From: roger@crux.Princeton.EDU (Roger Lustig)
Subject: Re: mutations, solmization in 18th century
Originator: news@nimaster
Reply-To: roger@astro.princeton.edu (Roger Lustig)
Organization: Princeton University
Date: Tue, 5 Jan 1993 18:31:31 GMT

In article <1993Jan5.044052.28723@news.cs.brandeis.edu> baltuch@binah.cc.brandeis.edu writes:
>Just when I thought I'd understood the system of Guidonian solmization,
>mutations and hexachords...

Ah pity da fool...

>First how I thought Guido's system worked: syllables ut (not do!), re, mi,
>fa, sol, la (six total, no ti) designate either C, D, E, F, G, A (hexachord
>of C) or G, A, B (=B quadro), C, D, E (hexachord of G) or F, G, A, Bb
>(=B molle), C, D (hexachord of F) while singing.

Right.  Worked just fine for the music of 1000 AD, and a little thereafter.
Note that this music was monophonic.

>One starts in one hexachord until encountering a note with no syllable
>and switches (does a mutation) _right_before_ (looks like the system required
>a bit of look ahead) on a pivot note, i.e. a note that belonged to (had a
>syllable in) both hexachords, by singing something like "syllable-of-pivot-
>-note-in-1st-hexachord syllable-of-pivot-note-in-2nd-hexachord" on the pivot
>note. So far so good. At least that's how I thought it worked.

Sounds about right.  

>Now I look into Tosi's "Observations on the Florid Song" (ca 1750) and it
>appears I was mistaken.

I'd say you made one mistake: taking everything seriously.  Tosi is 
describing something fairly simple and old-fashioned; moreover, he's
writing in Italy, where very little music theory of any kind tackled
the issues, problems, and categories of tonality as practiced in the 
1700's.  Tosi was describing the Old (and Official) way as taught for 
church use.

Note that in Germany, Mattheson and Buttstedt duked it out on tonality/
modality/solmization issues in the 17teens.  Later, Mattheson and Fux
corresponded -- to no great effect -- on the nature of mode.  You might
want to check out Joel Lester's book on early tonal theory.  (And catch
him in recital; he's playing really well these days.)

>Tosi writes Italians use (and should use) only ut, re, mi, fa, sol and la and
>rejects si as a French unnecessary novelty: "We Italians use only six
>syllables but those are sufficient for reading all the notes for those who
>know how to use them"

That's right.  Knowing how to use them includes not sweating any half-steps
that might cause problems if you took the system ultraseriously.

>"All the notes" in Guido's system is "all the diatonic notes plus Bb". Tosi's

Well, let's say "all the white-key notes plus Bb."

>"all the notes" it's likely could no longer be only those unless Tosi is
>pulling someone's leg, or was living way in the past. 

Tosi's theoretical tack, like that of his Italian contemporaries, was
indeed outdated.  But that's how they taught; singers learned to fill 
in the chinks any way they could.

>It's got to mean that by
>his time the system had been extended to hexachords on all of the eight
>pitches C, D, E, F, G, A, Bb, B or some other system was found to express
>chromatisms. Follow some guesses of mine based on the one basic guess that
>the system was indeed extended. (Implicit of course is the question, what is
>the right answer if my guesses are wrong) 

Well, hexachords other than the hard, natural, and soft ones (G,C,F) were
several centuries old by then.  Treatises of the Renaissance make this
clear: you can, if need be, select a hexachord on any note.  This practice
is one of the meanings of the term "musica ficta" -- in fact, the B flat
hexachord itself was often called "musica ficta," which makes sense, given
the percentage of ficta problems that involve Bb and Eb -- and leads to
the insight that musica ficta is not identical with chromaticism, but 
rather with an extension of diatonicism.  See Margaret Bent's _Diatonic
Ficta_ in Early Music History, v.4.  (She used to teach at Brandeis, btw.)

>First I felt I had to include Bb (an "honorary" diatonic note anyway) because
>Tosi writes E-la-fa which could only mean Eb and only if there is a hexachord
>on Bb. Of course that this is how altered pitches is expressed is a guess of
>mine to begin with but it's clear he does use E-la-mi when he means E natural.
>But this is not good enough: while it patches up the fa question it creates
>a new one as Eb is no la on any of the eight hypothetical hexachords.


>To have E-la-fa mean Eb one would have to assume that Guido's system had been
>extended to Gb, and as there's no a priori reason why Gb would be special,
>to all 21 notes, transforming it in effect into a "movable ut" system, except
>using only the six Guidonian syllables (no ti that is)
>
>But before taking such a bold step I think it's worth checking the basic
>guesses with anyone around here who'd know more, and in particular that guess
>that E-la-fa does in fact mean Eb (it's not very clear from the context)
>
>Another reason which would lead me to believe that this is in fact what
>Tosi meant is that with the eight proposed hexachords above one still
>could express only F#, C#, G#, D#, Bb and Eb, which would imply being
>limited in what one could solmize to only pieces going up to E major
>and Bb major, not to mention being forced to write chromatisms in a funny
>way sometimes.
>
>On the other hand I'm not sure then as to why he'd still use expression such
>as E-la-mi or E-la-fa and how you're supposed to choose the hexachord in terms
>of which you'd give the syllable of the note; he never writes E-all-syllables-
>-in-all-hexachords-containing-E 

Was Tosi really writing in 1750?  I seem to recall that he was a bit earlier, 
and that the translation into English came later.  (Sorry--all notes are
packed away right now.)  In any case, Tosi was using a system that was in
the process of crumbling.  

Roger