If you look at a standard piano with full register, you'll find 88 keys in white for notes in the C major scale and black for other notes which became standard for pianos in the late 18thcentury.
Almost every modern piano has 88 keys (seven octaves plus a minor third, from A0 to C8).
Many older pianos only have 85 keys (seven octaves from A0 to A7), while some manufacturers extend the range further in one or both directions. The most notable example of an extended range can be found on Bösendorfer pianos, two models which extend the normal range downwards to F0, with one other model going as far as a bottom C0, making a full eight octave range. Sometimes, these extra keys are hidden under a small hinged lid, which can be flipped down to cover the keys and avoid visual disorientation in a pianist unfamiliar with the extended keyboard; on others, the colours of the extra white keys are reversed (black instead of white).
The extra keys are added primarily for increased resonance; that is, they vibrate sympathetically with other strings whenever the damper pedal is depressed and thus give a fuller tone. Only a very small number of works composed for piano actually use these notes. More recently, the Stuart and Sons company has also manufactured extended-range pianos. On their instruments, the range is extended both down the bass to F0 and up the treble to F8 for a full eight octaves. The extra keys are the same as the other keys in appearance.
Or are they?
If you look under the hinged lids of a few piano keyboards you will find as in the above picture an unusual set of keys. These 19 notes form what is technically called the Boîte Diabolique, or in English the "Forbidden Notes". Most of these notes are either "superflat" or "unnatural" versions of existing notes one can play on the regular piano.
Take particular note of the red key in the middle. This is not an error, this is in fact quite deliberate. When struck, this key produces an H5 note. Because most of these notes occur as a result of the Pythagorean comma (which resulted in the retuning of pianos).
A key of notes is produced with simple mathematical ratios being 1:2 2:3 3:4 etc. The problem is that for the 13th note in the key, it produces a dissonant noise with another note in the series. With the publication of JS Bach's "Das Wohltemperirte Clavier" the practice of tempering was complete. By altering the notes artificially, the dissonance was removed and all keys could be played in harmony at the same time.
Essentially the Boîte Diabolique is all the notes removed as a result of "Well Tempering" the notes. The 19 notes in questions are the 8 "unnaturals", the 8 "superflats", a Z3 and a Z4 (which actually fit in between their respective F & A notes) and both of which occur in Bach's Mechanique Wohltemperirte, lastly the H5 which is last comma left about G5.
When notes from the Boîte Diabolique are played, it usually results in a general feeling of unpleasantness for the listener. In particular when H5 is played, some sensitive people may find that their ears will actually begin to bleed. For this reason, audiences for the most part ceased to hear the notes of the Boîte Diabolique unless accidentally played. With the advent of modern instruments and the ability to produce virtually any sound, it may be quite a fearful thing when again composers and musicians take up writing compositions utilising the Boîte Diabolique again.
Heaven help our ears.