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In one of the answers of this question, some pianos with 44, 61, 76, and 88 keys are introduced. I just don't get it. Why notes are not following any formula? I mean, a piano with 63 keys means that it supports 9 octaves. Why these seemingly irrelevant numbers?

Please note that I'm aware of this question, but in it, they only talk about the history (the how) of a piano with 97 keys, not the why.

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    61 keys is precisely 5 octaves. I do not know where you get the idea that 63 keys is 9 octaves. Please see my answer below where I explain exactly where the 61-key keyboard came from. – user1044 Sep 11 '11 at 1:37
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    Why SHOULD a piano cover a whole number of octaves? – Laurence Payne Jul 9 '17 at 16:15
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    63 keys might be considered 9 octaves if you only count the white keys, but that's kind of a nonsensical way of doing things since nobody manufactures a piano like that. The OP may have been confused about how many piano keys comprise an octave (it's 12, not 7). – nobar Jul 6 at 19:36
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    Note, that for a complete multiple of octaves, say n, 11n + 1 would be the formula. – guidot Sep 12 at 16:34
  • @guidot: There are 12 keys per octave (7 white and 5 black) -- so it's 12n. The +1 may be optional -- but smaller midi controllers tend to be 12n+1 (e.g. 25 or 37 keys). – nobar Oct 7 at 22:22
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I suppose the answer is that any manufacturer of a keyboard instrument, be it a piano, organ, accordion, etc., is free to build whatever instrumental mechanism to produce as many pitches as they want to create, and is free to design a keyboard to play those pitches. They put it on the market, and the successful models sell well, and establish a precedent, while the unsuccessful models do not sell well, and those designs become less popular.

In the early days of the harpsichord and piano (up until about 1815), it was a physical limitation of the mechanics of producing lower pitched notes or higher pitched notes that sound good and are stable. For instance, the exact compass of notes in the standard 61-key keyboard was settled on because it was judged not practical to produce lower pitches or higher pitches with the technology available at the time, e. g. an all-wooden piano frame rather than iron or metal, and using bronze strings, not steel. A keyboard was thus designed to play the pitches based on what the physical mechanism for producing the pitches could accommodate.

A standard harpsichord played exactly the pitches it did because of the amount of tension that a wooden frame could accommodate without warping, and because strings could only be engineered to be so thick or so thin and produce a good, stable sound. When composers wrote music for the harpsichord, they depended on all harpsichords being able to play the same pitches so that one particular piece of music could be played on any harpsichord. Of course all during the history of the harpsichord, different instrument makers experimented with variant designs with different pitches, but eventually a standard was established based on common practice and the marketplace.

Later on, the iron frame was introduced, alongside later technological developments for strings, involving other alloys and wrappings on the strings, and methods of stringing. From about the year 1815 forward, The exact compass of pitches on a piano, and the number of pitches it could play, and the number of keys on the keyboard, gradually began to expand as various manufacturers tried to develop new technologies and designs. From around 1815 to around 1920, there were many pianos on the market with widely varying numbers of keys, all based on mechanical considerations. Eventually we got from 61 keys to 88 keys. Then composition came into play: composers wrote a lot of piano music with the expectation that it be played on an instrument with 88 keys and pitches, so most people wanted to purchase a piano with 88 keys so they could play any piece of piano music on it.

In the last 100 years, with electronic instruments, other considerations come to bear. In the first half of the 20th century many electric keyboards such as some Hammond organ models had an "F" as the lowest pitch. This became unpopular in the rock era because the lowest pitch on the guitar and bass guitar are "E", so electric instruments with keyboards that had "F" as the lowest pitch were less useful in a band with guitars.

In summary, things are the way they are because of many centuries of development in the technology of acoustic, mechanical, electro-mechanical, and electronic instruments. Musical instruments are not designed and built based on "integer factors"; they are based on practical considerations of mechanics and acoustics and materials engineering.

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    Incidentally, some harpsichords were constructed so that they looked like they went down to an "F", but the black keys on that bottom half-octave actually played C, D, and E. Some literature seems to assume that there will be a "C" where the F# would normally go, a "D" where the G# would normally go, etc. since it requires an impossible reach on a full-sized keyboard. – supercat Jan 25 '13 at 1:22
  • Since posting my original answer, I have met a person in my home town who owns and performs with just such a harpsichord as you describe. – user1044 Feb 8 '13 at 19:15
  • @supercat in my experience this is called a "short octave," but I don't understand what you mean by "impossible reach." The notes on the black keys are closer than they otherwise would be, not farther. – phoog Sep 12 at 15:13
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    @phoog: Composers writing music for keyboards with a short octave may specify combinations of notes which are nearby on a short octave, but much further on a normal one. – supercat Sep 12 at 15:21
  • @supercat oh I see, like from a low C (on the "F#" key) to the G a twelfth above? – phoog Sep 12 at 15:23
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Note that the numbers of keys includes white and black keys, so an 88-key piano is just over 7 octaves and a 63-key keyboard is 5+ octaves (not 9).

As in most music (and much of life), non-logical reasons tend to be historical.

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Why would a whole number of octaves be logical or desirable? Music doesn't cut off at octave boundaries - if a piece is in C major that doesn't mean the lowest and highest notes in it will be C.

The short and sufficient answer to your question is that pianos don't have an exact number of octaves because there is no reason for them to.

  • I was recently having a look at Guido's Micrologus, and in discussing the extra double-letter notes between aa and dd, which some call superfluous, he says that it's better to have too many than too few. – phoog Sep 12 at 15:21
  • I can't help but notice that many answers for musical questions on this forum are explained in terms of mathematical formulas. It seems to me that this can sometimes mislead folks into believing music has to make mathematic sense or it's wrong. For some one who is trying to learn how to be creative, such a belief may be a hindrance. – skinny peacock Sep 13 at 15:21
  • Really? I see some numbers, not many formulas. – Laurence Payne Sep 13 at 16:49

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