Hexachords & ficta - online resources?
Brian Link
just enough of music theory and history to be dangerous.
I'm pretty confident in resolving early rennaisance ficta questions.
Tritones = bad. Parallel fifths/octaves = bad.
Now I'm working with Machaut transcriptions, and am at sea.
Does anyone have a link to some online resource describing how to
navigate hexachords? Is that B really a B, or is it a Bb? Or do I just
need to go back to school?
BLink
"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled."
- Richard Feynman
John Howell
>As I've admitted before in this newsgroup, I'm a performer who knows
>just enough of music theory and history to be dangerous.
>
>I'm pretty confident in resolving early rennaisance ficta questions.
>Tritones = bad. Parallel fifths/octaves = bad.
>
>Now I'm working with Machaut transcriptions, and am at sea.
>
>Does anyone have a link to some online resource describing how to
>navigate hexachords? Is that B really a B, or is it a Bb? Or do I just
>need to go back to school?
Not necessarily, but there's a learning curve. I can't help with
online, but I would recommend Alan Atlas, "Renaissance Music,"
Norton, 1998. It's the replacement for the venerable Reese
Renaissance book, and it's awfully well written--something you might
like to have anyway. But Chapter 17--"Editing a Chanson: Musica
Ficta"--is a pretty darned good introductory explanation, and is
written as such. (Chapter 21--"Editing a Chanson: Text Underlay"--is
ALSO very instructive.) I do prepare my Early Music Literature class
to deal with hexachords and ficta long before we get to that Chapter,
but you should have enough background to understand it. Just forget
everything you learned in Music Theory classes!
First, you have to understand the hexachords--natural, soft, and
hard--and be able to analyze the INDIVIDUAL lines hexachordally.
(Start with chant; it's great practice.) That's your basic late
medieval/renaissance starting point. It's how the composers were
trained, it's how they wrote the music, and it's how the singers were
trained to add the necessary ficta. And you do that by spotting the
halfsteps, figuring out which hexachord they represent, and noting
when you have to mutate from one to another.
Regarding the B or Bb, it's most often altered when it's "una nota
super la"--one note above the hexachord which then turns back and
does not go any higher. (Dealing with "key signatures" is more
advanced, but that's ONE thing you won't run into in Machaut!)
Example: the tune to "Greensleeves." Assuming the key of d minor
and starting on D, the 5th note is very often raised to B natural in
19th and 20th century arrangements, because the arrangers were
thinking in terms of melodic minor scales. But in the 16th century
it would have been sung Bb because it is, in fact, "una nota super
la" in the natural hexachord, regardless of whether there was key
signature or not. (Hexachords and key signatures were INDEPENDENT
VARIABLES, except that renaissance key signatures generally indicated
transpositions of the modes (and therefore the hexachords). Which is
why baroque minor keys often have "too few" flats by modern
standards, because modern standards hadn't been established yet.)
However, just to further complicate things, the usual C# and B
natural at the cadences DO follow renaissance ficta rules for
under-third cadences!
Then you have to identify all the cadences: And that means MELODIC
cadences formed by any two voices moving from an imperfect consonance
to a perfect consonance, not a HARMONIC cadence (which did not yet
exist). That's the second use of ficta: adjusting one of the two
cadencing voices so that one of them moves by halfstep and the other
by wholestep. It's most often the rising voice that's raised (giving
you F#s and C#s and such), but the descending voice can also be
lowered (giving you Bbs and Ebs and such).
Those are the two basic uses of ficta in most early music. Parallel
5ths and octaves have nothing to do with it. What you try to avoid
is any combination that gives "mi" against "fa" in two different
hexachords (except in later English music, where they LIKED that
clash!). And you'll discover that there is a hierarchy of cadences
(no surprise there), some of which are more clearly-defined than
others by both the actions of the other voices and the underlay of
the text. My tendency is to prefer a more modal sound and to use
less ficta. Wili Apel's generation tended to sprinkle Bbs all over
the page if there was even a single Bb anywhere. It becomes a matter
of personal taste, as does whether to use ficta at cadences in a
third voice to give a "double leading tone" cadence (the actual
"rule" for which is to avoid the tritone you would get if you did NOT
raise that third voice), which I would definitely consider doing in
Machaut, Dunstable and DuFay, but possibly not in Josquin. (By his
time you could no longer avoid all tritones, just pick among them.)
Oh, and since barlines didn't exist, and neither did modern barline
conventions, sometimes you have to back up from an altered cadential
ficta note and alter any immediately preceding notes on the same
pitch as well, or alter an ornamental under-third note moving into a
cadence (the so-called and incorrectly named "Landini" cadence).
