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On-line Book Review


Dimension: 22.2 x 15.1 x 3.1 cm
TITLE Bach und die drei Temporätsel: Das wohltemperirte Clavier gibt Bachs Tempoverschlüsselung und weitere Geheimnisse preis von Rolf Mäser. (=Basler Studien zur Musik in Theorie und Praxis. 2)
PUBL. DETAILS Bern: Peter Lang, 2000. 497p. Paperback. Price: £41,--.
ISBN 3-906764-77-X
TO ORDER Peter Lang AG, Jupiterstrasse 15, Postfach 277, CH-3000 Bern 15, Switzerland. Email:
DESCRIPTION Monograph devoted to various performance aspects of the Well-Tempered Clavier, especially the issue of tempo, which the author claims that Bach 'encoded' in the work.
READERSHIP Those readers who are interested in hidden numbers and tempo in Bach's music
RESEARCH CONTRIBUTION Numbers in Bach's music (but the author's claims are untenable from the viewpoint of source studies)

Bach’s Well-Tempered Clavier has been examined and discussed from many different angles in the past. Yet no one has approached the question of Bach’s tempo in the same way as Rolf Mäser who claims in this book that Bach ‘encoded’ tempo instructions for all the pieces of WTC in a meticulously clever and complex manner. He regards two volumes of the WTC as mathematically constructed entities in which both the length and order of pieces are carefully preplanned. Is his claim convincing? We will soon find it out!

Mäser starts his discussion by asking why we find no tempo indication in the majority of pieces in WTC; through a series of brainstorming sessions (which are actually quite thoroughly conducted, and he certainly considers those issues commonly addressed in the historical performance practice) he reaches the view that Bach somehow notated the tempo in the work, not in words but in numbers—a magic representation of numbers hidden from view and sound—the idea first presented by Henk Dieben in 1954.

Contents in brief
Teil 1 Die Verschlüsselung
Die drei Rätsel
Bachs Tempobezeichnungen
Wahl von Weg und Werk
Teil 2 Das wohltemperirte Clavier, ein Zyklus?
Die äussere Gestalt
Versteckte Motive
Magische Zahlen
Teil 3 Bachs Musikschrift
Musik -- Zeit -- Schrift
Grundlagen einer Entzifferung
Die 73 Schriftzeichen
Fremde Handschriften
Die Balken
Teil 4 Das Versteck
Vom Sichtbaren zum Hörbaren
Die Taktart ist das Versteck
Teil 5 Die Entschlüsselung
Das Ungleichheitsprinzip ist der Schlüssel
Das tempo giusto
Die Ordnung der Taktarten
Das Rätsels Lösung
Eine Metronomzahl für das tempo giusto
Die Ungleichheit wird messbar
Sekundäre Tempofaktoren
Teil 6 Artikulation und Dynamik
Von der Artikulation
Von der Dynamik
Anhang Bachs Werke mit Tempoangaben
  Register der wichtigsten Ergebnisse
written with vigour and care, but... 
The course of his discussion so far raises sufficient concerns to say the least. While I admit that he certainly considers a wide range of issues, I am puzzled why he does not take more seriously such important ‘musical’ issues as the motives, metre and texture of a piece, which in my view convey quite a lot of ideas about an appropriate tempo at which it ought to be played. The issue of genre is another: while tempo indications (in Italian) are commonly found in sonatas (which Mäser also acknowledges), he does not seem to take a close look at the fact that a ‘prelude-fugue pair’ is one of those that does not customarily have tempo indications. We must not forget also that even this Italian tempo indications do not indicate the speed in absolute terms in those days. While the issue of measuring the length of pulse or beat in a piece is a totally separate matter (which requires a completely different kind of research), it seems absurd to discuss the proportional differences of pulse in each piece of WTC without taking into account the above-mentioned musical issues that also govern the decision-making process of choosing a tempo.

The evidence he relies on his numerical structure of WTC (i.e. number of bars in each movement as well as the order of pieces in each part of WTC) is also weak, particularly the ways in which Mäser handles the source-related information, such as Bach’s notation, handwriting, working habits, circumstances at which individual pieces were written and revised and so on. As we now know, Bach did not compose the first piece in the collection first and the last piece last; he certainly copied it himself in this way for WTC I (D-B, Bach P 415), but it was not the way he composed it. For WTC II, we even do not know whether he ever copied it all by himself from the beginning to the end. (The source evidence suggests that he never did it.) When Bach made adjustments to the length of a piece, say the Prelude in D minor (BWV 875/1), many other pieces had already been written, and as far as I can see, it was done for musical reasons; I have no idea whether or not it was to adjust the length for its sake. If this theory is also to be established, then Mäser needs to work out an alternative theory of the magic rectangle for the version ante correcturam as well. At the moment, therefore, Mäser’s central hypothesis is untenable; he must explain that there are also many alternative versions of the magic rectangles which can accommodate the shorter versions of the pieces (as well as those that were first written in different time-signature and barring) in the collection.

Although the book was written with vigour and care, I am not convinced by his claim at this stage.

Published on line on 16 August 2001

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