Re: Re[2]: Patch: figured bass. [Comments wanted]

[Juergen Reuter]

On Mon, 10 Sep 2001, [ISO-8859-1] J?r?mie Lumbroso wrote:

> Hi Juergen,
> 
> 
> JR> Figured bass notation does not at all encounter harmonics, it just gives
> JR> fingerings relative to the bass note.  For example, if you have a chord
> JR> <c f a>, then the bass note "c" is engraved as note, and the fingering
> JR> numbers are:
> JR> 6
> JR> 4
> 
> JR> In other words, I see two possibilities of syntax: either you specify all
> JR> notes like in <c f a>.  Then lily has to separate the bass note
> JR> (i.e. the deepest note) c from all other notes (in the example, f and a).
> JR> The c is printed, and the f and a result in figures 4 and 6 (as counted
> JR> relative to the c), respectively.  After that, you have to apply some kind
> JR> of normalization, that should be done in scheme.  For example, the figures
> JR> "3 5" are normalized into the single figure "5", since the "3" is, by
> JR> default, always played, unless it dissonates (as in "3 4", which will stay
> JR> "3 4" after normalization).  There are roughly a dozen of such
> JR> normalization rules.
> 
> I really don't want to be rude, but you obviously have abso-
> lutely  no idea what you are talking about. Figured bass has
> nothing  to do whatsoever with fingering chord relative to a
> bass note. I'm guessing you just read this out of a book. If
> all this was about is putting chords out, why the heck would
> any body prefer writing numbers instead of the plain chords?
> I don't even know why you used the word "fingering" to refer
> to it.

Maybe use of the term "fingering" in this context is misleading.
Of course, I did not mean the numbers to represent the player's
fingers, but rather number of (diatonic) keys between the fingers
(i.e. intervals).  What I wanted to stress is the contrast to chord
notation as used today: The note that is written out in continuo is not
necessariliy the fundamental tone (is that the right english term?) of the
chord, as e.g. "c" in <c e g> or <e g c> or <g c e>.

For example, if you encounter a "c" written out, the resulting chord may
be a <c e g> (which is C chord in modern notation), namely if there are no
figures ("3" and "5" dropped by normalization).  But it also may be an
inversion of <a c e> (in modern notation, Am), namely if the figures are
"6" (once again, "3" is dropped here).  Similarly, it may be
an inversion of <f a c> (in modern notation, F), if the figures are "4 6".

So, while in modern chord notation, you write down the fundamental
tone plus *modifications* to be applied (just as C7 means <c e g> plus
additional bes as modification, or Dm is <d f a> rather than <d fis a> as
in D), the figured bass does not encounter fundamental tones, and hence
ignores *functional* harmonics completely (a term, as far as I
know, that arose not earlier than in the middle of the 18th
century).  Figured bass is just a means of compressed notation, with the
figures telling you where to put your finger rather than telling you the
inherent functional harmonics of the pice of music.

> 
> I'll  be  plain and simple. You are right, as I've explained
> previously,  figures indicate chords relative to the note in
> the  continuo (which is indeed, in most case the lowest note
> BUT  not  always:  I have examples of hands meant to cross).

That's interesting.  I've never heard of that.

> They  indicate a chord, but if you went out there and simply
> plucked  those chords, with the left hand playing the conti-
> nuo, you'd look bad. They're just there to tell to you which
> harmonies  to  use, but then, it's left to the player to im-
> provise  his  own  right  hand (usually by inspiring himself
> from the tunes he is accompaning).

Of course, but are you sure that freedom reaches so far as to play notes
below the bass note?  Why then is it called *basso* continuo or figured
*bass*?

> 
> I just realize you must have the modern definition (which is
> way  different from the baroque definition, as nowadays,  a-
> part from harpsichordist and organists, nobody is capable to
> improvise figured bass).
> 

I have the definition that we learnt in school when we studied baroque
pieces tried to write up a fully-fledged version of a continuo (in German
language, this is called "aussetzen" (to put out); I do not know the
proper English term).

> 
> 
> JR> Please also note that the conversion from figures to notes is not unique,
> JR> since it allows chord inversions.  The conversion from chords to figures
> JR> is, as far as I know, more or less unique.  "Less" means, that ornaments
> JR> are dropped when converting to figures; but they were anyway notated
> JR> sparsely in baroque music (which is the domain of figured bass).
> Never  were  there ornaments in figured bass, it's extremely
> rare a composer explicitly tells the executer that he has to
> ornate  such note. It's left to the performer, to create his
> own  tune. Ornamentation was NOT spare at all. D'Anglebert's
> music  pages  were  litterally (I mean it) darked with orna-
> ments! Just looking at his table will give you hint (most of
> it  was  copied by Mats in the trills.ly file).

I totally agree.  I just wanted to say that, from a technical point of
view, if a lilypond user puts in ornaments, they would have to be somehow
stripped off before generating figures.

> I'm against,
> and  always will be converting notes into figures. Most peo-
> ple  (including  me) will want to directly include their fi-
> gures (and note pass my some imprecise second mean).
> 

I agree in so far, as composers of the baroque period most probably
thought in terms of figured bass rather than in terms of what finally come
out during performance.  In particular, the piano part (or cembalo part,
if you like) mostly contains a fully written-out version that has been
added by some editor, while the original manuscripts almost always
contained the figured bass only.  However, it might be an interesting
challenge to enter both, a figured bass and a fully-fledged cembalo part,
and to let lily it automatically check the cembalo part against the
figured bass for consistency.  This is, why converting notes into figures
may be intersting.

Greetings,
           Juergen