Monzo's book

[David Beardsley, TD 206.9]
>
> So what does your book offer that one can't already find in
> the writings of Partch, Helmholtz or Doty? Or even a trip to
> the library wouldn't dig up?

Primarily, a comprehensive collection of lattice diagrams
illustrating historical tuning systems and harmonic gestures,
from c. 400 BC to 1999 AD, along with my prime-factor adaptation
of regular staff-notation to notate these systems.

Partch and Helmholtz devote a lot of space to experimental
investigations and other aspects of acoustics and composition
which are not specifically descriptive of tuning *systems*.
For instance, Helmholtz describes his experiemental apparatus
and Partch describes his instruements and the dramatic aspects
of his compositions, all of this in great detail. And Partch's
primary concern was with his own single ~43-tone system of
Monophony.

Doty's book is intentionally limited in scope to suit beginners,
and, altho still quite extensive (and very good), doesn't cover
anywhere near as many *specific* tuning systems as my book.

None of them give analyses of specific pieces or gestures
(with the two exceptions of Partch's 'modulation' and
'tonality flux' explanations), which I do.

This last point is especially important. As many of us here
have argued, theory divorced from actual music is rather pointless.
(Boethius's opinion notwithstanding). Partch certainly emphasizes
that fact, but he still doesn't give analyses of his harmonic
practice, except the very sketchy examples of 'tonality flux'
mentioned above.

As far as a trip to the library: if you live in or near
New York (as you do), go for it - there's a lot there.

But away from New York, I've had a *LOT* of difficulty finding
the information I was researching, even in large cities like
Philadelphia (surprisingly, especially considering all the
good university libraries here), Phoenix (even with a brand new
and very good central library), and San Diego (LOL here).

On that last point, I find it shameful that the city where both
Partch and Darreg spent the last years of their lives has such a
poor representation in its libraries of anything concerned with
their work (or of anything, period, for that matter).

And belive me, I've gotten out the earth-moving equipment to
do some serious digging. People living in more rural areas will
generally have even greater difficulty.

I know that for a lot of New Yorkers, the universe ends at
the Hudson River, or perhaps somewhere in New Jersey and Long
Island. But lots of microtonal folks live out here in the
hinterlands, and I suppose we suffer accordingly.

OK, enough ranting about libraries...

Besides, my particular lattice design, which is different
from all the others, isn't available anywhere else, except
on my website, and here on this List.

Much of the historical information in my book is based on the
systems analyzed by those three authors, but my objective
was to diagram those ratios all from the same 'perspective'
(i.e., from the same 1/1), to gain an understanding of how
the different systems _in toto_ relate to each other.

In addition, there is much new information added stemming from
Barbour, _Journal of Music Theory_, _Perspectives of New Music_,
_Xenharmonikon_, and from my own interaction and correspondence
with contemporary theorists and composers.

I've also been able to take advantage of several recent
English translations of such classic treatises as those of
Aristoxenus, _sectio canonis_, Nicomachus, Ptolemy, Boethius,
_musica enchiriadis_, Hucbald, Guido d'Arezzo, Marchetto,
Prosdocimus, Zarlino, Riemann, and Schoenberg.

(In particular, I've gathered so much information about
Schoenberg that I've decided to write an entire second book
exploring in more detail his theories and the work of his
students and predecessors - which is only natural, since I
admire Mahler so much, and I dig Webern a lot too.)

The book grew out of my frustration in dealing with ratios
of very large numbers in Partch and Helmholtz, and most of it
was finished before I ever saw Doty's book, which does have a
fair amount of the same information (in particular, his use
of lattices, which are, however, a bit different from mine).

Another thing you won't find anywhere else (except my website):
I have a few very speculative theories on possible examples
of higher-prime systems at earlier dates than those usually
cited - readers of this list will already be aware of these
(one example is that of Boethius which I just mentioned yesterday,
another is Marchetto of Padua).

In addition, I explore blues and rock music styles (for example,
Louis Armstrong, Robert Johnson, Etta James, Jimi Hendrix) which,
to my knowledge, have never been subject to extensive microtonal
analysis before, excepting Sims's work on Armstrong. (Note that
all these artists were African-American, which may or may not be
significant - at any rate, there's certainly a gap in the
understanding of microtones in African-American music, which
I hope to fill at least partially.)

Also, the work of several contemporary composers and theorists
- for example, Erv Wilson, Ben Johnston, Lou Harrison, Ezra Sims,
Terry Riley, Johnny Reinhard, Denny Genovese, Sasha Bogdanowitsch,
David Beardsley :) - is included, which obviously was impossible
for Helmholtz and Partch, and which lie outside the scope of Doty's
introductory _Primer_.

To a large extent, the differences may be summed up with the
statement that Partch and Helmholtz argued polemically in favor
of their JI or tempered systems, and Doty explains and illustrates
more-or-less basic concepts and ends there, whereas I've assumed
what all three of them said as given, expanded from there,
and tried to find underlying principles of unification.

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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>(In particular, I've gathered so much information about
Schoenberg that I've decided to write an entire second book
exploring in more detail his theories and the work of his
students and predecessors -

Joe, have you ever heard of Josef Hauer? This is an excerpt from H.H.
Stuckenschmidt's "Twentieth Century Music" (pages 91 & 92):

"...the Viennese composer Josef Matthias Hauer (1883-1959) probably wrote
'purely atonal melodies' before Schoenberg and his pupils. The earliest of
them date from piano pieces of 1914. The pieces, in fact, are complete
forms built up from purely atonal melodies of this kind. Hauer describes
his aims in a text-book on atonal music, entitled _On the Nature of
Music_, which was published in 1920. He starts from a notion of 'equal
temperament', that is, a chromatic technique which uses mathematical
procedures to combat the tendency of a tonic to become established. He
characterizes the music he advocates as follows:

In atonal music, however, which stems from 'totalities', intervals
alone are relevant. Musical expression is no longer achieved through the
use of major and minor keys and of specific instruments with a _single_
timbre: it is founded on the totality of intervals and timbres, and is
best and most clearly realized by using one single, tempered instrument.

He says further on:

The 'law' or 'nomos' [of atonal music] is that _all twelve notes_ of
the temperament are to be repeated over and over again.

Undoubtedly Hauer preceded the Schoenberg school in calling for and
employing all twelve notes of the melos. However, the idea was certainly
in the air at the time."

Though I've never heard any of Hauer's music, nor seen his book mentioned
in this quote (nor do I 'vouch' for any of the above), it all certainly did
catch my attention when I read it, so I thought I'd pass it along...

Dan