I got my basic training in all this, and the proper way to analyze
the music, in a summer session at Stanford many years ago. Putnam
Aldrich was in charge, and about to retire. Lyle Nordstrom was his
GTA. I don't think George Houle was there that summer, or he might
have come in late in the session, but I think Herb Meyers was another
GTA. It was a WONDERFUL immersion in early theory, not to mention
renaissance dance steps, but challenging to learn it all, and I've
been using it in my own editing ever since. Nineteenth-century
harmonic analysis simply doesn't make any sense prior to the Period
of Common Practice, and sometimes not even then, since the concept of
functional harmony took a while to develop. And I believe George
Houle also wrote a very clear explanation of all this, aimed at
performers, in his edition of the various versions of a certain
renaissance chanson, but I can't remember which one it is!
And then there's Mendel and his "secret chromatic art"!!!! But MOST
of the time the proper use of ficta is pretty clear, unless the
composer was showing off and doing something weird (which they DID!).
John
--
John R. Howell, Assoc. Prof. of Music
Virginia Tech Department of Music
College of Liberal Arts & Human Sciences
Blacksburg, Virginia, U.S.A. 24061-0240
Vox (540) 231-8411 Fax (540) 231-5034
(mailto:John....@vt.edu)
http://www.music.vt.edu/faculty/howell/howell.html
"We never play anything the same way once." Shelly Manne's definition
of jazz musicians.
Brian Link
As always you are such an invaluable help, as is rec.music.early. I
dread the day when they pull the plug on nntp - but at least I have
your email address =)
Even before my stint at IU with Binkley, I did at least grasp the idea
that ficta pre-1500 or so depended on the individual line. We did an
Ockeghem mass in Pro Arte with him where all we had were un-barred
parts (Missa Sine Nomine). He talked about the mass "cuiusvis toni",
which is pretty much an exemplar of the stuff we're talking about, but
I barely glimpsed the implications..
The thing that's always confused me is how a singer could tell which
hexachord they were in. But then, those singers weren't given a
specific text underlay either..
It's really hard for the average 21st century musician to not think in
terms of harmony. One thing I've grasped in directing the Machaut is
that the style takes the shape of
1. opening consonance (fifths or octaves) held for a bit
2. lots of movement leading to
3. an intermediate dissonance (thirds or non-root) followed by
4. more interesting movement leading to
5. a cadence on the basic consonance.
... repeat 2-4 at will. It's not a musicological analysis, but telling
the choir this does at least give them a framework from which to think
about this very unfamiliar music. With that in mind, folks seem to
realize that if they're holding a chord with a major 3rd, it means
they're not finished with the phrase yet.
One thing has cheered me through this process - I have a really
earnest group of volunteer, semi-pro and pro singers and we
communicate well. 25 voices doing the Notre Dame mass may not be
historically defensible, but it sounds pretty cool.. =)
BLink
On Fri, 30 Oct 2009 01:00:21 -0400, John Howell <John....@vt.edu>
wrote:
--------------------------
"The worst thing about censorship is [redacted]"
John Howell
>John,
>
>As always you are such an invaluable help, as is rec.music.early. I
>dread the day when they pull the plug on nntp - but at least I have
>your email address =)
And please, never hesitate to use it!
>The thing that's always confused me is how a singer could tell which
>hexachord they were in. But then, those singers weren't given a
>specific text underlay either..
In the former case, it's the way they were trained. If you spent
your student years solmizing chant melodies, it gets to be second
nature. Guido invented his hexachordal system because he was
assigned to be a music educator, NOT because somebody labeled him a
"music theorist," and don't ever forget it. (He sold it to the Pope
as being a way to ensure that the true 'Roman' form of the chant
could be disseminated and known throughout Christiandom, but he told
US that it was because it cut the training time for his choirboys
from 10 years down to 2!) And his system was so good that it was
still in use 600 years later. (Check out Thomas Morley, "A Plaine &
Easy ...")
And we also know, from a writer who claimed to have studied under
Josquin, that the first thing he did with a new choir was to teach
them how to set the words to the music. So if HE, as a composer,
could teach it, he had rules, and if he had rules, we can extrapolate
them. (Atlas goes into that in his Chapter on text underlay.)
>
>It's really hard for the average 21st century musician to not think in
>terms of harmony.
