Re: Landini cadence and "closest approach" (for Bob Valentine)

Hello, there, Bob Valentine, and thank you and Joseph Pehrson for your
kind words about www.medieval.org, the Early Music FAQ site of the
Medieval Music and Arts Foundation, edited by Todd McComb. This FAQ
includes the article on the Landini cadence mentioned in this thread,

http://www.medieval.org/emfaq/harmony/landini.html

You raised a very important point about "closest approach" and the
Landini cadence whose ramifications I realized only after my initial
reply, Your musical observation was a very insigntful one, and I hope
that I can do it more justice below.

> I just got a whole mess of CDs from the list on the medievel
> site. Great stuff and exactly what I was looking for. Regarding the
> first cadence, One thing I hear done sometimes is a sort of
> apogatura-kind-of-thing (to get scientific) where it goes

> E4 D4 F4
> B3 C4
> G3 F3

This is a very common 14th-15th century idiom, sometimes found in the
13th century and also in some later Renaissance/Manneristic pieces,
called a "Landini cadence," with an unstable major sixth momentarily
moving down to the fifth before the expected resolution which would
have occurred if the sixth had simply expanded conjunctly to an
octave.

The term I use for the momentary tone D4, or the vertical fifth G3-D4
or the overall sonority G3-B3-D4 in which it participates, is an
"antimediating" tone or sonority, as I'll explain shortly -- a
category for which the Landini cadence may be an especially familiar
example. Note that my terminology focuses specifically on Gothic and
neo-Gothic music.

> Now I hear it in tonal terms somthing like VII- II I which is
> unusual but right on target for a harmonic cadence in lydian (not
> that the authors were thinking in those terms). You could do the
> same thing with the second cadence.

Please let me begin by saying that there are many ways of hearing,
often with rich and surprising associations. For example, I once heard
a Burmese song called _The Southern Island_ which reminded me very
much of Machaut in a delightful way. The album notes said something
like this: "A typical Burmese chord consists of the raised fourth and
seventh, resolving into the fifth and eighth degrees."

From a stylistic or specifically intonational view, I would emphasize
that in a typical Gothic setting either G3-B3-D4 or G3-B3-E4 is an
inherently unstable sonority, and that the complex thirds and sixths
of Pythagorean tuning tend to reinforce this musical tension.

With G3-B3-D4 we have a _quinta fissa_ sonority, or fifth "split" by
the middle voice into two mildly unstable thirds (5 + M3 + m3,
64:81:96, a rounded 0-408-702 cents). WIth G3-B3-E4 we have a major
sixth sonority with major third below and fourth above (M6 + 5 + M3,
64:81:108, 0-408-906 cents).

Both these sonorities have G3 as the _fundamentum_ or "foundation,"
and both frequently resolve to a complete 2:3:4 trine on F, F3-C4-F4.

In a 14th-century Landini cadence, I would say that the pull of the
major sixth toward the octave is such a basic and compelling
progression that indeed the sixth is more the "main" interval, and the
fifth more like a decorative element.

In my view, a "harmonic/nonharmonic" dichotomy may oversimplify the
interactions between vertical and melodic elements in 13th-14th
century styles, just as Ludmilla Ulehla has cautioned about the
problems of attempting systematically to apply such categories to
20th-century European and related styles.

However, it is possible to devise categories which recognize both the
melodic motivations for a given note or sonority and the directed
vertical resolution to which this note or sonority may give rise.

In explaining why I call the Landini cadence a kind of "antimediating"
figure, I should explain that the progression from fifth to octave by
way of an unstable major sixth is very common in Gothic music:

D4 E4 F4
G3 F3

5 M6 8
3:2 27:16 2:1
702 906 1200

Here the major sixth G3-E4 "mediates" between the stable fifth and
octave, at once making it possible to move between these intervals
with purely stepwise motion in the upper voice (D4-E4-F4), and
introducing the vertical element of directed instability, the sixth
expanding to the octave by stepwise contrary motion.

