Basic Fingering Principles

When we are learning a new piece, we typically follow the fingerings given to us by the editor of a score or a piano teacher. Ultimately, however, we want to become self-sufficient and capable in working out fingerings that are practical and comfortable. While fingering can be complex and dependent on subjective preferences, there are some basic points that provide guidance and direction when choosing fingerings

Keep in mind that all scales and all arpeggios (except for Gb major and Eb minor) avoid the use of both the thumb and pinky on the black keys. While this principle is regularly applied, keep in mind that it is not uncommon to use the thumb on the black keys, particularly when improvising or sight-reading. Nevertheless, given that the pinky and the thumb are lower on the hand than the middle three fingers, they tend to function best on the white keys, while the three middle fingers work best for the black.

As a result, the index finger (2) and the middle finger (3) are often associated with the black key “two group” (C# and D#), and the index finger (2) the middle finger (3), and the ring finger (4) are often associated with the “three group” (F#, G#, and A#). The thumb is used for B, C, E, and F. This principle works uniformly for all of the black key major and minor scales in the right hand, and all of the white key major and minor scales in the right hand except for those that start on D, G, and A. Accordingly, we can associate the following notes/keys with the fingers indicated below (keep the enharmonic equivalents (C#=Db, D#=Eb, etc.) in mind for each note):

The thumb, of course, will also be regularly used for D, G, and A, as well. As a result, the fingerings for the black keys shown above will change (3, for example, will find itself on C#, or F#). Nevertheless, what is indicated above is such a regular tendency it can be followed and applied to the right hand for nine major and nine minor scales.
The same principle can be applied to the left hand. Since half of all of the major and minor scales in the left hand use the thumb on A, D, or G, however, the principle applies to only the C, Db, E, F, Gb, and B major and minor scales.

In a similar way, the chromatic scale is a good guide to finding fingerings. Here the thumb takes the white keys; when there are two white keys in succession, however, the thumb (1) and index finger (2) are used. The middle finger (3) is used for the black keys:

The principles given above apply most appropriately and favorably when the player takes the time to work out fingerings. Many other situations, however, require a different approach. When sight-reading, for example, one does not have the opportunity to use ideal fingerings; the fingerings we end up using are the ones that work at the moment. As a result, the thumb may regularly play on the black keys, and other unusual fingerings may occur.
In improvisation, similarly, more unconventional fingerings will result, such as regularly using the thumb on the black keys. In improvisation, however, much of what is played makes use of melodic vocabulary that players develop as patterns on the keyboard. This vocabulary typically evolves with set fingerings that often fall in line with conventional fingering practices.