Yahoo Tuning Groups Ultimate Backup tuning Re: Renaissance 5-limit harmony: of modes and triads

Recently there have been a number of interesting posts about the
various senses of "tonality" (and "atonality"), with some mention of
16th-century Western European practice. Also, I would like to thank
Joe Monzo for some earlier dialogues via e-mail on related topics,
which have helped spur me to write this article.

In my view, the specific conventions of key-oriented tonality in the
18th-19th centuries in European composition represent the taste of one
era rather than some "universal" tendencies of musical evolution, or
even of European musical evolution. If we explore the 14th, 16th, or
20th century, we find other conventions in effect -- not surprisingly,
conventions with some common assumptions or stylistic norms which seem
to link them to 18th-century practice and theory, or vice-versa.

For whatever reason, traditional 20th-century music history often
tends to take 18th-century practice as the norm for "tonality," and to
judge other periods in terms of the presence or absence of
18th-century features. It seems to me that with equal (in)validity,
one might take, for example, Schoenberg's 12-tone system as the
evolutionary "goal," and argue that composers of the 14th-19th
centuries were "attempting" to use all 12 steps of a chromatic scale,
leading finally to the "inevitable" triumph of dodecaphony.

Here I would like to suggest a different approach to Renaissance
tonality, which focuses on vertical as well as horizontal aspects in
16th-century terms, with reference to medieval tonal and harmonic
paradigms also.

While I find the term "modality" not unapt to describe one aspect of
medieval and Renaissance tonal practice, this term can hardly
encompass in itself the vital _vertical_ dynamics of the music, as
shaped both by the changing norms of complete stable harmony and by
the choice and interaction of directing two-voice progressions in
moving between stable harmonies, or in some cadential progressions
from an unstable to a stable sonority.

Specifically, I shall here argue -- to a great extent expanding on the
views of writers such as Richard Crocker and Carl Dahlhaus, although
the responsibility for any infelicities is purely mine -- that
Renaissance tonality is based on a fascinating interaction between
a new aesthetic of 5-limit sonorities and a traditional medieval set
of 3-limit directed progressions. This interaction, as much as the
choice of modal scale materials, helps to shape the unique qualities
of harmony in the 16th and earlier 17th centuries.

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1. Early tertian tonality: new sonorities, old progressions
-----------------------------------------------------------

In describing the tonality of the Renaissance and Manneristic eras --
say from 1450 to 1650 -- the term "modal" is indeed _one_ useful tool
of orientation. Theorists of the era from Tinctoris (1477) to
Glareanus (1547), Vicentino (1555), Zarlino (1558), Lippius (1612),
and Bernhard (c. 1655?) themselves take the modes as an important area
of polyphonic practice and theory. Indeed, in the famous debate
between theorist and critic Giovanni Maria Artusi (1600, 1603) and the
Monteverdi brothers (1605, 1607) whose "modern" style he attacks, both
sides accept the system of 12 modes, but disagree as to whether it is
possible to compose a successful piece mixing several modes.
Interestingly, the Monteverdi brothers cite some conventional
16th-century pieces to show that this is indeed a technique available
in traditional practice as well as in the new practice they champion.

At the same time, 16th-century concepts of modality are often
pragmatic and flexible -- as are many later approaches to key-based
harmony. Thus Vicentino describes the prevailing style of his day as
"mixed and tempered music," referring to the typical mixture of modes
as well as the tempering of the fifth on keyboard instruments (with
1/4-comma meantone or 31-tet his apparent model).

To place Renaissance and Manneristic concepts of polyphonic modality
in context, we must also consider the issues of vertical sonorities
and progression, in fact issues also emphasized by these theorists.

Here I shall argue that one interesting way of viewing Renaissance
tonality is to see a kind of fluid fusion betweeen two guiding forces:
a "modern" desire for full 5-limit or "triadic" sonority as the norm
of complete harmony, that is, Zarlino's "third-plus-fifth-or-sixth"
and Lippius's _trias harmonica_; and a continued orientation to
traditional medieval progressions based on a 3-limit or trinic
system.

In the medieval tradition of the 13th and 14th centuries, we may say
that two-voice progressions and multi-voice sonorities are "in sync,"
both being based on fifths and fourths as the most complex stable
intervals. Directed cadential progressions typically involve two-voice
resolutions from an unstable interval to a stable one by conjunct
contrary motion (e.g. m3-1, M3-5, M6-8, m7-5). Writing for three or
more voices is based on the stable trine (outer octave, lower fifth,
upper fourth) as the unit of complete harmony, and on progressions
from unstable combinations to stable trines, ideally complete.

This trinic tradition nicely correlates with a "3-limit" concept of
stability, and with Pythagorean tuning as an apt acoustical
expression.

During the 15th century, however, the ideal of sonorous euphonious
shifts toward a more and more pervasive "5-limit" concept, with thirds
and sixths increasingly favored as the norm. This stylistic change
correlates with a shift from Pythagorean tuning to tertian just
intonation systems or meantone temperaments for keyboards as ideal
acoustical expressions.

