I realise there are a few black keys missing on the piano keyboard, and that the scale is some weird “steps” thing, but isn’t there a song, or at least a cord somewhere that needs a E# or B# to sound correct? Is the piano the only instrument missing those notes?
What does a pianist do in such cases?
E# exists – it’s an F. Here’s an image for how to note the key of C# major:
There’s an E# there, but you’d play an F. Each note on the piano keyboard is the same percentage frequency away from each other – C, C#, D, D#, E, F, F#, etc. It’s an exponential scale (I think?), so that from C to C an octave higher, the frequency doubles, from D to higher D it doubles, etc. Each step (C->C# or E->F) is a semitone, not a whole tone.
So, E# is a note in music theory, but it’s also an F.
I welcome corrections to the above from someone who took more than just a few piano lessons.
My kid has a shirt that reads: “E# = F… Einsteinian theory for musicians.” He thinks it’s hilarious.
This thread may be best suited to Cafe Society. I’ll relocate it.
The one I’ve seen says “Fb=mc²”.
Those notes are not missing. The names you’re using for those notes generally are missing. By definition, E#=F, and B#=C, and the need to actually call them E# instead of F, or B# instead of C, is specialized and rare. The notes exist, it’s a matter of nomenclature.
Or to put it another way: If you play every key on the piano, black and white, in order, then at every interval, the frequency will go up by the same proportion. The keyboard is complete. The only reason we separate them out into white and black keys, and give single-letter names to the white keys, is that some combinations of notes sound more pleasing or “complete” than others, and the key color and note names make it easier to organize that. Playing CBAGFEDC (the opening to “Joy to the World”) sounds better than playing all of the notes in that range, or playing just the first eight of all of the notes.
I’m not sure where this was relocated from. It seems like GQ would be the proper forum.
OK, so the most natural interval in music is the octave. That’s because when you go up an octave, you double the frequency of the sound. If you imagine the sound waves, they fit together naturally. However, if that was the only interval we used, we wouldn’t be able to produce very interesting music, so we add the second most natural interval … the fifth. When you go up a fifth, you multiply the frequency by 3/2, and we you go down a fifth you multiply it by 2/3. Because of that the notes fit together well, almost as nicely as notes an octave apart.
If you go up 12 fifths, you end up almost (but not quite) seven octaves above where you started, and you will have produced all 12 of the notes on the chromatic scale, with the naturals and sharps. If you do the same thing going down, you get all the chromatic scale with naturals and flats. Originally, the sharps and flats were slightly off from each other, but J.S. Bach created a system called tempered tuning, which fudged the sharps and flats into being the same, and wrote a series of keyboard works, one in each key, proving the new system worked.
It’s just occurred to me, that I’m not quite clear why seven notes get to be naturals (i.e., white keys) and the other five are flats/sharps. I’m sure it has something to do with the seven octaves to get 12 notes, but someone smarter will have to explain that.
To echo, and possibly dumb down, what others have said:
Even though it looks like there are missing black keys, and hence missing notes, between E and F and between B and C, there isn’t really a note that’s halfway between E and F. There’s the same amount of sonic “distance” from E to F as there is from F to F# or from D# to E. This amount of sonic “distance” is called a half-step. On a piano, no two notes are any closer together than this.
Some other instruments that can vary their pitch continuously can, theoretically, play notes that are between those available on a piano (e.g. higher in pitch than an E but lower than an F, or higher than an F but lower than an F#), and a piano that’s out of tune might play such pitches instead of the ones it’s supposed to play; but such notes are not recognized/used in traditional western music.
In my experience, you run across Fb and Cb more often than E# and B#. The key of Cb is all notes flat. I find it easier to play in Cb than B. Everything flat as opposed to five sharps. You’re not going to see the key of C# (all sharps) very often; it’s easier to play in Db. BTW- all these alternate note names are called enharmonics…
One spot in the pit orchestra parts for a show I was playing was in the key of Cb. It’s not uncommon for it to show up, so no big deal, but then the key changed… to B. Part of a rewrite, I suppose.
Didn’t Duke Ellington write the B# Jam Blues?
It’s the C-Jam Blues in B-Flat (also known as “Duke’s Place”).
Logarithmic scale, actually.
I was this close to writing log scale, but then I thought about how the frequency increases so quickly with each note and figured that’s probably exponential. Thanks for the correction!
Thanks for all the help here guys. I guess the keyboard just looks incomplete but really isn’t. Thanks again.
My understanding is that at the time this stuff was being sorted out minor scales were popular, and thus the key they started naming things with was called A minor, so naturally its assigned notes were a-b-c-d-e-f-g-(a).
Whether the scale is logarithmic or exponential depends on what is compared to what.
Can’t that be said about any logarithmic scale (and vice versa)?
Yes.
It’s the frequencies that I believe increase logarithmically, which is what we’re generally concerned with. I guess the ratios increase exponentially? Dammit, I’m a musician, not a mathematician!
My sheet music copy of Eric Clapton’s Tears in Heaven has several instance of E# in it. As noted, at that point in the music I play an F on the piano.