TUNING digest 875

In studying the issue of notation, I believe we are losing sight of the
difference between 1)symbolic representation of on paper and 2) hearing
interval relationships exactly.

12-tone ET notation does not guarantee that a player can _hear_ the exact
relationships indiated on hard copy by convention. In fact,
_professional_ playing involves alterations to an absolute for reasons of
expressions (e.g. leadings, mellowings, nuances, resonances).

Hard copy notation can never supplant actual internalizing of new
intervals (more accurately presented in the mind than on paper).

Re: Adam's comments: there is no just 4/5/6 triad in my string quartet
Cosmic Rays. I suspect, having talked with Adam about this last spring,
that the heterophonic "unason" on a Ptolemy-indicated Phrygian scale (c.
200 A.D. Alexandria) with its melodically outlined 5/4 of 386 cents was
scalding in
its perceived muddle. Not trying to make excuses for honest imperfections
in a premiere performance, further performances better chiselled out
delicate ensemble playing.

I might suggest that a new composition rightfully "rifles" the
expectations of listeners who have studiously researched that which
already exists in music. The Ives _Universe_ reviews demonstrated to me
the reality that each reviewer hears in an entirely different way.
(Stunning, really, when compared to informed commentary by those more
familiar with the sound product first hand.)

Re: systems, I don't believe there is any virtue in sticking to a
particular system of tuning, per se. Anyone care to comment?

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com


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Apologies for the length of the following message, but I thought I should
say a few things in defence of Ben Johnston's notation.

Daniel Wolf said (Sat, 26 Oct)
> So for the players* sake, I like to have as little ambiguity
> as possible and would like all identical written intervals
> to have identical size. Johnston*s notation does not do this, as it is
> based upon a scale with a mixture of three and five intervals, and depends
> upon identification of a tonic. Thus, within the key of C, for example,
> Johnston*s fifths C/G and D/A are not both 3/2 intervals. Moreover,
> Johnston*s notation obviates the fact that the conventional staff notation
> is a perfectly natural vehicle for Pythagorean intervals.

Ben prefers a 5-limit syntonon diatonic default for two reasons, I think: he
chose to explore the 5-limit thoroughly before moving on gradually to higher
primes, so he devised his notation initially within a 5-limit environment,
while perfectly aware that it was extendable. Since these 1960s
"hyper-chromatic" works form the most "atonal" (faute de mieux) portion of
his oeuvre, the syntonon diatonic itself is not of importance on the aural
surface of the music, but it provided the 5-limit default he wanted. In
later works, especially from the neo-classical phase of the last ten years,
the syntonon diatonic is all the more clearly worth preserving as a default.
I would imagine also that Ben believes, like Zarlino, that the syntonon
diatonic is the ideal representation of the major scale/Ionian mode, towards
which singers at least will aim if unhampered by intonational distractions
from accompanying instruments (I would endorse this).

Ben absolutizes his notation in two ways: A = 440 is observed, even though
A+ = 440 would often remove the need for a great many plus and minus signs
from his scores; secondly, if I understand correctly, C is fixed as an
arbitrary 1/1 for notational purposes, regardless of the tonal centre of a
passage (if any).

Adam Silverman (or any other friends of Ben) is welcome to correct me if any
of the above details sound dubious or plain incorrect.

For my own theoretical purposes I remove these two anchors, and relativise
the system completely; since I'm dealing with modal or tonal music, 1/1 is
be identified with whichever letter-name is the modal final or tonal centre.
I would use a syntonon diatonic default for pieces dating from the late Ars
Nova or afterwards; earlier Ars Nova pieces have to be considered on their
merits with regard to their suitability for just or Pythagorean intonation;
Ars Antiqua I give a 3-limit default. In 5-limit Renaissance a capella
music, a further licence is the gradual sinking of the 1/1 pitch (which need
not happen quite so frequently as is usually maintained for JI
performances).

