Re: Reply to Joe Monzo, on tritones and Mark Lindley

Hello, there, and here are replies to a couple of points from Joe
Monzo in our continuing dialogue.

>> Many chants also have prominent tritone relations, e.g.
>> between F and B-natural in G Mixolydian (Modes 7 and 8, or
>> _tetrardus_).

> Well... of course we can't be certain about what happened
> in practice, but indications are that the B-natural in these
> modes was frequently, or perhaps virtually always, altered thru
> _musica ficta_ to a Bb.

While Bb may _sometimes_ occur in chants and monophonic songs centered
on G Mixolydian, I agree with such scholars as Gordon Anderson that
melodic figures with tritonic outlines such as B3-A3-G3-F3-G3 are
characteristic of this family of modes, and need not be altered.

In later medieval discussions of chant, the view is sometimes
expressed that Bb is most common in tritus or Lydian on F, rather
common in protus or Dorian on D, less common in deuterus or Phrygian
on E, and least common in tetrardus or Mixolydian on G. One could look
into distinctions between authentic and plagal modes, also, but this
is a rough summary.

This discussion also raises a fine point about the medieval and
colloquial modern senses of _musica ficta_. In the latter usage, it
often simply means "unwritten accidentals inferred by the performers,"
a sense including an added Bb, for example to avoid a tritone.

In a medieval sense, however, _musica ficta_ means any use of a note
foreign to the usual _musica recta_ gamut which includes the seven
diatonic notes plus Bb, whether by express indication in a manuscript
or by a performer's inference. Thus adding an unwritten Bb to a chant
would in this medieval sense be an exercise in _musica recta_, while
an F# expressly indicated in a 14th-century manuscript would be
_musica ficta_ (although not in the modern sense of an "inferred"
accidental).

It gets even more involved: thus either B or Bb is normally _musica
recta_ because both notes are integral to the gamut or hexachord
system; but the Bb immediately above Gamma Ut (more or less equivalent
to Bb2, without any suggestion of absolute pitch) is _ficta_ because
it's not part of any recognized standard hexachord.

I mention this because it's quite normal for both senses of _ficta_ to
come up in discussions of this kind.

> PS - Please give the citation for Mark Linley's study of
> 14th-century keyboard music. I'm fascinated.

Here are some works of Mark Lindley on the topic of medieval and
Renaissance intonation, and there are more on topics such as early
meantone tunings that I could add:

Lindley, Mark, 1980a. "Pythagorean Intonation and the Rise of the
Triad," _Royal Musical Association Research Chronicle_ 16:4-61. ISSN
0080-4460. A germinal source, this article explores the artistic and
expressive value of Pythagorean tuning in a 13th-14th century Gothic
context, and then presents both theoretical and musical evidence for
an ingenuous modification of this tuning around 1400 to suit a new
stylistic leaning toward more blending thirds (see also Section 4.5 of
this article).

Lindley, Mark, 1980b. "Pythagorean Intonation," _New Grove Dictionary
of Music and Musicians_ 15:485-487, ed. Stanley Sadie. Washington, DC:
Grove's Dictionaries of Music. ISBN 0333231112. This short article
gives a handy summary of Lindley's longer study on "Pythagorean
Intonation and the Rise of the Triad" (see previous item).

Lindley, Mark, 1980c. "Temperaments," _New Grove Dictionary of Music
and Musicians_ 18:660-674, ed. Stanley Sadie. Washington, DC: Grove's
Dictionaries of Music. ISBN 0333231112. This concise survey gives an
overview of developments from the late 15th century on, with a large
bibliography.

Most respectfully,

Margo Schulter
mschulter@value.net