However, in practice and theory, the traditional "3-limit" or trinic
resolutions continue to guide harmonic progressions -- albeit
progressions often transformed by the emerging Renaissance norm of
"5-limit" or triadic sonority. Especially important are those
resolutions proceeding from a third or sixth to a traditionally stable
3-limit interval: e.g. m3-1, m3-5, M3-5, M6-8.

Before seeing how these resolutions are superimposed or harmonized to
guide progressions between full 5-limit sonorities, let us consider a
curious aside: might 16th-century tonality be at once in some sense
both "modal" _and_ "major/minor"?

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2. Renaissance harmony: both modal _and_ major/minor?
-----------------------------------------------------

While the "major/minor" concept in traditional musical historiography
and analysis is more or less equivalent to what I term the "key
system," here I would like to suggest that in 16th-century terms,
16th-century music involves a contrast between complete tertian
harmonies with either a major third or a minor third above the
bass. At the same time, the flow of these vertical sonorities as well
as the progressions of the individual melodic lines may be classified
by the system of modes, with conventional and not-so-conventional
accidental inflections available.

In fact, a contrast between what what might be called major and minor
_triads_ is readily compatible with modal tonality not only in the
16th and earlier 17th centuries, but indeed in the 20th century, when
composers sometimes make the differences between modes yet more clear
by avoiding inflections of a kind routine in Renaissance and
Manneristic polyphony.

While Vicentino (1555) does not, to my best knowledge, focus on the
contrast specifically between sonorities with string ratios of
15:12:10 and 6:5:4, he does discuss the contrast between major and
minor thirds, finding the former "infinitely preferable" for the
concluding sonority of a cadence. Interestingly, Vicentino asserts
that the bass is the guiding voice of the polyphonic texture.

Both Zarlino (1558) and Lippius (1612) do explore the contrast between
the division of the fifth with the major third below and minor third
above (string-ratio 15:12:10), and the converse arrangement with minor
third below (string-ratio 6:5:4). These theorists, recognizing 12
modes, group them into modes with the major third above the final
(Ionian, Lydian, Mixolydian) or minor third above the final (Dorian,
Phrygian, Aeolian).

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3. Modal triadicism and the new alternation
-------------------------------------------

In discussing the complete harmony of the third-plus-fifth-or-sixth,
later the triad of Lippius, Zarlino describes and commends a vital
feature of much 16th-century tonality which sets it apart both from
medieval trinicism and from 18th-19th century key tonality: the
frequent alternation of the harmonic and arithmetical divisions of the
fifth -- or, in more recent terms, major and minor triads.

This ideal alternation of the two divisions of complete tertian
harmony might be seen as a 16th-century counterpart to the 13th-14th
century alternation of stable trines with unstable sonorities of
various sorts. It is, of course, a much more "delicate" contrast, a
gentle swaying between the more sonorous 5/M3 or 5|M3-m3 (major third
below) and the somewhat less sonorous and conclusive 5/m3 or 5|m3-M3.

One way of looking at this aspect of harmony would be to say that
16th-century tonality is more "fluid" with its continual alternation
of major and minor triads, while 18th-19th century key tonality is
more "polarized," with major keys tending to dwell more persistently
on major triads, and minor keys, minor triads.

A related aspect of style is the greater variety of harmonic motions
typical in Renaissance as opposed to typical key harmony: in the
earlier variety of triadicism, bass motions of a second or third often
roughly balance those by a fourth or fifth. Around 1610, Giovanni
Coperario teaches four-part harmony by cataloging progressions
according to the motion of the bass by a second, third, or fourth,
etc., after first noting as one of the introductory rudiments of music
that at closes the bass generally falls by a fifth, or rises by a
fourth.

The Dutch harpsichordist and just intonation exponent Peter van
Marissing has intriguingly suggested to me in personal correspondence
that bass progressions in thirds may have a certain affinity to
Renaissance meantone with its pure or near-pure thirds, while the
pervasive emphasis on motions by a fifth or fourth in later Baroque
through Romantic music might correlate with the fifth-leaning
tendencies of post-1680 well-temperaments as well as 12-tet. Certainly
the third-oriented harmonic progressions of the 16th-century are
characteristic (whether diatonic or chromatic), although one might
wonder about the directions of the interactions involved between the
shift toward key tonality and the shift from meantone to
well-temperaments in the later 17th century.

Such possible tonality-tuning correlations aside, an important point
here is that "5-limit" harmony or a close approximation
(e.g. Renaissance meantones, 31-tet, 19-tet) with its contrasting
harmonic and arithmetic divisions of the fifth -- or major and minor
triads -- or otonal and utonal sonorities in a Partchian sense --
lends itself either to modal or key-based tonality.

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4. Renaissance progressions and Gothic traditions
-------------------------------------------------

Although there are many ways of realizing a modal tonality with
5-limit sonorities, 16th-century harmony more specifically often
features progressions between such 5-limit sonorities guided by
"3-limit" progressions borrowed from earlier Gothic practice.
Exercising due caution, I should emphasize that the following examples
represent a modern interpretation, not a connection between Gothic and
Renaissance cadences drawn by Renaissance theorists themselves.

