I am starting by stating a very obvious fact, the piano is a keyboard instrument. Everyone knows it. However, this statement has to be more refined as people very often stop at this point. Thus, the piano is a keyboard stringed percussion instrument. It is very important to make any piano learner aware of these facts as they need to know well what the nature of their instrument is. That also influences its playing technique as well as their understanding of certain musical pieces written for the piano (or occasional places from the pieces) and various arrangements and transcriptions for another medium but transferred to the piano. The piano was invented in order to satisfy a few requirements which were not possible with other keyboard stringed instruments: the harpsichord and the clavichord. The harpsichord is a keyboard stringed plucked instrument where plectrums are plucking the strings, similar to the way the fingers and plectrums are plucking the guitar's or the harp's strings, with a substantial difference of not being able to nuance each note as the player wishes. The clavichord is a keyboard stringed percussion instrument, sharing some similarities with the piano, but in somewhat different ways. Instead of having the hammers hitting the strings and immediately going away of the strings as it is the case with the piano, it has tangents (small metal blades) hitting the strings and with the mechanism much simpler than the piano mechanism. After a string is struck, the tangent stays in contact with it and keeps the string and the felt made damper slightly raised allowing the string to keep sounding, even vibrating in its pitch if we keep changing the intensity of the pressure upon the key. While the harpsichord provides brilliance and relative power (certainly much more power in comparison to the clavichord) and having technical devices similar to the organ stops where we can have simultaneous sound of the real pitch as well as its octave higher and octave lower pitches, if we choose to use these (even having a lute sound stop), it lacked in expressive nuancing of each note, already mentioned. The only other dynamic change, other than the stops, were two different keyboards, one for louder and one for softer playing, but each of them are not touch sensitive as it is the case with the piano keyboard. On the other hand, the clavichord was a total opposite. It cannot match the harpsichord power and brilliance, but it can provide us with very fine and subtle nuancing of each note with its very simple yet very direct and responsive mechanism, and it contains a feature that even the piano does not have- we can vibrate the notes when we wish to do so, therefore we have the "vibrato" expression. It has a very touch-sensitive keyboard, unlike the harpsichord. Now, the piano was invented to join the best characteristics and qualities of both of these predecessors, meaning that we have a very rich world of all sorts of musical expressions. The piano can be very soft as well as very loud, tender and intimate as well as brilliant, powerful, kingly, lyrical and dramatic, slow and fast. The notes sound much longer than on the harpsichord or the clavichord and, as a consequence, the chords and melodies can contain many more notes of longer durations. Coupled with the huge range of dynamic nuances per note, suddenly the piano becomes almost a singing instrument or an entire orchestra, when compared to its predecessors. While it is true that the harpsichord and the clavichord, also as the piano, have reinforced vibrations of the sustained note while playing other notes if they match the harmonics which allow the strings to vibrate sympathetically, the piano goes even further because it has the sustain pedal which lifts off the entire system of dampers allowing really each string to vibrate as long as we keep the pedal depressed and in this way opens up even more options for the sympathetic vibrations of other strings activated by the harmonics of the main notes, much more than if we play solely with the fingers, as it is the case with the harpsichord and the clavichord. That is a reason why some people say that the pedal is the piano's soul, of course if used properly as an enriching element to a well developed and honest finger and manual technique. Otherwise, if the finger/manual technique is not well developed, the pedal creates unpleasant sound blurs. Now, this is one of the reasons why it is beneficial for pianists to have, at least, some harpsichord or even clavichord experience. A pianist needs to learn to control very precisely each finger's movement in terms of a well defined, almost laser like way where rhythmical precision is essential. Also, neat and well organised hand positions can be well trained here. Any sloppiness in this respect is excluded. We can be helped in these matters by having some harpsichord experience (also experiences gained on the clavichord, fortepianos and old 19th century pianos). Another very helpful point gained from the harpsichord is the subtle and skilful use of various articulations (combinations of short and long notes, detached or connected) and some rhythmical (agogical) liberties, but done in a very controlled way. Since the harpsichord's inexpressive keyboards don't allow dynamic nuancing, a player is forced to make it up by using a great variety of articulations. Any short detached note is perceived as softer when neighbouring a longer note, which is perceived as louder. This is a very useful expressive tool which can be used in a very effective way. Another expressive device is therhythmical streching or squeezing, the rhythmical liberties called the agogics.
The clavichord, as well as the older versions of the piano (various 19th century pianos and 18th century fortepianos), can help the pianist in re-visiting the world of fine and subtle dynamic nuancing, made possible by very direct and responsive keyboards of these instruments. Modern pianos vary considerably in their feel under the fingers and some of them are more robust then others. This is one of many reasons why some pianists either loose or never develop a very wide dynamic range and fine and subtle dynamic nuancing and voicing. Many a lesson can be learned from the use of the aforementioned instruments. Another instrument that belongs to the keyboard family, but in a different way, is the organ. That is a keyboard wind instrument, an aerophone instrument. The previously mentioned instruments are chordophone instruments. In a way, it is more similar to the harpsichord than the clavichord, since it also contains multiple keyboards which are inexpressive, not touch-sensitive and the expression is managed pretty much similar to how we would do it at the harpsichord, but with a substantial difference of the sound production. An air stream is passing through a pipe creating the sound, and therefore the sound can be sustained for a very long time. In the organ playing, we no longer have to do many different ornaments playing around the main note, necessary to artificially prolong the sound on the harpsichord. Here we can hold the note for as long as we want, never losing its power. Also, the huge variety od sound timbres used in a tremendously big number of combinations and having a huge dynamic range of the instrument in general, can teach us further very valuable lessons which can enrich our piano learning/playing. The organ also has the pedal keyboard, which has to be mastered and is adding to the instrument's expressive capabilities (there are also pedal harpsichords and pedal clavichords, used in older days by organists to do their home practising). While the pedal keyboards add to an instrument's expressive and musical qualities, they also add to its difficulties in terms of playing technique. The co-ordination between the hands and the feet is tremendously demanding. When mastered, it helps the piano playing in the sense of the raised awareness of each finger's motions and the whole system of thinking while performing. But, there is also the help which goes the other way around. The piano (in the older days the clavichord) can help enormously to the organ playing and the harpsichord playing, teaching and training the player to be more sensitive in his/her musical, expressive and subtle aspects of music performance. That also raises the player's awareness of various processes involved in the playing technique and all the parts of the player's playing apparatus are much more responsive to each, even the smallest, demand from the performer's mind. In other words, we train our playing technique to obey our will to the maximum. These are the reasons why many great musicians were advocating the use of all instruments belonging to the big keyboard family. Many greatest musicians were very proficient in several keyboard instruments.
J. S. Bach was a great master of the harpsichord, the clavichord and above all of the organ. His sons musicians, too. Other great musicians being trained at several keyboard instruments include Mozart, Beethoven, Mendelssohn, Liszt, Saint-Saens, Brahms, to name but a few. In more modern days, the great Italian pianist Arturo Benedetti Michelangeli was also a trained organist, or the great harpsichordist Wanda Landowska was a very fine and subtle pianist.
I would like to encourage the piano learners, as well as other colleagues of mine, to play at least one other keyboard instrument, even if it is to a very limited extent, it still means a lot, both artistically and in terms of playing technique.