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I am pretty convinced it is not just for historical reasons. I have found a mathematically-sound explanation of the twelve-tone musical scale, thanks to this question. Does anyone know a similar, human-readable explanation for the piano key layout? I suspect the current layout is optimal in some sense, for example it maximizes the number of consonant chords that can be played only with the white keys. |
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Interesting question, although my answer might be more historical than you'd like ;-) One answer is that it gives you all the notes of the diatonic scale on the white keys, so by transposing to C major you can play any major-key melody that doesn't modulate using only the white keys. Another way of saying this: assume that you are working in our musical system, which has twelve-tone equal temperament as the background "system", but within that the diatonic major scale is the most commonly used set of pitches. Then assume that you want to have one particular diatonic scale easy to play, and that you'll put the other pitches on harder-to-reach keys. Subtract the diatonic pitches C-...-B from the set of all twelve pitches and you are left with C#/Db, D#/Eb, F#/Gb, G#/Ab and A#/Bb. Put these "between" the diatonic keys, in the right order in the chromatic scale, and you have something very close to the standard piano keyboard. (You can't add any more "half-steps" between E and F, or between B and C, without expanding your tuning beyond 12-tone equal temperament). Wikipedia and Grove Music online (subscribers only, unfortunately) note that the original organ keyboards (13th century) had only the pitches of the C major scale, plus B flat, because that made up more or less the entire pitch resources of the religious music sung at that time (and instruments would have been used only for accompanying sung music -- at least in church). On those keyboards B and B flat were both "white keys", with no "black keys" at all. The first surviving organ with a fully chromatic keyboard, from the late 14th century, still has B flat as a "diatonic"/"white" key. I would guess that as keyboard music developed as its own genre, it became much more useful to be able to play fast runs in the major scale -- lots of early keyboard music is based on existing pieces of vocal music with the addition of fast, "improvisational"-sounding ornaments. At least at first, the chromatic notes would have largely been used in chords, not scales, so it would be an acceptable trade-off to have those keys harder to get to in exchange for being able to play the main scale quickly. Even quite a bit later, around 1600, there are pieces which are written in G major or F major, but where all the fast bits ignore the key signature sharps or flats and just use the diatonic keys -- it was easier to play fast scales on the "white" keys with the technique they used. Finally, it's worth noting that people have often built keyboards with more than twelve tones to the octave. In the 16th century it was common to have the Eb/D# key "split", with the front half playing one of the two pitches (Eb) and the back half the other (D#). This was done by people who valued having perfectly-tuned chromatic notes over being able to easily navigate all scales at high speed. The extreme of this way of thinking, pre-20th century, is probably the 1555 Archicembalo, which has 36 keys to the octave! And 20th/21st century microtonal musicians have done lots of similar things. There is a nice introduction to different tuning systems both historical and modern at Kyle Gann's page. |
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place the 1st finger of the right hand on E and the 5th finger of the same hand on the next C and you'll see why. EDIT: Ok, I'll develop the answer. If you notice distance between the beginning of the white keys and the beginning of the black keys, it's more or less the distance between the tip of the thumb and the index finger. This distance was not randomly chosen, it fits the hand anatomy. It's best seen as I first described, with your 1st finger on E and 5th on C, you can see that the other fingers (2, 3 and 4) are naturally placed on F#, G# and A#. And then you ask me, but what about the other group of two black keys on the octave (C# and D#)? If fit's the same way, but now with only two fingers of your choice. Well, then why does the white keys where chosen to be the "white keys"? It's because they provide the diatonic scale on C, which is the most "natural" scale. If you take a look on the proposed fingering of the majority of songs, you'll see that it tries to avoid placing the thumb on a black key, because it does not fit well. With this layout, it's possible to minimize the horizontal distance between keys, making it possible to easily reach large intervals (octaves) without compromising the comfort factor of playing smaller intervals (it also minimizes the travel time between keys without compromising the comfort factor). This layout dates from before the 15th century, if my memory is not failing. (don't quote me on that one) In my humble opinion, it's the most logical layout, and that's why it survived through centuries. You even have some letter-printing telegraph keyboards which follows the same strategy. I'm sorry for the lack of explanation in the first answer. |
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The diatonic scale, as well as the 12-tone chromatic scale, are both by-products of overtones. If one examines the harmonic series, the first six pitches created from a fundamental (initial) tone outline a major chord. Arnold Schoenberg goes into great detail about this subject in his book The Theory of Harmony. Pitches from a diatonic scale being played together are generally considered consonance, while chromatic notes being introduced to this scale would be considered dissonance. Schoenberg posits that all notes create consonance, referring to the chromatic notes as a more distant consonance. If you continue to follow the intervals, by the ninth note in the series you have an outline of the major scale. The notes we don't have are the fourth, sixth and seventh scale degrees. These pitches are all somewhat sensitive pitches. The fourth and Seventh degrees played together form a tritone; which, for a large portion of musical history, was referred to as 'El Diablo" (Johann Fux's The Study of Counterpoint makes an amusing reference to this) and completely left out of composition all together. The sixth scale degree is the root of the relative minor scale, making it sensitive and also a somewhat distant consonance. All of this to say that the diatonic scale satisfies the ear by creating consonance, as well as resolution of dissonance, in more perfect ratios that are traditionally aurally pleasing. The piano's arrangement, as well as many other musical concepts, can be attributed to the overtone series and its effect on the way we perceive music. |
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Optimality of the twelve-tone musical scale explains why we have (7+5) keys in an octave. The 7 white keys form the the diatonic scale which is at least 9000 years old! The 5 black keys form the pentatonic scale and this scale is also ubiquitous. Maths shows that these scales do stand out if we insist on having the frequency ratios 2:1 and 3:2 in the scale. |
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That snippet about B and B♭ in earlier keyboards helps me to understand why German music uses the letter H. I guess that using A,B,C,D,E,F,G and H gives the option of playing in C maj and F maj.Thus one could modulate a little. |
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