Here are some other examples of mediating tones and sonorities
approached obliquely and resolved by directed contrary motion:

E4 D4 C4 G3 B3 C4 A3 B3 C4
E3 F3 G3 F3 A3 F3

8 m7 5 1 M3 5 1 M2 5
2:1 16:9 3:2 1:1 81:64 3:2 1:1 9:8 3:2
1200 996 702 0 408 702 0 204 702

In the Landini cadence, however, we have a "time-reversed" version of
the 5-6-8 figure with the mediating sixth:

E4 D4 F4
G3 F3

M6 5 8
27:16 3:2 2:1
906 702 1200

The term "antimediating tone/sonority" for the note D4 and the
sonority G3-D4 -- the melodic and vertical dimensions of this M6-5-8
idiom -- may suggest that the decorative fifth at once makes the
resolution from major sixth to octave a bit _less_ direct and
"efficient," and makes the upper part _less_ conjunct. Putting this
another way, we have a momentary diversion from the expected
consummation of M6-8, and a very graceful melodic figure of the third
D4-F4 in the upper voice.

> Is the use of the D just an embellishment? Was it common, as it
> seems to go against closest approach (and I know they don't do the
> E4 D4 E4 F4 sequence that you would hear if it was a V I cadence a
> few centurys later).

After my first and rather hasty reply, I realized that while there
isn't a conflict with the "closest approach" principle as defined in
the 14th century (and later), you have most insightfully pointed out
an issue of what I might call "most direct or efficient approach."

Here a look at some three-voice cadences common in the 13th century
may be helpful.

As discussed above, I would regard the major sixth of the Landini
cadence as the more "basic" interval, and the antimediating fifth as
more decorative. However, to place this idiom in perspective, we
should note that all of the following are common in the 13th century:

E4 F4 D4 C4 D4 F4
B3 C4 B3 C4 B3 C4
G3 F3 G3 F3 G3 F3

(M6-8 + M3-5) (M3-5 + m3-1) (M3-5)

As it happens, all of these cadences on F fit the 14th-century
"closest approach" rule, which says this: "A third expanding to a
fifth, or a sixth to an octave, should be major; a third contracting
to a unison should be minor."

However, your question may relate to what I call "most direct
approach." In the first or second cadence, every unstable interval
resolves by stepwise contrary motion, the most efficient or direct
resolution possible.

In the third cadence, however, the minor third between the two upper
voices of G3-B3-D4 resolves instead by similar motion to the upper
fourth of the trine F3-C4-F4. This choice might be motivating by a
liking for the melodic minor third in the highest voice, and also by a
desire to arrive at more complete and sonorous trine rather than the
simple fifth F3-C4 of the second cadence with "most direct approach."

With the Landini cadence, we have more of a partial qualification to
"most direct approach" -- the major sixth does resolve to the octave,
but not without the more or less momentary diversion of the
intervening fifth.

For example, one early 14th-century treatise, maybe one ascribed to
Philippe de Vitry or a student, declares that "the major sixth
proceeds to the octave, and without fail" -- a bit of an
overgeneralization, but a very nice statement of a general
expectation.

Marchettus of Padua, in 1318, likewise discusses the use of a "feigned
color" or deceptive cadence in which the major sixth does not expand
to the octave, but contracts to a fifth by a progression in stepwise
contrary motion involving a direct chromatic semitone. This is the
exception that proves the musical rule, we might say.

The Landini cadence, by contrast, seems a gentle and graceful
decoration of the basic M6-8 resolution. It embellishes rather than
obscures the directed cadential action.

There are some fine points I could add on questions of degrees of
consonance and intonation, but this is already a long reply.

In fact, my main concern is that I don't want the length to inhibit a
very engaging dialogue, and I'd emphasize again that there are many
ways of hearing and analyzing.

Most appreciatively,

Margo Schulter
mschulter@value.net