There are several technical questions about the correct sound production that start to worry each pianist at a certain learning stage:
1) The cause of hand straining.
2) The cause of static, nonflexible wrist.
3) How to make strong fingers and tenacious, alive and sensitive fingertips.
4) How to learn “to sing on the instrument”.

The causes of hand straining
Hand straining is generally caused by an undeveloped contact between what pianist wants to say (his internal idea) and how to correctly express it on the instrument. I.e. pianist has “knowledge”, but no “abilities”. For example, pianist imagines sound with movement, but doesn’t know what his wrist is responsible for and how it expresses the idea about sound movement. If pianist doesn’t extend his internal idea of sound in movement with his wrist, then the static character of his wrist begins to influence the internal idea of sound movement — sound movement in pianist’s imagination begins to gradually die away. I.e. wrong or lacking movements negatively influence our internal ideas. Therefore, muscle strains gradually cause psychological strains.

All this, I repeat, is caused by the lack of “abilities” of pianist. When pianist, while playing, hears that his internal idea absolutely doesn’t match with real sounding produced on the instrument, he begins to strain because his energy starts collecting not finding the way out.

Now let’s see what happens when the contact “head—hands—head” is developed. Muscles of hands and wrists naturally begin to move, breathe, expand as in inhaling, and relax as in exhaling. All thanks to the fact that the movement of hand muscles is completely connected with pianist’s internal idea. And if pianist wants to change something in his internal ideas (e.g. dynamics or articulations), the movements of hand muscles rearrange for the necessary internal idea right away.

And in order for all movements to be smart and natural, pianist has to have exact internal ideas of what he wants to say, just like a healthy person who knows what he wants to do (e.g. to take an apple) and knows how he’s going to do it (e.g. will take an apple).

Fingertips
Fingertips are responsible for a qualitative expression of sound idea. This is why pianist’s languid fingertips are caused by the lack of exact and qualitative internal idea of all gradations of sound: timbre, harmony, dynamics, balance, texture and pedal. This is why it’s usually hard for pianist to do even simple dynamics.

E.g. a teacher asks his student to play one place in the piece a little quieter, and all pianist feels in that moment is that this place has to be played not so loud, a little quieter. I.e. nothing certain. He strains internally a little bit and begins to touch the keyboard a little lighter being afraid that one of the sounds disappears or “gets out”.

When pianist has precise internal idea of all gradations of sound, then in the instance of dynamics change pianist imagines the desired sound and qualitatively completes the request of his teacher knowing what to imagine and how to express it.

Therefore, if pianist has precise internal idea of all gradations of sound, his fingertips become tenacious, strong, sensitive and “smart”. Fingers themselves begin to feel where they need to open up more to touch a larger area of a key (to produce maximum volume and singing sound). The 1st finger’s fingertip is also forced to learn playing a note independently without relying on the wrist.

Pianist learns a new sensation that he touches the sound, not the key.

“Singing on the instrument”
Every musician, when viewing from aside, is able to precisely determine, whether someone’s instrument “sings” or not. He will explain it simply — if a pianist allows sound to fly, live and vibrate to the end, then his instrument sings. And if he strains, hammers and covers sound with a “copper basin”, then pianist’s instrument doesn’t sing. And he himself doesn’t play, but knocks the instrument.

But how to sing on the instrument?
It’s voice that’s needed to sing — and in the case of pianist it’s his internal idea of sound with movement. Pianist is able to talk with this voice while playing (with bass, alto or soprano). And to do that he may play scales with internal idea of sound movement paying attention to correct wrist, elbow and torso movement.

But in order to sing with this voice, and not talk, pianist acquires the “knowledge” of correct intonation of sounds and “abilities” to competently express intonation on the piano with the help of weight and correct sitting position.

And when pianist masters correct intonation with weight and idea of sound in movement, he learns a new tremendous sensation that he sings while playing on the instrument. And this, by the way, allows even more freedom in muscles because pianist’s energy, thanks to weight, flows through legs, pelvis, torso, hands and fingers to the keyboard of the instrument. Pianist learns a sensation when one sound flows to another. And it gives a sensation of legato singing — bell canto.

To conclude, the correct sound production is:
1) Exact internal ideas of what pianist wants to say.
2) Sensitive, alive fingertips, correct movements of wrist, elbow and torso which fully pass internal ideas about sound to the instrument.
3) The skills of correct intonation with weight, i.e. ability to “sing on the instrument”.