords of the second corresponding to the four varieties
of sevenths occur, though many of them are extremely rare. I have
called them independent chord forms because in most cases their
roots are different from the roots of the chords preceding and f ol-
lowing them. In all cases the dissonating tone is prepared and re
solved in the usual manner.

We come now to the modes, and to the question of their rela

tionship to Palestrina s harmony. Does Palestrina exhibit a prefer
ence for one mode or another? Do pieces in the various modes show
characteristic and distinctive harmonic patterns? Do they show
distinctive patterns of modal cadences (i.e., cadences classified ac
cording to the location of their final harmony) ? Of cadence forms
(i.e., authentic, plagal, etc.)? The answer to all these questions is
an unequivocal affirmative. Let us review briefly the harmonic and
cadential facts revealed in the sample, and then see if we can find
plausible explanations of them.

Palestrina uses the modes in the following rough proportions:

dorian, 30%; mixolydian, 25^; ionian, ^&%\ aeolian, i$%\ phry-

1 14 ESSAYS ON MUSIC

gian, io^&; lydian, one-tenth of one per cent. Pieces in the < minor >
modes preponderate slightly over those in the major/ in the ratio
of about five to four; but major harmonies are slightly in excess of
minor harmonies. However, if we compare the harmonies normally
ma jor B flat, C, F, and G(g) with those normally minor
d(D), e(E), and a (A) the proportion is almost exactly 50-50.
Pure chance, or mathematically contrived by Palestrina? Neither
hypothesis seems tenable. Rather I should see in these facts evidence
of the composer s fine musical instinct and sense of harmonic
proportion.

In order to show harmonic relationships more clearly, the writer

drew a series of graphs, in which the various components were ar
ranged in a cycle of fifths: for the modes, and the modal cadences,
the order was lydian, ionian, mixolydian, dorian, aeolian, phrygian;
for the harmonies, B flat, F, C, G(g), d(D), a(A), e(E), and b.
The first set of graphs represented the complete sample, i.e., con
tained a mixture of all the modes. These graphs showed, as might be
expected from the modal percentages already given, a normal and
fairly regular distribution curve. The graphs for harmonies and for
modal cadences resembled each other strikingly, and showed even
more symmetrical curves.
Now when the modes were separated, and graphs drawn for
samples that were exclusively ionian, dorian, etc., pronounced in
dividual differences appeared. Each mode had its characteristic
pattern of distribution of harmonies and cadences, which differed
from all the rest. Let us take them in order, and note the most
striking facts.

The lydian graph is the most irregular of all, and this is taken to
be the result of individual variation, in a very small sample, repre
sented by only one piece of 52 measures. It is therefore impossible
to describe Palestrina s normal or average use of the lydian, since
he wrote only a handful of pieces in this mode.

The ionian mode has a numerically strong tonic C, and a domi

nant G(g) which is almost equally strong. The subdominant F,
however, is only about half as strong as the dominant/ Next in
strength is the submediant a (A) .

In the mixolydian, on the other hand, the dominant d(D) is

much weaker than the subdominant C. D harmonies are, however,
more frequent in the mixolydian than in any other mode. In both

ANDREW C. HAIGH 115

Ionian and mixolydian, B flat harmonies are insignificant. They are

much stronger in dorian, aeolian, and lydian.

The dorian presents the interesting spectacle of a mode whose

dominant a (A) is stronger than its tonic. Its subdominant G(g)
is rather weak, its mediant F relatively strong. As might be guessed,
dorian has the largest proportion of A harmonies of any mode.
Aeolian has the strongest tonic of all the modes, slightly exceed
ing the mixolydian in this respect. It also has the largest proportion
of minor harmonies. It leans heavily on its subdominant d(D), its
dominant e (E) being very weak. Its submediant F is fairly strong,
exceeding its mediant C.

The phrygian, at the end of the cycle of fifths, has a pattern which
differs most strikingly from all the others (except possibly lydian) .
It has a very weak tonic, with a subdominant a (A) greatly in
excess. It has no proper dominant b (B) , but it might be permissible
to consider d(D) its dominant, in view of the special form of
"phrygian" cadence. d(D) harmonies prove to be about on a level
with e(E) harmonies, as are also those of the submediant C.

The pattern of the modal cadences in the various modes corrobo

rates in a striking way the pattern of their harmonies. In all cases
except the phrygian, the cadences on the modal tonic are greatly
in excess of any of the others (about 4.8% to 6j% of totals). In the
phrygian mode, cadences on e(E) represent only about 25% of the
total, being exceeded slightly by cadences on a (A). Furthermore,
those modes which show a preference for dominant harmonies
(ionian, dorian), show an even more decided preference for ca
dences on the dominant ; the modes showing a preference for
subdominant harmonies (aeolian, mixolydian), show a similar
preference for cadences on the subdominant. The authentic ( V-
F) form of cadence is most prevalent in all the modes; but the plagal
(TV-F) form reaches the highest percentage in aeolian, mixplydian,
and phrygian.

