Music theory 100: why are there both sharps and flats?

[packbat]

There are longer and more accurate answers but this one is gonna start with a piano keyboard like you might find in the US. (Here's a picture, if you don't have one handy - it's the black-and-white part.)

The white keys on the piano keyboard all have standard names. If you look at the black keys, you'll see there's sets of three white keys containing two black keys alternating with sets of four white keys containing three black keys. The leftmost white key in each set of three-and-two is a C, and if you move to the right from there, it steps up through the alphabet with each white key until it hits G, after which it goes back to A, followed by B, followed by another C.

(Don't ask us why it starts at C and not A; we don't know.)

If you use just the white keys, you'll end up with a C major scale. That's probably why those keys are white and the others are black, actually: if you do that pattern of skip-one, skip-one, don't-skip, skip-one, skip-one, skip-one, don't-skip, then you get a major scale, so they picked one of the major scales and separated out all the keys you skip from it. If you wanted a different major scale starting on some other key, you'd do the same pattern of skips and not-skips - whole steps and half steps, pairs of half steps and single half steps - starting anywhere else.

Actually, let's go ahead and do that. Let's start at D.

D. Skip hops a black key and lands on E, good so far. Skip ... hops a white key and lands on a black one. Okay, so the next letter would be F, so let's call this a modified F - it's F up one key, or F-sharp. Step (no skip) puts us back on G, which is nice - we're on comfortable territory again. Skip lands on A. Skip lands on B. Skip ... overshoots C and lands on a black key, so let's say C-sharp, following the rule from before. Step lands on D and we're done.

Okay, now E. Skip lands past F, so F-sharp. Skipping again lands past G, so G-sharp. Step lands on A. Skip lands on B. Skip lands past C, C-sharp. Skip lands past D, D-sharp. Step lands on E to complete it.

Now F. Skip lands on G. Skip lands on A. Step ... falls short of B.

That's why we have both sharps and flats. We have this one convention of white keys = letters, this second convention of scale = each letter in turn, and this third convention that overshooting a white key letter means sharp. But this isn't overshooting, this is undershooting. This is anti-sharp. This is B-flat.

(And afterwards a skip puts you on C and then you skip to D and E before stepping home to F.)

Thanks for listening - I just ... I just needed to say this somewhere. For reasons. Sharps and flats are both important.

(For extra credit: if you start at an A and use all the white keys, you end up with A minor, another very popular style of scale. If you figure out the pattern of steps and skips with that one, you can create other minor scales starting on any of the keys.)

(Note also: we've been talking about sharps and flats as black keys, but 'sharp' and 'flat' just mean one key, of any color, over. C-flat looks exactly the same as B, and B-sharp looks exactly the same as C. It's very cursed and musicians try to avoid using them.)

(Also cursed: double-sharps and double-flats. Triple-sharps and triple-flats ... honestly, we've never seen those in the wild, so they lose accursedness points on account of excessive rarity.)

Comments

[lb_lee]

Double sharps and double flats... o_o *memories of a wayward youth with the bassoon* *shudder*

[packbat]

Oh no - do they inflict a lot of those on bassoon players? I don't know that they ever troubled us with any when we were learning the piano growing up.

[lb_lee]

I doubt bassoons get them any more than anyone else, I just remember us encountering them a few times and that was enough to put the fear of god in us, haha! We were in school band and stuff, so sometimes we were given music with them. (I think it was mostly more complex stuff for competition though, since our school stuff generally wasn't that exciting. Bassoons are not known for their epic solos!)

[packbat]

Mmmm - I remember Adam Neely saying in a video that melodies are less clear and prominent in the bass register, so there being fewer bassoon solos makes sense!

And our piano lessons were private lessons, and not too adventurous with keys as we recall. The most complex music we played were Scott Joplin rags.

[lb_lee]

Scott Joplin has great stuff though!

[packbat]

He super does! Not too long ago, we ended up going on YouTube to try to find a really good performance of "Magnetic Rag", just because we remembered playing that piece and loving it. If we had a full-sized keyboard, we'd probably spend a while relearning some of the pieces just because they're so lovely.

[lb_lee]

Ooh, I'll have to check it out, I have a bunch of recordings of his stuff and did a school project on him in the eighth grade. He seems to have been a cool guy!