Re: Yates: the American Experimental Tradition (Monz)

Hello, there, and I suspect that the reference in Yates to the hexachord
composition of John Bull refers to a famous keyboard piece using 19 steps
in the octave (Cb-E# as I recall) based on the hexachord syllables
transposed to various notes.

Some people in the 20th century used this piece as an argument for "equal
temperament" (meaning 12-tone equal temperament) for Elizabethan or
Jacobean keyboards around 1600, but Mark Lindley has expressed a view
similar to the one which I suspect Yates is adopting: that pieces of this
kind were very likely intended for some virginals or harpsichord in
extended meantone with 19 or more notes.

For the famous hexachord fantasia, one could use an instrument like the
Neapolitan 19-note chromatic harpsichords (Gb-B#), retuning B# to Cb for
this piece; with a 31-note archicembalo like that of Vicentino or Stella
or Colonna, all the notes would be there without any adjustment needed.

Here I assume something like 1/4-comma meantone. On a 19-tET keyboard like
that of Costeley, or the almost identical 1/3-comma tuning of Salinas, the
same note would serve for Cb or B#, and again no adjustment would be
needed.

The one question with this piece is whether at any point intervals
intended as equivalent to major thirds are spelled as diminished
fourths: Vincenzo Galilei used this kind of spelling as an example of what
only a 12-tET instrument like the lute (or one in an unequal 12-note
well-temperament, one might add) could handle.

One article mentions this possibility, but Lindley implies that this kind
of conflict for extended meantone doesn't arise in the Bull piece
(sections with sharps and sections with flats occur, but not mixtures of
these accidentals at the same time), and I don't recall seeing such a
problem.

Needless to say, I sure wonder what that "Pythagorean Temperament" might
have been. Neo-Gothic equitones temper fifths in the wide direction to get
14:11 major thirds and the like, but maybe that would be different from
what is suggested by Yates.

I'd add that Pythagorean intonation can support some very complex
polyphony, with the late 14th-century variety of style a fine
example. (People sometimes debate what kinds of tunings might have been
used in practice, especially by singers and players of flexible-pitched
instruments, but I love improvising in this kind of style in a usual
Pythagorean tuning of Eb-G#, not to mention tunings with fifths wider than
pure.) Here I suspect that "simple" could be taken to mean "verticality
based on fifths and fourths as the main concords," and "complex" to mean
"based on stable thirds and sixths." Around 1960, this was the prevailing
view of music history, not so surprisingly.

One might also add, as sometimes discussed here, that the transition in
the 15th century seems to have been mainly from Pythagorean to meantone,
with 5-limit just intonation as a more of a model and ideal for voices and
other flexible pitched instruments than a standard keyboard tuning,
although Lindley and others have noted that complex schemes combining
Pythagorean and "5-limit just" elements might have played a role in the
transition to meantone around 1450 or so.

Most appreciatively,

Margo Schulter
mschulter@value.net

Margo Schulter wrote:

> Needless to say, I sure wonder what that "Pythagorean Temperament"
might
> have been. Neo-Gothic equitones temper fifths in the wide direction
to get
> 14:11 major thirds and the like, but maybe that would be different
from
> what is suggested by Yates.

I expect he meant schismic temperament, so if nobody has any better
ideas let's say that. As you've said before, there are examples of
schismic thirds being used at the end of the Pythagorean era. So he
probably found some of those, but didn't have any particular fifth
size in mind.

If that's right, he was incorrect to say the temperament was newly
rediscovered, because Helmholtz/Ellis covers it. But maybe he didn't
know that.

Graham

--- In tuning@y..., "Graham Breed" <graham@m...> wrote:

/tuning/topicId_21296.html#21309

> Margo Schulter wrote:
>
>
> > Needless to say, I sure wonder what that "Pythagorean
> > Temperament" might have been. Neo-Gothic equitones temper
> > fifths in the wide direction to get 14:11 major thirds and
> > the like, but maybe that would be different
> > from what is suggested by Yates.
>
> I expect he meant schismic temperament, so if nobody has any better
> ideas let's say that. As you've said before, there are examples of
> schismic thirds being used at the end of the Pythagorean era. So he
> probably found some of those, but didn't have any particular fifth
> size in mind.
>
> If that's right, he was incorrect to say the temperament was
> newly rediscovered, because Helmholtz/Ellis covers it. But
> maybe he didn't know that.

Hi Graham and Margo,

I too suspected that Yates was referring to Helmholtz's schismic
temperament. My feeling is that by "new" he was referring to
"within the last 100 years" (which would cover Helmholtz...
Yates's article was written around 1960).

My 2 cents.

-monz
http://www.monz.org
"All roads lead to n^0"