The notation can also be extended for the description of tempered systems
which are derived from the 5-limit, such as the meantone family of tunings;
other temperaments, such as certain 18th-century irregular temperaments (and
of course 12-TET) are better suited to a 3-limit default. The choice depends
on whether roots of the syntonic or the Pythagorean comma are employed in
the construction of the temperament; some tunings, such as Kirnberger II,
are ambiguous in this respect, and can be described in two ways.
Furthermore, aurally near-identical tunings will receive different
descriptions if their derivations are different: for instance 1/10-comma
meantone and 12-TET are extremely close approximations of each other, but
the former is properly describable in terms of (81/80)^(x/10) deviations
from the syntonon diatonic, while the latter is most certainly not.

Daniel Wolf again:

> In very microtonal passages, pitch height may not match notational height.
> I have decided to accept this point in lieu of going to a further step and
> using a notation with more than seven nominals, such as the
> twelve-nominal notation proposed by Wilson in Xenharmonikon.

Funny you should mention this, because one of the virtues of a 5-limit
notational default is that pitch height _will_ correspond to notational
height for much, much longer than a 3-limit default. This is a fairly big
gain to offset your objection to the contextualisation of interval sizes in
5-limit default notation. Still, I'm not determined, as I said above, to
defend a 5-limit default where it conflicts with the style of the music, or
with the derivation of a tuning system. Which brings us on to your next
point:

> I am not particularly attached to my notation but I do find it curious
> that so many people have made transcriptions of Partch scores in
> Johnston*s notation which goes against both the whole limit (factoring)
> idea of Partch, and Partch*s decided invertibility. Moreover, the
> instances in Partch*s music which are based upon the syntonic diatonic
> scale are minimal.

Adam Silverman will no doubt defend himself capably here, but I could make a
couple of comments. Ben's notation, like his music, quite deliberately works
within, and extends the very tradition that Partch largely spurned. The
staff notation used in that tradition was designed from the beginning for
vocal performers who, of necessity, had to be able to conceptualise the
sound in advance, in order to perform; instrumental performers were happy
with tablatures for centuries until these systems faded away for various
reasons in the 18th century. Since Partch concentrated heavily on
fixed-pitch instruments, he was at liberty to use tablatures, or otherwise
depart from the notational norm that he grew up with. The important use of
voices and strings in Ben's works, together with his desire to work within
that tradition renders his notation the best suited to his purposes.

Does it suit Partch though? This is one corner of the "authentic Partch"
debate, which I'd prefer not to enter (although I'll remind readers that if
we had always followed artists wishes, the Canterbury Tales and much of
Kafka's work would have been destroyed, to take two examples from a great
many -- and is recording really consistent with corporeality?).
Nevertheless, for those used to Ben's notation, the transcription of
Partch's scores offers considerable analytical leverage; it's not in every
case a plot to have performances on non-Partchian instruments. I can't see
that a 5-limit default creates any great obstacle to our understanding of
Partch, any more than a 3-limit default would -- if you're most familiar
with the former, and you haven't a pair of 5-limit tinted spectacles glued
to your face, what's the problem?

Daniel, since I'm not entirely sure I understand "Johnston's notation ...
goes against both the whole limit (factoring) idea of Partch, and Partch's
decided invertibility", could you please expand on this, so that I can be
certain of your objections? (And by the way, your apostrophes appear as
asterisks -- have a look at your e-mail editing arrangement.)

Johnny Reinhard said (Fri, 25 Oct):
> My experience with Ben Johnston gives high marks for exactitude, but
> loses too much due to the slowness with which it is read. Often
> conflicting directions are used for a single note and so a mathematical
> calculation is necessary. This process takes one out of real time.

I doubt if Ben would ever have claimed that his notation allowed fluent
prima vista performance, but what are these "conflicting directions"?
Whatever some might say of Ben's notation, I can't see that inconsistency is
a possible objection. Are you claiming there is an intrinsic flaw in the
notational system, or just talking about an occasional slip of the pen?
Perhaps an example would help.


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