Why is there no black key on a keyboard in between the notes of E and F?
In: 9
The eight white keys from A to A form a “natural minor” scale. The eight white keys from C to C form its /relative/ major scale, C major.
The reason that there are no black keys between B and C or E and F is because in these two scales that the modern keyboard layout is based around, those two “intervals” are already a “half step” – that is, from B to C and E to F are a smaller relative jump in pitch than then rest of the jumps from note to note.
The reason all the jumps are not the same comes from how we hear tones together and what the “sound like” to the ear. Listen to a whole tone scale and you will head that it is odd, doesn’t seem like it’s going anywhere and not very satisfying the way a major scale is.
As for why there are black keys in the first place, there was experimentation with adding these “half steps” inside scales to allow for more complex harmony inside of a piece. Things to look up on this subject would be secondary dominants and modal shifting.
Originally though even with the black keys, a harpsichord would still be tuned in a specific key and playing outside of that key would not sound the same. Nowadays we almost exclusively use “equal temperament” which is where each of the 12 half steps half been adjusted to be mathematically equal portions of the “octave”, and close enough to the relative ratio pitches that we still hear them that way.
The benefit is that not a player can play in any key without worrying about the tuning being all wacky. The downside is that no chord is actually quite perfect, even on a freshly tuned instrument.
Look up “just intonation” for examples where this equal temperament has been ditched, and you will find that the harmonies are particularly sweet and satisfying.
Ah.. a bit of physics, a huge amount about human hearing and brains, and a lot of music theory. I’m coming at this from guitar so pardon me if I get this slightly wrong.
It might seem confusing, but an octave has 12 notes with a consistent difference in frequency between them. So each key on a piano is actually the next step (regardless of if its a black or white key).
A piano is setup in the key (or scale) of ‘C’ the white keys correspond to whole notes for that scale and and the black keys correspond to half notes. If you played in a different key (for example the key of ‘D’) the the whole notes and half notes could be a mix of white or black keys. But its always 8 whole notes and 4 half notes in a given octave, spaced the same way you see the black keys on a piano, just shifted by the key.
So that pattern on the piano keyboard is really more about how our ears and brains think certain notes sound next to each other.
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.
The most ELI5 is that they’re already only a half step apart.
When you go up the major scale: C-D-E-F-G-A-B-C, those increments aren’t all the same size. By convention / definition, we have decided the pattern goes whole step, whole step, half step, whole, whole, whole, half.
* When there is a **whole** step between letters, there’s room for a black key that plays the half step between those letters. For example C-sharp (aka B-flat) is the half step between B and C.
* When there is a **half** step between letters, like E and F, there is no room for a black key because *E and F are already only a half step apar*t! An F-flat is just E. An E-sharp is just F.
Because there are only 12 notes in music (if we aren’t considering the various octaves).
1. C
2. C#/Db
3. D
4. D#-Eb
5. E
6. F
7. F#/Gb
8. G
9. G#/Ab
10. A
11. A#/Bb
12. B
The black keys on a keyboard are the “half steps” between the white keys. So if you start at middle C, you have:
C-C#-D-D#-E (going left to right)
or E-Eb-D-Db-C (going right to left)
Mathematically, the difference in sound between E and F is equivalent to the difference between C and C#, hence the half step. This is also why there isn’t a black key between B and C, because a B# is just a C, and conversely a Cb is just a B.
I hope this helps. I am by no means a music theory expert. This is simply how my band teacher explained it to me when I was younger =^.^=