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The Klindworth reading of this troubled poem is the best though Kullak used Chopin's autographic copy. There is no metronomic sign in this autograph. Tellefsen gives 69 to the quarter; Klindworth, 60; Riemann, 69; Mikuli, the same; Von Bulow and Kullak, 60. Kullak also gives several variante from the text, adding an A flat to the last group in bar II. Riemann and the others make the same addition.

'Metageometries' have been invented by Riemann and Lobatschewski as rivals to the assumptions of Euclid, and the brilliant writings of Poincaré have explained the human devices on which mathematical concepts rest. Euclidean geometry is reduced to a useful interpretation of the data of experience; it is not theoretically the only one.

The idealists in poetry, music, and philosophy gave place to great men of science, to figures such as those of Ludwig and Liebig, of Gauss, Riemann, and Helmholtz. There came also historians like Ranke and Mommsen, musicians like Wagner, philosophers like Schopenhauer and Lotze, a statesman like Bismarck.

In different degrees of tempo, strength and rhythmic accent it should be practised, omitting the thumb and first finger. Mikuli's metronome is 144 to the quarter, Von Bulow's, 114; Klindworth's, the same as Mikuli, and Riemann is 72 to the half, with an alla breve. The fingering in three of these authorities is almost identical. Riemann has ideas of his own, both in the phrasing and figuration.

As for fingering, Mikuli, Von Bulow, Kullak, Riemann and Klindworth all differ, and from them must most pianists differ. Your own grasp, individual sense of fingering and tact will dictate the management of technics. Von Bulow gives a very sensible pattern to work from, and Kullak is still more explicit.

M. Violle has published an important series of experiments on the speed of propagation of very condensed waves, on the deformations of these waves, and on the relations of the speed and the pressure, which verify in a remarkable manner the results foreshadowed by the already old calculations of Riemann, repeated later by Hugoniot.

He also fingers what Von Bulow calls the "chromatic meanderings," in an unusual manner, both on the first page and the last. Mikuli places a legato bow over the first three octaves so does Kullak Von Bulow only over the last two, which gives a slightly different effect, while Klindworth does the same as Kullak. The heavy dynamic accents employed by Riemann are unmistakable.

This learned and worthy doctor astonished the musical world a few years by his new marks of phrasing in the Beethoven symphonies. They topsy-turvied the old bowing. With Chopin, new dynamic and agogic accents are rather dangerous, at least to the peace of mind of worshippers of the Chopin fetish. Riemann breaks two bars into one.

It is so lovely that not even the Brahms' distortion in double notes or the version in octaves can dull its magnetic crooning. At times so delicate is its design that it recalls the faint fantastic tracery made by frost on glass. In all instances save one it is written as four unbroken quarter triplets in the bar right hand. Not so Riemann.

It contains a remarkable passage of consecutive fifths that set the theorists by the ears. Riemann manages to get some new editorial comment upon it. The nimble study, No. 9, which bears the title of "The Butterfly," is in G flat Von Bulow transposes it enharmonically to F sharp, avoiding numerous double flats. The change is not laudable.