Chopin's famous fundamental five finger position (e, f#, g#, a#, b) is ingenious for finger independence, especially flat fingers (in PP), but inimical as a fundamental beginning position for the following reason:
We have to practice and perform F and FF quite often in the 21st century - as the repertoire and the instrument evolved (crossed strings, double octaves, metal frame, double thrills!) and thus the advantage of a pentacluster, or scale, including elevated black keys (e.g. starting from e versus c) is eclipsed by the difficulty and awkwardness of positioning the fingers FF with comfort and dependability on the narrow(er) black keys (3 on g#, 4 on a#). In the words of pretty woman (1990): they are "slippery little suckers".
For a dependable starting position use r.h. 12345 on bcdef, third finger on d in the middle, a well balanced pentacluster.
PS: More pianist lore: There are 88 keys on the modern piano, of which 52 are white and 36 are black, a ratio of 13:9 (IMAX).
poly - many
dáktulos - finger
Polydactyla: multiple-finger (double notes) passages such as (possibly alternating) thirds, fourths, fifths, or sixths.
One, two, three and
three, four, five.
Frédéric François Chopin, 1810-1849
The assignment of more than one voice to one hand demands different applications for the two finger sets. A melodic line can be played legato applying arm weight with one set (usually upper part) and an accompanying figure can be played with fingers and/or wrist application with the second set. Essentially we should have a quartet of different instruments at our disposal.
Fingerings for scales, arpeggios, and more generally passages are principally based on groups or clusters. Clusters are based on the notes lying under one hand (or fist, as Beethoven termed it), a thumb transition usually defines a new cluster. The more clusters in a passage, the higher the possible resolution for articulation; the fewer, the higher the possible speed. Seek to understand the underlying fingering principles of clusters and apply accordingly.
Chromatic scales fingerings:
The old school:
1/3 2/4 . 1/3 2/4 . 1/3 2/4 . 1/3 etc.
The new school:
1/3 2/4 3/5 . 1/3 2/4 . 1/3 2/4 etc.
The excellent: Read more
The reason for so much attention to ornaments in the early piano schools is based on the fact that there was not much else to occupy and train fingers with in order to improve dexterity - a time before large scales and arpeggios. The thumb was rarely used for transition and because of the pivotal importance of the thumb in piano technique, the only options was to exercise trills, mordents, slurs, appoggiaturas, acciaccaturas, arpeggiation, larger ornaments, and up to five note cluster runs. Ornamentation was conceived so that any two fingers within a cluster could be used without changing the position - e.g. r.h. 5,4,3,2,1 on g,f,e,d,c: any note could be ornamented by mordent, trill, double trill, slur (turn), or double slur without changing the fingers laying on the local cluster. Take the first invention by Bach and play c,d,e,f,g with 1,2,3,4,5, play the entire piece with 5 finger cluster positions, and experiment with ornamenting any of the notes; Bach himself left two versions suggesting more variations.
The technique using dynamic arm weight in staccato or martellato octaves on they keyboard is similar to dribbling a basketball or using a yoyo: it uses a bouncing movement to get from note to note and place to place.
Fingering obeys two main principles: melodic/structural and passage/ornamental:
Fingering for melodic expression, in which the most suited fingers are used to play an articulated melodic arc with absolute attention to dynamics, accentuation, articulation, and legato. If at all possible, tactile connection of the melodic line must be pursued, which often necessitates finger substitution on the key. Think of melodic fingering as expressive choreography.
Fingering Principles for melody:
Sing and articulate! Connect notes with a physical gesture; use finger substitution like an organist.
Fingering for speed in patterned passages, in which fewest thumb-under and -over crossings are pursued and the hand positions are perceived and executed as arpeggiated (i.e., compressed) clusters in which fingers submit to arm movements. The arm leads, the hand follows, the fingers fall into place. Think of passage fingering as "arming,” like the bowing of a stringed instrument.
The pianist's hands have to be cultivated to become
Watch makers with precision instruments AND metal smiths with hammers
Surgeons with laser scalpels AND stone masons with mauls
Poets with quills AND Knights with lances
And then learn all the professions in-between.
Holding the top notes in chords in order to melodically connect is an important and undocumented pianistic tool.