Two measures of the monumental achievement represented by Cris
Forster's _Musical Mathematics_ are the vast musical spaces
encompassed by the palatial precincts between the covers of this
book, and the yet vaster musical spaces to which the book is a
beckoning open portal or gateway. It is a palace with paths
leading to many other palaces, whether previously unknown to the
reader, or revisited with the benefits of a new perspective
gained from Forster's breathtaking survey.

As I will not be the first to observe (Cameron Bobro, for one,
having precedence), this work is at once a compendious reference
and a friendly companion, with readable type and a binding and
generous page margins which permit opening the pages wide and
making the best use of the information which is there. Getting
this material to fit in "only" something like 950 pages was
itself a delicate task, and happily the author and publisher
succeeded without compromising an attractive and engaging format
which is a feast for the eyes, mind, and ears.

Yes, a feast for the ears, because this is a book which is meant
to be put into action, "action" here meaning the production and
experiencing of actual musical sounds. While the focus, as the
full title announces, is _Musical Mathematics: On the Art and
Science of Acoustic Instruments_, even a digital synthesizer can
permit a fascinating first-hand exploration of the aural
territory that this book maps with expertise and scholarly
humility.

For example, I am having great fun exploring some of the genera
of the great Islamic theorist al-Farabi as summarized at
pp. 650-654, including a number derived from the classic Greek
theorist Aristoxenus, whose mathematical imprecision is duly
explicated elsewhere in these pages. There is the fascination of
knowing that the instrument on which I am seeking these genera, a
24-note digital archicembalo with two 12-note chains of fifths
tempered slightly wide (and the fourths slightly narrow), would
have hardly have been envisioned either in ancient Greece or in
the 10th-century (by a European reckoning!) world of the Islamic
Renaissance. Yet the genius of the imprecise "geometric" concept
of musical space by which Aristoxenus devised his chromatic
tetrachords may be their very impressionistic nature, inviting a
variety of interpretations, some of which Forster lucidly
explores in the context of al-Farabi.

Perhaps there is no deeper praise for this book than to say that
I hope its readers will early and often put it into action,
whether modestly on a synthesizer or more boldly on an acoustic
instrument of one of the various kinds addressed by Forster, and
possibly even built according to a plan he here provides.

* * *

By this point, I hope to have conveyed my overwhelmingly positive
response to this comprehensive and yet amazingly compact volume
as at once a guide to the mathematics of musical acoustics and
tuning, and an engaging survey and reference on a number of world
musical traditions ranging from ancient Greece, Europe in the
meantone era of the 15th-18th centuries, and China over this same
long span of time, to the Balinese and Javanese art of gamelan,
the intricate raga tradition of India, and the Near Eastern
musical genius of the 8th-14th century Islamic Renaissance as
expressed today in the Arab and Turkish maqam traditions, the
closely related dastgah tradition of Iran, and a Kurdish
tradition evidently drawing on maqam and dastgah music alike.

Here I will be addressing especially some topics relating to the
medieval and Renaissance/Manneristic eras in Western Europe, say
roughly from the 6th to the early 17th century, and to Near
Eastern music. My viewpoint will surely be influenced, not to say
biased, by my own primary background and training (mostly by
self-education) in 13th-14th century medieval European polyphony,
supplemented over the last nine years or so by an interest in the
maqam and dastgah traditions as reflected by the tunings of the
Islamic Renaissance and also modern Near Eastern practice and
theory.

Before delving into some topics raised by this book or spinning
off from it, I would like to say that Cris Forster has scored a
stunning success in making some basic material from theorists of
the Islamic Renaissance such al-Farabi, Ibn Sina, and Safi al-Din
al-Urmawi available in English for the first time, and in a handy
compilation skillfully narrated and generously illustrated with
charts, diagrams, and musical examples. This, alone, would make
_Musical Mathematics_ an invaluable achievement.

Seeking to share in the spirit of scholarly humility which
Forster expresses, I must tell my delight at actually learning,
for example, the forms in which Ibn Sina himself gave certain
tetrachords whose rotations or permutations are often ascribed to
him. Having encountered different cited forms over the years both
on the printed page and in sources such as the scale archive
offered along with Manuel Op de Coul's outstanding and freely
available program Scala, I was deeply moved to encounter his own
original versions of "the very noble genus" with ratios of
104:91:84:78 (8:7-13:12-14:13) and 16:14:13:12 (8:7-14:13-13:12).
Knowing these two versions set down with admiration by Ibn Sina
about a millennium ago deepens my sense of wonder and admiration
that all permutations or arrangements of these three melodic
steps (14:13, 13:12, 8:7) offer beautiful realizations of or
variations upon Near Eastern modalities both old and new.

An advantage of such a handy reference is that it provides a
highly accessible overview in itself while also directing the
interested reader to sometimes more detailed sources such as the
Baron Rodolphe d'Erlanger's French translations of Islamic
Renaissance texts in the first four volumes of his classic
six-volume collection _La Musique Arabe_. I say "sometimes more
detailed" because Forster manages to include often rich and
lavish detail within the constraints of space set by his
framework. Thus while his book supplements rather than
substitutes for the longer sources, the reverse is also true.

First focusing in the supplementary topics which follow on some
points relating to early European music of the 13th to early 17th
centuries, I will then term to the very extensive and admirable
treatment of Near Eastern music.

[The full review and commentary will include these supplementary
topics.]

Most appreciatively,

Margo
mschulter@...