Ars Subtilior & Willaert files

Many thanks to Margo for her scholarly insights. I hope to try 'em
out before long. Interesting that Medieval thirds might be tuned
both Pythagorean for cadences and JI otherwise, at least according
to that one authority of the time.

However, note that I no longer have access to a TX802 (it was at
college) --although I do have a Kurzweil K2000 and Yamaha TX81Z in
my home studio.

Carl, I unfortunately have had trouble working with Scala, but it
might be easiest to have it generate pitch bend messages for my
existing MIDI file, rather than make a table on a synth and have to
remap the MIDI pitch numbers.

>Carl, I unfortunately have had trouble working with Scala, but it
>might be easiest to have it generate pitch bend messages for my
>existing MIDI file, rather than make a table on a synth and have
>to remap the MIDI pitch numbers.

Do you still have the 802?

A Scala-pitch-bent MIDI file should work too. Scala is
idiosyncratic, but not too hard to use really. Or, did you have
trouble getting it to run (Mac user, maybe)?

-Carl

Hi, there, Carl and Harold (whom I'm about to quote) and all:

> Many thanks to Margo for her scholarly insights. I hope to try 'em
> out before long. Interesting that Medieval thirds might be tuned
> both Pythagorean for cadences and JI otherwise, at least according
> to that one authority of the time.

Please let me thank you for your most gracious words as well as your
beautiful performances of this music, and add out of an abundance of
cation a clarification that both Christopher Page and I are here
addressing specifically the question of medieval _English_ intonation; for
Continental 13th-14th century music, regular Pythagorean tuning is the
usual keyboard solution.

As it happens, 12-equal isn't so far from Pythagorean, and thus a quite
reasonable compromise for your fine Ars Subtilior renditions, Harold.
Especially with brighter timbres (e.g. plucked ones), major thirds at 400
cents can sound quite active and exciting -- appropriate for this music,
although ironically the kind of effect which, for example, might have
made the harmonium when tuned in 12-equal not-so-popular for playing
European Renaissance-Romantic music based more or less on ratios of 5.

Thank you playing some of my favorites, and for capturing some of the
exquisite balance between the vertical and horizontal elements --
including, of course, the complex and sophisticated rhythms, as in the
Baude Cordier piece _Amans ames_.

I should add that I really loved the Willaert setting, which I learned is
in no less than seven voices! While I might simply have done this in
meantone (TX802 P04 for 1/4-comma with pure 5:4 major thirds), your
timbres were at once very appealing and (at least to me) stylistically
compatible with 12-equal. One could argue that there is also a
16th-century precedent for this kind of timbre/tuning accommodation: in
1581, Vincenzo Galilei (father of the astronomer Galileo) noted that
12-equal, which he considered a "perfect" tuning because of its symmetry,
was ideal for lutes, but on the harpsichord with its more "vehement" sound
production, 2/7-comma meantone (the favorite tuning of his former teacher
and frequent opponent in theoretical debates Zarlino) sounded better.

Anyway, you put together one beautiful performance: to me this seems like
maybe the more "traditional" side of Willaert, and I was reminded of the
style of some early 16th-century German songs by Senfl, for example, as
well as maybe some Spanish settings from the same epoch.

If I may ask, how did you record this music: by multi-track recording from
a MIDI keyboard, for example? Am I right that this could be done either by
recording each layer as audio output from the TX-802, or by capturing MIDI
keystrokes and then playing them back?

Carl: again, I would emphasize that the following scale from an English
treatise of 1373 on organ design is simply one possible answer to how
English music might have tuned on keyboard at that time. I've taken Bb as
part of the regular Pythagorean tuning (Bb-B), since this note like the
seven diatonic ones is regarded as _musica recta_ or part of the regular
gamut, in contrast to other _musica ficta_ or "invented" accidentals. The
other accidentals are placed so as to divide a whole-tone into 18:17:16
(string ratio, with the smaller 18:17 below, e.g. F-F#-G).

<http://www.bestii.com/~mschulter/english1373.scl>

In this interpretation, the most impure fifth is B-F#, about 15 cents
narrow -- curiously similar to the popular early 15th-century modified
Pythagorean tuning of Gb-B on the Continent, an interesting choice on
keyboard for early compositions of Dufay, for example, where this is the
"Wolf" or diminished sixth, narrow by a full Pythagorean comma
(531441:524288, ~23.46 cents).

Anyway, especially since this is MMM, now my challenge is to make some
recordings illustrating some of these tunings -- and some possibly
refinements of 14th-century Pythagorean tuning where major thirds and
sixths in directed progressions expanding to fifths and octaves can be
tuned rather _wider_ than usual Pythagorean.

However, Harold, getting back to your musical offering: in addition to
producing some beautiful performances, you've illustrated an important
point: musical values and sensitive performance involve more than the
choice of a tuning system.

Again, congratulations -- and many thanks!

Most appreciatively,

Margo

Hi Margo,

>Carl: again, I would emphasize that the following scale from an English
>treatise of 1373 on organ design is simply one possible answer to how
>English music might have tuned on keyboard at that time. I've taken Bb as
>part of the regular Pythagorean tuning (Bb-B), since this note like the
>seven diatonic ones is regarded as _musica recta_ or part of the regular
>gamut, in contrast to other _musica ficta_ or "invented" accidentals. The
>other accidentals are placed so as to divide a whole-tone into 18:17:16
>(string ratio, with the smaller 18:17 below, e.g. F-F#-G).
>
>< http://www.bestii.com/~mschulter/english1373.scl >
>
>In this interpretation, the most impure fifth is B-F#, about 15 cents
>narrow -- curiously similar to the popular early 15th-century modified
>Pythagorean tuning of Gb-B on the Continent, an interesting choice on
>keyboard for early compositions of Dufay, for example, where this is the
>"Wolf" or diminished sixth, narrow by a full Pythagorean comma
>(531441:524288, ~23.46 cents).

Thanks for the follow-up (and .scl file)!

-Carl