It should be emphasized that these results are averages obtained

from fairly large modal samples. Within these samples, a respectable
range of individual variation was found. The writer believes, how
ever, that these patterns, so distinctive for each of the modes, could
not have happened by chance or by purely random choice. The
operation of pure chance, he believes, would have reduced the

ESSAYS ON MUSIC

harmonic and cadence patterns to a much greater uniformity _ as

is implied by the author quoted at the beginning of this essay.

It would be very difficult to maintain, on the other hand, that

Palestrina deliberately and arbitrarily set a harmonic pattern for
each of the modes, and on the average adhered to it. What, then, is
the explanation? The writer offers a theory of modal harmonic
gravitation.

The idea of the attraction of harmonies to a tonic or key center

is of course nothing new; it can be found in almost any textbook
on harmony. Dominant and subdominant are attracted strongly to
the tonic; second dominants, and farther outlying harmonies are
attracted less strongly, and normally through the closer harmonies.
But the theory of modal harmonic gravitation here advanced is
quite at variance with this idea: harmonies are attracted, not toward
the modal tonic, but toward the center of the total harmonic
sphere, in which the modal tonics occupy varying positions. This
would account for several odd facts noted in the discussion above:
the fact that the modal tonic 5 harmonies are in some cases not the
strongest numerically; the fact that the tonic leans in some cases
toward the dominant/ in other cases toward the subdominant.
At this point it may be objected that, by my arbitrary arrange
ment of modes, harmonies, and cadences in a cycle of fifths, I have
artificially produced the results which I claim to have discovered
as indigenous characteristics of the Palestrina style. In rebuttal I
would call attention to the following points: (i) any arrangement
(e.g., a diatonic one) would show the same numerical relationships
of harmonies, etc., as presented in the preceding paragraphs; (2)
in the music of Palestrina, root progressions by fifths (or fourths)
are greatly in excess of root progressions by seconds or by thirds _
roughly in the proportions 5:3:2 and these proportions are not
substantially altered, no matter how we divide the sample (by class
of composition, by mode, etc.); (3) the arrangement in a cycle of
fifths always results in a curve which approaches the form of the
normal distribution curve. (2) and (3) would seem to indicate that
the arrangement chosen corresponds to some inherent properties of
Palestrina s music,

To return to modal harmonic gravitation: why should it operate

as described? Presumably not to please the analyst, who may like
to see normal distribution curves emerge. I am not sure that I can

ANDREW C. HAIGH II 7

give a complete answer; but two circumstances seem to point to

influences which may have affected the composer s choice, whether
consciously or unconsciously, and whether restrictively or effec
tively.

1. Many writers have noted that the impulse toward the tonic
was weaker in the music of the sixteenth century than in that of
our era. In the Gregorian melodies, the final can hardly be de
scribed as a tonic, in our sense. The dominant or reciting note
probably approaches this function more closely. In most sixteenth
century music, the final harmony is properly described as a tonic,
though sometimes a weak one, by our standards. The leading tone
was normally used in final cadences, even in those modes (mixolyd-
ian, dorian) where it would appear to vitiate the strict modal
canon. But there was not the same compelling impulse to return
to the tonic, or to imply or refer to it constantly. This relatively
weak pull toward the tonic would leave the field open to other
forces or attractions, which might in some cases be away from the
modal tonic.

2. The range of Palestrina s harmonies, though wider than com

monly supposed, was narrow as compared to that of the eighteenth
and nineteenth centuries. Thus there was in the harmonic sphere
a certain constriction or pressure, limiting complete freedom of har
monic motion. This limitation was greatest at the peripheries of the
sphere. If we take F and e(E) as the extremes of the cycle of fifths
(since B flat and b were so rarely used) , we note that these periph
eral harmonies can proceed, by the normal root progression of a
fifth, in one direction only inward toward the center of the
series. And we find that their frequency of occurrence amounts to
only about 1 2 % and 9% respectively roughly half the frequency
of the other harmonies. The next in the series (reading inward),
C and a (A), can proceed only one degree outward, and then are
forced to return toward the center. This restriction is apparently
not very serious, since their frequencies are only slightly below
those of the inner harmonies. The peripheral pressure of the series
of harmonies, then, would suggest a reason for the preponderance
of harmonies at the center of the sphere.

If the forces and restraints noted above were quite unhampered

in their operation, we might expect to see, in the whole sample,
completely symmetrical distribution curves for harmonies and

1 18 ESSAYS ON MUSIC

modal cadences, when these are arranged in a cycle of fifths. But

such is not the case. The center of the total harmonic sphere would
be equally shared by G(g) and d(D) harmonies, or by mixolydian
and dorian. However, d(D) harmonies and dorian cadences, in the
complete (mixed) sample, are slightly in excess of G(g) harmonies
and mixolydian cadences (20.6% to 19.4% for harmonies; 23.6%
to 22.79?? for cadences). The next pair, C and a (A), or ionian and
aeolian, are almost equally balanced, and very little inferior to the
central pair. Then there is a big drop to F and e(E) harmonies
(i i-59& and 8.4%), and an even bigger drop to lydian and phrygian
cadences (4*7^ and 4.2%). Finally the curve approaches zero at
the B fiat and b harmonies (1.6% and .04%) .

