Why is there no black key on a keyboard in between the notes of E and F?
In: 9
Short answer:
The C major scale sounds nice for our ears. It requires a whole step from C to D and from D to E, but only a half step from E to F. If we had C major only we would have white keys only. So the black keys appear by half or whole steps in other scales. In the end one key to the next is always a half step and that there is no black key between E and F is behause this is already a half step die to the C major scale.
Long answer:
This is in some sense based on the Harmonic series. First we have to understand why there are 7 tones (white keys) before the same note is repeated. This number is kind of arbitrary and is a result of training our ears to the sound of „nice“ and „not so nice“ intervals. In some cultures there would be 5 tones only (Pentatonic) before a key gets repeated (like in Wind chimes).
When playing the key of let‘s say 100 Hz on the piano, you hear the tone G. For better understanding on the piano I will wrongly say that 100 Hz is a C it is easier to see on a piano. Now every other string inside of the piano that has a multiple of this frequency starts to vibrate as well. The 100 Hz (C) very strong of course, the 200 Hz (C again) a little less. The 300 Hz string (G) much less, you can barely hear it, and so on: 400 Hz (C again), 500 Hz (E), 600 Hz (G), 700 Hz (a slightly flat B) and 800 Hz (C again), 900 Hz (D) and 1000 Hz (E). Eventually every tone would appear at a very high frequency.
As said, we felt through the centuries of to development of the European music that taking the first 7 different tones „that sound good“ should be used before one gets repeated. As one can see, doubling the frequency results in the same tone (and vice versa). So to get 7 notes between the two Cs of 200 and 400 Hz we take halfs or quarters of the other notes and they are still the same. The result is:
C 200 Hz
D 225 Hz
E 250 Hz
F 267 Hz
G 300 Hz
A 333 Hz
B 350 Hz
C 400 Hz
These are more or less the white keys of a piano. Between E and F the frequency distance is quite low. Taking the same scale for each of these white keys, we sometimes need other distances and need the additional 5 black keys. These additional black keys appear between the higher distances in frequency and not between E and F or B and C.
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