Sure. We can't turn off our ears. But we CAN learn to think, as far
as possible, they way they thought back then, and it's pretty clear
that in at least the high class music, they thought in linear terms,
and with no barlines to get in the way, in terms of individual
melodic shapes in the individual lines. Think of 16th century
polyphony in terms of combining individual lines of chant, with their
alternating groups of 2s, 3s and 4s, and it probably comes pretty
close to they way they thought. That's why I get rid of the barlines
in a lot of my own editions.
All the very best! I certainly respect your desire to get everything
right, but in the end it always HAS to come down to personal taste.
Brian Link
I posted something to Facebook along these lines, and an old friend
responded with an anecdote he'd heard from Ben Bagby.
Bagby'd suggested that the choristers used the Guidonian hand like
Gameboys. Hyperactive kids learning the scales by frenetic
finger-jiggling. Having worked with boy-trebles, I can really picture
this.
On Fri, 30 Oct 2009 22:30:09 -0400, John Howell <John....@vt.edu>
wrote:
>At 6:25 PM -0500 10/30/09, Brian Link wrote:
John Howell
>Please forgive me for top-posting...
>
>I posted something to Facebook along these lines, and an old friend
>responded with an anecdote he'd heard from Ben Bagby.
>
>Bagby'd suggested that the choristers used the Guidonian hand like
>Gameboys. Hyperactive kids learning the scales by frenetic
>finger-jiggling. Having worked with boy-trebles, I can really picture
>this.
Well, that's a very creative thought. But there's some question
about how much the "hand" was used. (I'm not saying it wasn't,
although for sure Guido didn't invent it, which would have placed its
genesis at some point after his death.) And while I don't know all
that much about hyperactivity, I do know that it's thought to be tied
into diet and foods and drinks with hyperglycemic indexes and other
modern things which simply didn't exist in those previous centuries.
But it's a lovely mind picture!
Margo Schulter
> As I've admitted before in this newsgroup, I'm a performer who knows
> just enough of music theory and history to be dangerous.
>
> I'm pretty confident in resolving early rennaisance ficta questions.
> Tritones = bad. Parallel fifths/octaves = bad.
Dear Brian,
Please let me apologize for another thread where I should have been
keeping up with the group and offering a timely reply rather than
one the next year (although still, arguably, in the same decade, if
one defines this as 2001-2010).
The rule against parallel fifths and octaves applies fairly
consistently starting around the mid-15th century. In the earlier
15th century it starts applying more consistently in multi-voice
pieces, but with important liberties like this type of cadence
(standard in the 14th century) where a major sixth and major tenth
expand to octave and twelfth:
G# A
C# D
E D
The tritone question is also sometimes rather subtler than the
rules against "mi contra fa" might suggest, but that could be
a long discussion.
> Now I'm working with Machaut transcriptions, and am at sea.
>
> Does anyone have a link to some online resource describing how to
> navigate hexachords? Is that B really a B, or is it a Bb? Or do I just
> need to go back to school?
To what John has said, I might add that one online resources is the
Early Music FAQ edited by Todd McComb, which has a page on the topics
of interest, with some material on the 14th century:
<http://www.medieval.org/emfaq/harmony/hex.html>
I'll reply to another of your posts on Machaut, also.
Best,
Margo
msch...@calweb.com
Margo Schulter
>
> It's really hard for the average 21st century musician to not think in
> terms of harmony. One thing I've grasped in directing the Machaut is
> that the style takes the shape of
> 1. opening consonance (fifths or octaves) held for a bit
> 2. lots of movement leading to
> 3. an intermediate dissonance (thirds or non-root) followed by
> 4. more interesting movement leading to
> 5. a cadence on the basic consonance.
Hi, Brian.
From the viewpoint of a possibly very weird 21st-century musician,
the idea is to hear and think in a different system of verticality:
1. In writing for three or four parts, the complete trine (outer
octave, lower fifth, upper fourth, e.g. D-A-D) is the standard of
stable euphony; pieces often begin generally end on this sonority,
or on its prime consonance of the fifth (less sonorous than if the
octave and upper fourth are also present, but still richly stable).
2. The most powerful and compelling cadences have unstable sonorities
resolving to a complete trine or its prime consonance of the fifth --
or sometimes to a trine-like sonority featuring the twelfth rather
than the simple fifth. The most effectively directed resolutions
involve progressing by _stepwise contrary motion_ from an unstable
to a stable interval. In the 14th century, "modern" theory emphasizes
the 3-1, 3-5, 6-8, and 10-12 resolutions; but for Machaut and some
other composers of this era, traditional 13th-century resolutions
like 2-4 and 7-5 are still part of the style, despite the "modern"
view that seconds and sevenths are too dissonant to be used boldly
in this manner.
