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A piano trio is a group of piano and two other instruments, usually a violin and a cello, or a piece of music written for such a group. It is one of the most common forms found in classical chamber music. The term can also refer to a group of musicians who regularly play this repertoire together; for a number of well-known piano trios, see below. The term "piano trio" is also used for jazz trios, where it most commonly designates a pianist accompanied by bass and drums, though guitar or saxophone may figure as well. Works titled "Piano Trio" tend to be in the same overall shape as a sonata. Initially this was in the three movement form, though some of Haydn's have two movements. Mozart, in five late works, is generally credited with transforming the accompanied keyboard sonata, in which the essentially optional cello doubles the bass of the keyboard left hand, into the balanced trio which has since been a central form of chamber music. With the early 19th century, particularly Beethoven, this genre was felt to be more appropriate to cast in the four movement form. Piano trios that are set in the Sonata tradition share the general concerns of such works for their era, and often are reflective directly of symphonic practice with individual movements laid out according to the composer's understanding of the sonata form. In the Classical era, home music-making made the piano trio a very popular genre for arrangements of other works. For example, Beethoven transcribed his first two symphonies for piano trio. Thus a large number of works exist for the arrangement of piano, violin and violoncello which are not generally titled or numbered as piano trios, but which are nonetheless part of the overall genre. These include single movements as well as sets of variations such as Beethoven's Variations on 'Ich bin der Schneider Kakadu' Op. 121a and Variations in E flat major Op. 44. After the Classical era, works for piano and two instruments continue to be written which are not presented as in the sonata tradition, or are arrangements of other works.
[2]Paolo Prandoni, [3]LCAV, EPFL
The Karplus-Strong algorithm is a simple method to generate synthetic
sounds with arbitrary pitch. In this notebook we will explore a few
variations of the method to illustrate some basic notions of
discrete-time signal processing.
In [1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import IPython
In [2]:
plt.rcParams["figure.figsize"] [2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will look at the practical issues associated to
plotting the DFT and in particular the DFT of real-world signals. We
will examine how to map the DFT coefficients to real-world frequencies
and we will investigate the frequency resolution of the DFT and the
effects of zero padding.
In [1]: