Johnston's notation

A brief cautionary note concerning Ben Johnston's notation:

On Wed, 23 Oct 1996, Adam B. Silverman wrote:

> ... and Ben Johnston's notation, best described by
> John Fonville in "Perspectives" issue 29, No. 2 (1991). These
> both describe the pitches very closely, although Johnston's are only
> really useful for JI, and do not include the convenience of enharmonic
> spellings.

I feel I must reluctantly take issue with this appraisal of John Fonville's
Perspectives article; while Fonville deserves praise and encouragement in
his efforts to bring Ben Johnston's music before a wider (academic) public,
I have been disturbed by some misunderstandings which threaten to confuse
anyone new to Johnston's (and indeed Partch's) theorising. I can't recall
everything that worried me, and I don't have the article to hand at this
moment, but I do clearly remember the most important matter, which is as
follows: Fonville employs the terms "otonal" and "utonal" in a manner which
contradicts their original usage in Partch -- a usage which Johnston has
preserved. In Partch, strictly speaking, only a sequence of intervals can
have the property of otonality or utonality; in Fonville, on the contrary,
a single interval considered in isolation will have these properties. For
Fonville, "otonal" means that the highest prime appears in the numerator,
and "utonal" that the highest prime appears in the denominator. Fonville
was at liberty to devise new terms for the purpose, but he chose, rather
perversely, not to do so; this new and conflicting usage threatens to
undermine the important and much more elusive distinction that Partch and
Johnston draw by means of these two terms.

As for the supposed limited usefulness of Johnston's notation, I would
again tentatively beg to differ, since I have myself been generalising this
notation for the purpose of representing meantone temperaments, and for
analysing Renaissance polyphony in JI terms. Readers may see for themselves
whether they approve of the results at:

http://boethius.music.ucsb.edu/mto/issues/mto.96.2.6/mto.96.2.6.walker.html

and in recent exchanges on mto-talk, the e-mail list accompanying mto
(Music Theory Online).

If my comments on Fonville are not clear enough for some readers, I'd be
prepared to expand a little. The same volume of Perspectives (1991)
contains Steven Elster's analysis of Johnston's String Quartet No.6, and of
course he explains "otonality" and "utonality" in a clear and orthodox
fashion (he could hardly have analysed this quartet otherwise!).
--
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/

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