Note also that some "near-conjunct" resolutions of the 13th century
occur in this era, also, e.g. 2-5 or 9-12. Machaut, like earlier
composers from Perotin around 1200 on, has quite a taste for the
major ninth, which as Anonymous I and Jacobus of Liege (likely the
same writer) note around 1300-1325, becomes especially concordant
(although still unstable) if it is the outer interval in a sonority
with two euphonious fifths, e.g. G-D-A.
One area where Machaut follows a modern, 14th-century practice is
in following the rule of "closest approach": one way of putting this
is that major intervals generally expand to their cadential resolutions,
while minor ones contract, in progressions by stepwise contrary motion.
Thus min3-1 but Maj3-5; Maj6-8; Maj10-12; Maj2-4; and min7-5. This
principle of closest approach in directed progressions (not necessarily
"cadences" in the sense of ending a phrase or section of the piece)
is a very fertile source of accidental alterations.
Putting this together, here are some typical three-voice progressions.
Note that while a three-voice resolution may very usefully be analyzed
as a kind of alliance or combination of two-voice progressions, the
alliance is a meaningful and unifying one, producing something greater
than the sum of the parts. We might say that the two-voice resolutions
"pull together" to the stable goal: the complete trine, fifth, or
sonority with an outer twelfth.
C# D B C G# D E F D C D C
G# A G F C# A D C B C G F
E D E F E D G F E F E F
Maj6-8 Maj3-5 Maj10-12 Maj2-4 min3-1 min7-5
Maj3-5 min3-1 Maj6-8 Maj6-8 min7-5 min3-1
3. A lot of polyphonic art involves the tasteful activation of
a listener's conditioned reflexes, so to speak: the delightful
_anticipation_ of a directed progression, often fulfulled but
sometimes thwarted. Since inflections (especially sharps) in
one or more open voices often signal the forming of a "closest
approach" sonority moving toward a stable resolution, Machaut
and his contemporaries can add to the listener's delight by
making an inflection which doesn't immediately resolve as
expected, causing a bit of suspense and whetting the appetite
for more.
Sarah Fuller has written some wonderful articles on this facet
of Machaut's style, which is much in accord with the early
14th century composition and theorist Marchettus of Padua, who
recommends sometimes making a "feigned color," meaning a deceptive
accidental alteration that doesn't resolve as expected. While this
theorist discusses an idiom which may be more relevant to his own
early 14th-century Italian setting than to Machaut, the general
idea of using inflections that suggest, but don't always lead to,
a direct resolution is very much a part of Machaut's technique!
4. There seems to a scale of consonance/dissonance in Machaut
which reflects a mixture of 13th- and 14th-century concepts,
blended most happily and often adventurously! Here's one take:
(A) The complete trine, simple fifth, or outer-twelfth
sonority (most richly a complete trine plus a twelfth,
as often in his Mass for four voices) is the stable
basis of the style, although endings on bare unisons
or octaves may occur in multi-voice pieces (e.g. _Ma fin_)
as well as two-voice pieces.
(B) The "split fifth" sonority with an outer fifth divided
into a major third below and minor third above, or vice
versa (e.g. G-B-D or E-G-B) is the mildest unstable
sonority, sometimes resolving to a fifth or trine, and
sometimes used for variety and color without any direct
resolution. For example, in a directed context, G-B-D
to F-C (stepwise contrary motion in all voices) or
F-C-F (highest voice leaps up a third).
(C) A mild "sixth combination" with a sixth above the lowest
voice, typically in connection with a third and/or tenth,
is also relatively concordant, and typically invites a
direct resolution to a complete trine -- or, if the tenth
is present, an outer-twelfth sonority, e.g E-G#-C# to
D-A-D, or E-G#-C#-G# to D-A-D-A. In a directed context,
the thirds, sixths, and tenths are generally major, with
inflections if necessary -- closest approach!
(D) Also pleasantly concordant, although with a stimulating
element of tension, are 13th-century sonorities that the
14th-century "moderns" would often prefer to avoid or
reserve for incidental ornaments: the "split ninth" with
two euphonious fifths, F-C-G or G-D-A; and sometimes
an outer fifth with a fourth and major second, C-F-G
or C-D-G. Machaut sometimes also has an outer minor seventh
"split" into two fourths, e.g. D-G-C; but in a 14th-century
setting where the consonant nature of the fourth is often
more equivocal than that of the fifth, he may favor it less
than Perotin and some other composers of the 13th-century
era.