In the samples separated by mode, our theory of attraction to the

center of the harmonic sphere accounts for the preference of some
modes for dominant harmonies, of others for subdominants/ but
not completely. It breaks down (though slightly) in the mixolyd
ian and dorian, where the preferences are reversed. If we are to
presume that the theory represents a fundamental law or uni
formity, an explanation must be found for the exceptions. Two
related facts of the music of Palestrina s time suggest themselves for
consideration: the developing feeling for "tonicity," and musica
ficta.

It has been noted by many writers that the feeling for tonicity in
the sixteenth century, while weaker than in nineteenth-century
music, was growing, and was in the process of obscuring modal
differences, and reducing all the modes to two types major and
minor. The use of the modes had largely disappeared by the middle
of the eighteenth century. The feeling for tonicity demanded a
leading tone, and we find that in Palestrina s music the penultimate
harmony in authentic final cadences is almost without exception
major. Musica ficta, of course, served other purposes as well me
lodic ones, as in the well-known rules: "mi contra fa, diabolus in
musica" and "una nota super la, semper est canendum fa." But it
is impossible to say how rigorously these rules were applied. Indeed
it is not hard to find situations where they could not be applied,
because the use of musica ficta would contravene some other, more
stringent rule. I think we can assume a certain reticence in the use
of musica ficta, where a solution of a problem which did not require
musica ficta suited the composer s purposes just as well.

ANDREW C. HAIGH 1 19

Now in the dorian final plagal cadence, the penultimate harmony

is always minor, which requires the note b flat. Similarly in the mixo-
lydian, the final authentic cadence requires f sharp. Mixolydian has
a perfectly acceptable plagal cadence not requiring wusica ficta;
and although the dorian authentic cadence involves c sharp, it is
the required leading tone. It should be noted, however, that mixo-
lydian contains more D harmonies, and dorian more g harmonies,
than any of the other modes. Thus the comparative freedom of
motion of the inner harmonies would leave room for other forces
in this case the pull of the tonic and reticence in the use of
musica ficta to operate.

One other pronounced effect of the modes can be seen in the

form of the cadences. Authentic cadences are greatly in excess in
all the modes (56.7% to 75.6%) except in phrygian, where they
drop to 44.5%. Phrygian, naturally, has by far the largest percent
age of "phrygian form" cadences (i 2.9%). It also has a large pro
portion of plagal cadences (17.2^), being slightly exceeded only
by aeolian (17.8%). "2-1" cadences (e.g., d-f-b to c-e-c) are most
numerous in phrygian (16.8%), being closely approached only by
ionian (14.5%).

The picture presented here is that of a struggle between two

opposing forces: the modes, traditional, backward looking, and the
major-minor system of tonality. That the modal influence on the
harmonies was still strong is evidenced by the distinctive modal har
monic patterns; that these patterns show certain slight unexplained
irregularities seems to me evidence of the pull of tonality. This con
flict may explain why the curves are not in all cases just what the
theory of modal gravitation would lead us to anticipate; however,
their chief import, that of modal influence on harmonic distribution,
seems to me incontestable.

There is one other influence, perhaps the most important in the

stylistic picture, which I have not considered, because it is not
amenable to statistical treatment. It is the composer s creative genius,
which is subject to no restrictions save his artistic probity. There
is no reason why a sixteenth-century composer should not have
written polytonal music if he chose as in one remarkable in
stance 8 he came close to doing. In many of Palestrina s pieces the
patterns diverge rather widely from the norms given above (see
the secular madrigals, particularly "Placide Tacq " and "La cruda

1 20 ESSAYS ON MUSIC
mia nemica"). Palestrina was not a slave to the musical conventions
of his time, though he chose to work within them, for the most part.
Neither was he insensitive to the newer developments of his era, as
is shown in the remarkably modern sounding madrigals mentioned
above. Here is one more bit of evidence (if further evidence were
needed) that Palestrina is among those musical great who, like Bach
and Brahms, represent the summation and culmination of their times,
rather than the exploration, pioneering, and revolution of a new
age.

1. Present writer s italics.

2. Morris, R. O., Contrapuntal Technique in the Sixteenth Century, London,

Clarendon Press, 1922, pp. 43, 44.

3. Jeppesen, Knud, The Style of Palestrina and the Dissonance, translated by

Margaret Hamerik, London, Oxford University Press, 1937.

4. Read the passage (too long for quotation here) in Jeppesen, The Style of
Palestrina and the Dissonance, p. 76. See also Shirlaw, Matthew, The Theory of
Harmony, London, Novello and Co., New York, W. H. Gray, pp. 4, 6.

5. The results of this research are to be found in Andrew C. Haigh, The

Harmony of Palestrina [Thesis, PhD.], Harvard University (1945) .

7. Capital letters indicate major harmonies; lower case letters indicate minor
harmonies.

8. "Der Juden Tanz," by Hans Neusiedler, in Davison, Archibald T. and

Willi Apel, Historical Anthology of Music, Harvard University Press (1046)
p. 108. J ^