Let us consider, for example, this very common 14th-century cadence:

g'-a'
d'-e'
bb-a

Here we have an M3-5 resolution between the two lower voices, and an
M6-8 resolution between the outer voices -- producing the total and
compelling result of an unstable M6/M3 or M6|M3-4 sonority expanding
to a complete trine.

In a four-part Renaissance setting, we often find the same M3-5 and
M6-8 resolutions, but with a difference:

d''-c#'
g' -a'
d' -e'
bb -a

Here the traditional M6-8 and M3-5 progressions still guide the
movement, but we arrive at a now-stable 5-limit sonority, the fourth
voice supplying a once-unstable major third, realized in a Renaissance
just intonation or in 1/4-comma meantone as a pure 5:4.

From this comparative point of view, let us consider another
characteristic 16th-century progression:

g'-a'
d'-f'
b -c'
g -f

From the perspective of overall sonority, we have a smooth progression
between two 5-limit harmonies. Looking at the lower three voices, we
have:

d'-f'
b -c'
g -f

These voices form a popular 13th-century cadence, the lower voices
resolving M3-5, and guiding expansion from an unstable 5/M3 or 5|M3-m3
to a complete trine. The fourth voice of the Renaissance progression,
again, changes the situation from an alternation between unstable
cadential sonorities and stable trines to a more subtle progression
between 5-limit sonorities, often guided by older 3-limit resolutions.

As it happens, both of these Renaissance progressions actually involve
a sequence of two harmonic divisions of the fifth, or major triads;
but a related kind of progression realizes the alternation of the two
divisions recommended by Zarlino as an ideal of good harmony:

a'-b'
e'-g'
c'-d'
a -g

Here the arithmetic division a-c'-e'-a' is followed by the harmonic
division g-d'-g'-b', with an m3-5 resolution between the two lower
voices (for Zarlino, m3-5 and M3-5 are both options in multi-voice
writing, although he prefers the former in two-voice writing in order
to avoid a "nonharmonic relation" of the tritone arising from M3-5,
e.g. between f and b in a progression of g-b to f-c').

If we once again look at the lower three voices alone, we have:

e'-g'
c'-d'
a -g

This is another typical 13th-century progression, now with an unstable
5/m3 or 5|m3-M3 expanding to a complete trine by way of an m3-5
resolution between the lower voices. In the Renaissance version, the
fourth voice again transforms this progression into a more subtle
sequence of two third-plus-fifth-or-sixth sonorities, here with an
ideal alternation of arithmetic and harmonic divisions of the fifth.

Our discussion has been very sketch indeed, not considering, for
example, the role of the suspension, a vital resource in the 16th
century which Zarlino and others consider the essence of the best
cadences. However, even these examples may suggest some of the ways in
which traditional 3-limit resolutions interact with new 5-limit
sonorities to yield unique and beautiful progressions.

---------------------------------
5. Implications for tuning theory
---------------------------------

Theorists such as Easley Blackwood and Paul Erlich, approaching a
variety of tuning systems, seem to take 18th-19th century key systems
as a point of orientation. Their invaluable contributions shed light
on one part of the problem -- while leaving other approaches open to
exploration.

If we take the transition between "3-limit" and "5-limit" systems in
Western Europe as falling somewhere around the late 15th century, say
arbitrarily at about 1482 (the date of Ramos's treatise proposing 5:4
and 6:5 thirds), then the history of 5-limit harmony in this tradition
might be very crudely bifurcated into divisions of roughly 1482-1682
(modal harmony, meantone temperaments for keyboard) and 1682-1882 or
so (key harmony, well-temperaments for stringed keyboards rivalled at
the end of the era by 12-tet). Shortly after 1882, we move into
Debussy's experiments with what might be regarded "post-key" and
"post-5-limit" structures and progressions; in some cases, "revivals"
of modal harmony.

Needless to say, these dates are conveniences; one might argue, for
example, that likely "5-limit" (i.e. meantone) tunings and
increasingly "5-limit-oriented" sonorities are associated with Conrad
Paumann's organ compositions around 1450. Similarly, during the epoch
of 1650-1680, an approximation to key-oriented tonality may have been
associated with modified meantone tunings not too far from some of the
formal well-temperaments documented starting with Werckmeister (1681
and later).

Whatever dates we choose, an important conclusion is that the 5-limit
modal tonalities of the Renaissance and Manneristic periods represent
a vital alternative to 5-limit key tonality. Both historical
practices, of course, are part of the source materials for
20th-century practice, and for the development of new tuning systems
and harmonic theories.

Most respectfully,

Margo Schulter
mschulter@value.net

Re: Renaissance 5-limit harmony: of modes and triads

🔗M. Schulter <mschulter@xxxxx.xxxx>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗Joseph L Monzo <monz@juno.com>