(E) In accordance with 13th-century theory and practice, Machaut
favors sonorities, often directed, which may be described as
"relatively tense but somewhat concordant or compatible"
combining major seconds or minor sevenths with more mildly
unstable thirds and sixth, and frequently inviting directed
resolutions. Examples are G-D-E to F-C-F (a kind of
alternative to the more common G-B-E to F-C-F) with the
upper major second expanding to a fourth; and E-G-D to F-C
(with the outer minor seventh contracting to a fifth).
(F) Sonorities including a minor second or major seventh may be
considered more acutely or strongly dissonant, as also those
with a vertical tritone or diminished fifth -- but that
doesn't mean that these sonorities might not occur, and
sometimes boldly.
For someone coming from a background in 15th-19th century counterpoint
and harmony, the following hints might be helpful -- although feedback
would be useful in seeing if my intuitions are right:
* Yes, a complete trine and its variants are richly
stable and conclusive sonorities! People attuned
to other world musics where such sonorities are
favored, or to "quartal" styles in jazz, may find
this territory not too unfamiliar.
* Likewise, categories (B) and (C) are indeed unstable:
and being able to _feel_ their instability, and
_anticipate_ likely resolutions (especially when
those suggestive inflections occur), is critical
to appreciating cadential action and the long-range
structures that are shaped by its direction (and
artful indirection also).
* Categories (D) and (E), in the 13th century or in
a 14th-century composer like Machaut, have a proven
potential for driving conventionally-oriented analysts
crazy! While its possible to do lots of editorializing
about this, the best antidote is to get accustomed
to the musical language as it is, and discover how,
in practice and theory, it's beautifully apt and
expressive. In fact, much of what's going on here
is analysed by Jacobus of Liege early in the century.
He describes, for example, the appeal of the "split
ninth" sonority and the option of a minor seventh
resolving to fifth, as notably happens in Machaut's
_David_ hocket.
5. In a larger structure, it's very common to have an intermediate
cadence or "pause" taking one of two forms. The first takes advantage
of the contrast between two kinds of closest approach progressions.
Typically, final cadences are _intensive_, with _ascending_ semitones.
E F G# A E F D C
B C E D D C B C
G F C# D G F E F
In contrast, one favorite intermediate cadence has _remissive_
resolutions involving _descending_ semitones:
D E D E D E F E
A B Bb A C B Bb E
F E G A F E G A
This a common scheme is to have a remissive progression as an
intermediate cadence, and an intensive final cadence. Some
typical schemes might include (and surveying Machaut on this
point might be fun):
Rem.... Int Rem.... Int Rem... Int
G A E F D E C# D G A F# G
D E B C A B G# A D E C# D
Bb A G F or F E E D or Bb A A G
Of course, a composer may interpose and play with lots of other
actual or "suggested and then diverted" cadential centers, so
this is just a sample of what you might find.
Another technique is to end a section on a mildly unstable
sonority of the (B) or (C) type as listed above, often
suggesting a resolution which might follow immediately,
or after some delay, or possibly might get diverted completely
to some other direction. When a (C) sonority with the sixth
is used, sometimes the expected resolution follows as a matter
of course in forms with repeats or returns to the beginning.
For example, suppose our main center is D-A-D, and we open
on that trine, and later have a section concluding, or really
pausing, on E-G#-C#. Returning to the opening D-A-D, we have
a completed cadence -- leading into more musical action.
This is a form of interrupted cadence -- maybe just interrupted
for a moment before the following section brings a welcome
resolution, and maybe leading into some delightful diversion
so that there's a bit of creative tension for the listener
until the next satisfying cadence in an expected or unexpected
direction.
> ... repeat 2-4 at will. It's not a musicological analysis, but telling
> the choir this does at least give them a framework from which to think
> about this very unfamiliar music. With that in mind, folks seem to
> realize that if they're holding a chord with a major 3rd, it means
> they're not finished with the phrase yet.
This is quite correct as far as it goes: while a lot of learning
is through experience, filling in some concepts about the usual
sonorities and resolutions may help, if to provide an
alternative "map" to other constructs people may have which can
result in confusion or "language interference" as linguists
might call it. Maps may be helpful, but the actual aural terrain
is the thing!
> One thing has cheered me through this process - I have a really
> earnest group of volunteer, semi-pro and pro singers and we
> communicate well. 25 voices doing the Notre Dame mass may not be
> historically defensible, but it sounds pretty cool.. =)
Since from my college days (c. 1970) I recall that there was at
least one colorful 14th-century description of a rather large
ensemble of musicians, maybe more as a literary figure than as
report of what was usually done, you might justify this kind
of performance as "poetic license."
With many thanks,
Margo Schulter
msch...@calweb.com