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Success alone can decide as to the justification of such an attempt, which postulates physical reality for the fundamental principles of Riemann's geometry outside of the domain of their physical definitions. It might possibly turn out that this extrapolation has no better warrant than the extrapolation of the idea of temperature to parts of a body of molecular order of magnitude.
In Germany the standard work of reference is the third edition of Glasenopp, in six volumes, four of which are now in print. Other German writers are Porges, Wolzogen, Pohl, Nohl, Tappert, Chamberlain, &c. The best histories of Modern Music in general are Langhaus's larger work and Riemann's "Geschichte der Musik seit Beethoven."
In all the editions, Riemann's excepted, there is no doubt left as to the alternations of metres. Riemann is conducive to clear-sighted phrasing, and will set the student thinking, but the general effect of accentuation is certainly different. All the editors quoted agree with Von Bulow, Klindworth and Kullak.
The fiery recitatives of No. 18 in F minor are a glimpse of Chopin, muscular and not hectic. In these editions you will find three different groupings of the cadenzas. It is Riemann's opportunity for pedagogic editing, and he does not miss it. In the first long breathed group of twenty-two sixteenth notes he phrases as shown on the following page.
The question whether the structure of this continuum is Euclidean, or in accordance with Riemann's general scheme, or otherwise, is, according to the view which is here being advocated, properly speaking a physical question which must be answered by experience, and not a question of a mere convention to be selected on practical grounds.
They remind one that a composer has been dead either a much shorter or a much longer time than one supposed; and one gets down Riemann's "Musical Dictionary" and realises with a sigh that the human memory is treacherous. Who, for instance, that is familiar with Schubert's music can easily believe that it is a hundred years since the composer was born and seventy since he died?
I prefer the Klindworth editing of this rather sombre, nervous composition, which may be merely an etude, but it also indicates a slightly pathologic condition. With its breath-catching syncopations and narrow emotional range, the A minor study has nevertheless moments of power and interest. Riemann's phrasing, while careful, is not more enlightening than Klindworth's.
Von Bulow fingers the first passage for the left hand in a very rational manner; Klindworth differs by beginning with the third instead of the second finger, while Riemann dear innovator takes the group: second, first, third, and then, the fifth finger on D, if you please! Kullak is more normal, beginning with the third. Here is Riemann's phrasing and grouping for the first few bars.
That natural sincerity of feeling kept Haydn on the right path through all the weary Esterhazy years, when he was surrounded by French influences and every influence that made for artificiality and falsity. The clavier music, with the exception of a few bits, is of no great importance; still, I have played much of it with pleasure in Dr. Riemann's edition, and found many charming things.
Riemann's geometry will be the right thing if the laws of disposition of practically-rigid bodies are transformable into those of the bodies of Euclid's geometry with an exactitude which increases in proportion as the dimensions of the part of space-time under consideration are diminished.
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