source file: mills2.txt
Date: Thu, 18 Jul 1996 14:32:00 -0700

Subject: Digest 600, XH16 article, Brian

From: Paul Rapoport <rapoport@mcmail.cis.mcmaster.ca>

I have finally had a chance to re-examine Brian McLaren's report of my
notation article in XH16, auspiciously appearing in Tuning Digest 600 on
this forum. A few days ago I asked for more comments from others.
Understandably, none arrived. (I'm pretty busy too.)

What I tried to do in that article was derive a system which is based on
the one we know which would theoretically cover any ET. Some of the
solutions are awkward, because once I figured out what to do, I pushed the
result as hard as I could. Consequently, to notate 171-tET the way I did
may just seem quaintly humorous. But for a large number of ETs, probably
up to 72 or 100 or so, I think I showed that using traditional notation
plus signs for various kommas works, and works systematically. That is the
key concept, because until now there have been widely divergent
approaches. My systematization doesn't do away with those, of course, but
it strongly suggests that non-systematic approaches won't work for more
than a few tunings, because relationships among them won't appear. 

Yes, this amounts to an expansion of Pythagorean notation, with the
addition of signs for the syntonic komma, the diesis, the skhisma, and the
diaskhisma. In the process, some theorems are discussed and proved about
the relation of the kommas to each other. Below are paraphrases of some of
Brian's points (some only, not all that I take issue with), enclosed in
angle brackets, plus my discussion. His exact words are in quotation
marks. I'd be interested in others' reactions. I am aiming here for a
rational (and calm) objection to points I disagree with, no more. 

1. Brian says that <I have an "implicit presumption" that one ought to
relate "all the especially 12-like tunings with good fifths."> I don't.
The basing of a notation system on fifths is all I did, whether or not
those fifths are good or bad, or whether an ET has fifths at all. For
those that don't (e.g. 13-tET), I proposed a general solution to notate
them within the same framework. 

2. <ETs 9, 10, 23, 22, and 21 cannot be usefully notated using a 5-limit
method.> The article shows how to do this. Of course many may prefer the
method for ETs with recognizable fifths; see point 1. 

3. <ETs generally do not allow themselves to be seen as an "outgrowth" of
just intonation.> Many uses of ETs do exactly that, especially the ones
that allow recognizable tonal or modal progressions. This does not mean
that they grew from JI historically, which is a different and differently
arguable point. 

4. Brian spends some time discussing why small intervals, e.g. 1/17 or
1/31 octave don't sound like JI, for no reason I can determine. 

5. <Easley Blackwood's microtonal etudes suffer because he tried to make
them all as 12-like as possible.> Not quite; he tried to make them as
tonal/modal as possible. <The etude in 19 is weak because Blackwood didn't
showcase exotic, non-Pythagorean intervals.> One might as well devalue
12-tET tonal music because it isn't atonal, or the other way around, for
that matter. There is little point in criticizing something for what it
deliberately *doesn't* do, unless it makes a claim that nothing else is
acceptable. We need to separate criticizing the premise from criticizing
the result. I'd prefer more exotic music too, but that isn't what 
Blackwood set out to do. 

6. <A string of MIDI numbers (0 to 127) and a MIDI file format constitutes
a notation.> It does, but not one anyone I know would want to perform or
analyze from. Brian goes on to claim that <I reject pieces of music which
aren't in traditional notation,> a point which he dreamed up himself. 

7. <"Essentially no one attends or gives live acoustic concerts any
more."> Statements like this lead people on this forum to ignore Brian.
More on this later. 

8. <For 25-tET, "a notation which implies that there are more tones than
sharped or flatted versions of C, D, E, G, and A proves less than
useful."> Sorry, no sale. Keeping to that principle of notation would
imply that the only structure in 25-tET is groups of pentatonic scales.
But 25 has a quite usable major 3rd and natural 7th, which staying with C
D E G A won't reveal adequately. 

9. <Blackwood's (and my) notion that E and F are the same note (in 20, 25,
etc., any ET with a 720-cent fifth) is "willful obfuscation."> It is true,
however. Several articles show why. But it is possible both to use and
relieve this fact in a systematic way. My article does this, but Brian
doesn't seem to recognize that. 

10. <22-tET has nothing in common with traditional tunings.> Does anyone
agree with this? 

11. <The notation of distinctly un-Pythagorean ETs in this manner doesn't
work, e.g. 13- and 14-tET.> My solutions for these and others like them
reveal exactly what he says is lacking. For example, there is no major or
minor third in 14, and no perfect fifth in 13: this emerges from what I
suggest be done to notate these ETs. 

12. <14-tET is nothing more than two sets of 7-equal.> This comment is
similar to Brian's comment about 25 being nothing more than 5 sets of
5-equal, and equally incorrect. Blackwood's 14-note etude and mine in 25
should be enough to show that. 

13. <35-tET is a nightmare to notate.> Anyone who reads my article is
invited to determine that this is not so. If anyone wishes, I'll apply the
method I've evolved to that, since I didn't illustrate it in my article.
It is a curious case, but by no means dreadful. 

14. <Sharps and flats are most useful in tunings which sound like they
have semitones.> This is too vague for me. Besides, sharps and flats
aren't defined in terms of semitones, but at least initially as 7 perfect
fifths (up or down), in a Pythagorean sense, anyhow. What interests me
most are cases where the fifths are so far from just that the sharp and
flat end up denoting either fairly large or fairly small intervals. 

15. <"The use of sharps and flats in 19 is willfully perverse."> There are
many counterexamples to this categorical denial. Of all ETs, 19-tET is
closest to 12. In another note, Brian seemed troubled that a double-sharp
in 19, being two units of the tuning, conflicted with what it should be,
namely a whole step, which is 3 units in the tuning. But in 19-tET F
double-sharp and G are not the same note, as will be recognized by anyone
dealing with 19 as a tonal/modal tuning. 

At the end of his review, Brian suggested that my article was an admirable
advance in examining the notation issue. I can't see why, since he
discussed mostly things he disliked. (I have omitted mention of the few
things he liked and dicussed.) But I'll emphasize that my post here isn't
primarily an argument with Brian McLaren. It's a discussion about matters
of notation, which I see in a broader context than one of convenience or
necessity: a context which may reveal structures and at the same time be
useful for all the things notation is intended for. 

None of this excludes doing things differently. Although I agree with
anyone who notes that I don't base my method on primes beyond 3 and 5, I
disagree with anyone who claims I reject all possibilities that do go to 7
and beyond. Writing an article or several about 3 and 5 does not imply
ignorance of or disdain for something else. More about that another time.
I have another article to write still about 3x5, and many ideas about 7
and beyond. Of course, many others have had such ideas also. 

Finally, Brian's apparently less well thought out statements can be
misleading and even damaging. We all need to make it clear when we are
discussing things we know something about and when we're not, and to give
or at least imply reasons for conclusions to un-obvious questions.
Otherwise we risk being written off totally. In Brian's case, he has a lot
to offer; he may know more about microtonality than I do. In addition, he
has been helpful to many people beyond description, and his bibliography
on microtonality is no less than amazing.

But everyone must read his articles carefully. I am sure he would invite 
no less an approach.

==========================      =================================
Dr. Paul Rapoport               e-mail:	rapoport@mcmaster.ca
SADM (Music)	                   tel: (+1) 905 529 7070, ext. 2 4217
McMaster University                fax: (+1) 905 527 6793


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