Arthur Friedheim (1859-1932) should not be confused wih Ignaz Friedman (1882-1948)
or Carl Friedberg (1872-1955), both of whom were also celebrated concert pianists and
teachers and made rolls, but were not Liszt pupils.
Arthur Friedheim’s memoirs ‘Life and Liszt’ were published in 1961.
GLISSANDO
A white note upwards double-handed glissando, as in Liszt’s Mephisto Waltz, is played
by the nails of the second, third and fourth fingers combined of each hand (Liszt
fingering) or by the thumbnails of each hand (Chopin fingering). A right-hand black note
glissando and a right-hand chromatic glissando are played by the nails of the second,
third and fourth fingers combined.
In a glissando contact should be light and not deep into the keys and should be with the
nail and not with the fleshy part of the finger.
GOLDEN RATIO
Piano music
In mathematics two quantities are in the golden ratio if the ratio between the sum of the
quantities and the larger quantity is the same as the ratio between the larger quantity and
the smaller. The golden ratio is a constant, is an irrational number and is (1 + #5) ÷ 2
which is 1.62 to the nearest two decimal places. Many artists and architects have
proportioned their works to the golden ratio and composers such as Mozart, Beethoven
and Chopin are said to have used it in their works, consciously or unconsciously. In
terms of barring, the climax in Debussy’s Reflets dans l’eau marks out the golden ratio as
does the commencement of the fugue in Bartók’s Sonata for two Pianos and Percussion.
The golden ratio in the form of a golden rectangle contributes to overall visual
satisfaction. In a similar way, it has been hypothesised that the golden ratio contributes
to overall musical satisfaction by being a natural way of dividing a musical composition.
The reciprocal of the golden ratio is called the conjugate golden ratio and in a quirk of
mathematics exactly equals the golden ratio minus 1. For ease of illustration the
conjugate golden ratio will be used.
The present writer has done research into the ‘golden ratio hypothesis’ in relation to the
Etudes opus 10 and opus 25 by Frédéric Chopin and the Sonata in B minor by Franz Liszt.
The details of the present writer’s research, and the conclusions reached, are set out in
‘Golden ratio in Chopin Etudes’ and ‘Golden ratio in Liszt Sonata’.
Chopin Etudes