TUNING digest 878

Johnny Reinhard (Sun, 27 Oct 1996)

> Please understand this as a salve to understanding. 1200 points on a
> line representing an octave is a continuum. Would 1300 or 2000 points
> make a discernable difference? I think 1200 is just past the
> threshold of pitch accuity for human beings. In essence this is the
> digital equivalent to CDs and DATs. So much pitch information is
> available as to appear infinite. Nice proportion, I think.

Thanks for the reply. I'm perfectly happy with cents measurement
wherever it may be appropriate, and with the size of the unit (although
I can still hear beating easily enough at mid-range frequencies with a
quarter cent difference). If I was treating one of Ben Johnston's scores
as data for a MIDI rendering, and cents values were required by the
program used, then I wouldn't have the least worry about such a
translation -- computers won't attach any theoretical significance to
the way the data is presented. For computers, we are concerned with
input and output only; but composers have every right to concern
themselves with more than this in scores for human performers. While you
may not think so for Ben's notation, how would you react to a
publisher's proposal to dispense with flats, double flats and sharps in
a new edition of, say, Beethoven's piano sonatas, leaving single sharps
only to produce the same result, on the grounds that all these
superfluous accidentals were merely "a personalized mythology of
meanings of relationships" (to quote you)? After all, a G#-C-D# chord
will sound no different on the piano than an Ab-C-Eb chord, so why not
end this proliferation of accidentals?

> Ben Johnson once wrote a piece for me for bassoon and tuba. We spent
> so much time deciphering the notation into cents that valuable
> rehearsal time was lost. The piece was performed beautifully in tune,
> but perhaps at a third too slow, or more.

Don't misunderstand me -- I have great admiration for careful performers
of Ben's music, and I wouldn't be surprised if your performance was
more accurate than many others which didn't involve cents translations
during rehearsal. This still misses the theoretical point I was making:
Ben wishes to notate the relationships to show the intervallic structure
of the piece -- call it Platonizing if you like. He has said in public
(perhaps someone can remind me where) that of course the expected
accuracy of intonation will vary from one passage to another: for
instance, the fast semiquaver runs in the 9th Quartet, with inflections
up to the 31-limit, will never be played at tempo with painstaking
accuracy, nor does it matter, since the notes pass by too quickly for
any listener to notice. But since Ben chooses to notate the pitch
relationships precisely, the acceptable margin of vagueness is a matter
for performers to determine sensitively.

I'd be fascinated to know whether Ben participated in your rehearsals,
and if so whether he commented on the cents translation. If he was
there, I wouldn't expect him to have objected -- why endanger a premiere
(and a good one at that, no doubt)? Composers have to be pragmatists at
some point, while theorists (like me) have the luxury of following
through all logical consequences faithfully. In this case, Ben (like
many extended JI composer) is making a statement in his notation that
pitch need not merely be regarded as a continuum, from which pitches are
selected on an arbitrary, subjective basis (again this is the old
Ptolemy vs. Aristoxenus battle).

I understand your desire that a lingua franca be settled upon for
microtonal notation, but I offer these theoretical reflections in order
to point out that this is only one possible priority -- those
participating on the tuning list (or in the AFMM) don't necessarily form
one big happy family, but perhaps, rather, opposing parties who have
found a modus vivendi in order to pool resources. Even the word
"microtonal" is not necessarily a label happily accepted by all working
within JI.

00:49:34 -0500
Adam B. Silverman said (Mon, 28 Oct 1996)

> As I stand now, I think that Dan's ideas are very good; while Ben
> gives special accidentals to 7 and higher primes, he combines 3 and 5,
> with both using the 81/80 (+/-) diacritical. Dan's system (an I
> understand it) uses sharps and flats (double sharps, etc.) for an
> ever-extensible Pythagorean chain, and applies + and - only for the .
> intervals on the 5-plane Therefore, the 5-relationship of any major
> chord built on an uninflected pitch will be followed by a -. I
> haven't used Dan's notation because it wasn't very practical to study
> with Ben and confuse him with a very similar yet different notation.

The 3-limit default is surely the much more obvious system -- it is far
more readily understood by musicians unfamiliar with JI, who will find
the complications of 5-limit default notation forbidding or even
senseless at first. I very much doubt that Ben would have adopted a
5-limit notation without having considered the 3-limit alternative, so
I'm uneasy about Adam's treatment of the latter as if it were something
new that would have "confused" Ben. Barbour, for instance, settled on a
3-limit default without hesitation in *Tuning and Temperament*. I use a
5-limit default for music that I consider to be 5-limit (say, Josquin);
if I were dealing with much earlier music, I would readily switch to a
3-limit default. Whether Ben should have retained his 5-limit notation
after he had moved beyond the 5-limit in his own compositions is another
question, which I think only Ben himself could answer. The alternative
would have been to fall back to a 3-limit notation (congenial enough for
a string quartet composer) from the 4th quartet onwards. Ben would no
doubt object that our intuitive grasp of the major and minor scales
falls within the 5-limit, and not the 3-limit; if this is so, then it is
most natural to ask performers to inflect from this 5-limit default.
(This is also intended as a reply to Daniel Wolf's points.)

>Similarly, in my string quartet, I use A+=400
> (while Ben always uses A=440)

I'm glad to hear it; as I said, this, in conjunction with C=1/1,
inevitably results in a great many minus signs which could easily be
avoided.

> A tricky situation (one of the thorny
> sides of this notation) is that in music that I have analyzed as
> 5-limit (such as Lassus, Gesualdo, Palestrina, even Chopin), it can
> drop by 7 or 8 commas in a short piece.

I've dealt with this matter in my article in mto2.6 ("Intonational
Injustice") -- you might look at "Diatonic Ficta" by Margaret Bent
(*Early Music History* Vol. 4) to see why a gradual descent in pitch was
not a problem for a capella polyphony of the 15th/16th centuries (she
doesn't deal specifically with syntonic comma shifts though, but I know
that she is happy to include them within the scope of her arguments).

Adam, thanks for your comments on signatures, and on Partch's choice of
intervals -- I'd very much like to discuss signatures in greater detail
off-list in the near future.

--
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/

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