Flats and sharps in music theory

June 27, 2008 2:42 AM

In music, why does the key of F have a B flat and not an A sharp? Is there actually a difference, or is it just musical tradition that a flat is used in this key and not a sharp?

Likewise with the other key signatures: why doesn't the key of G have G flat in the key signature instead of F sharp?

posted by stenoboy to Media & Arts (33 answers total)

There's already an A in the scale: F G A B flat C D E F8. If you wrote it F G A A sharp C D E F it could be more confusing. Why is there no B? How would you write the key signature?
posted by stereo at 2:51 AM on June 27, 2008

The scale of F is F, G, A, B♭, C, D, E, F. Notating the B♭ as A# would require sprinkling the stave with accidentals every time it occurred, and would leave the stave's B line unused.
posted by flabdablet at 2:53 AM on June 27, 2008

Because it makes music much easier to read. If F major had both an A and an A sharp in it, you'd constantly need accidentals to tell you whether to raise or lower that particular note.

Here's one way of explaining it (I'm not sure if it's correct, but it makes sense to me):

Imagine you want to write out a scale but you don't know the key signature - let's say F major. So, you start at F then fill in each line and space all the way up to F.

Now, you also know the order of tones and semitones required to make a major scale (t, t, s, t, t, t, s).

Working out the correct key signature is just a matter of altering any notes of the scale to make them fit the tone/semitone pattern. It turns out that the only one that needs altering is the B, which needs to move down a semi-tone to fit the pattern. Voila, the key signature of F major is one flat (B flat).

Does this help?
posted by dogsbody at 2:59 AM on June 27, 2008 [2 favorites]

It is a B flat, and not an A sharp - only on a keyboard instrument (or similar, like a fretted string instrument) do these notes happen to be the same. When I play F major and F sharp major on the violin, the B flat (in F maj) and the A sharp (in F# maj) are different - the A # is slightly higher than the B flat.

The reasons to do with notation are also valid.
posted by altolinguistic at 3:51 AM on June 27, 2008

in a nutshell: two reasons

1. you want seven notes in the key you're playing to have seven different names. So if you're playing in G major, you'll have an F# and not a G♭, and if we both convene we're playing in G major, when you say "F" I'll assume it's an F# (you would say "natural F", otherwise)

2. before the introduction of the tempered scale, a B♭ and an A# were (and on untempered instruments, still are) two slightly different notes.
posted by _dario at 4:28 AM on June 27, 2008 [1 favorite]

They're enharmonic.
posted by Jaltcoh at 4:35 AM on June 27, 2008 [1 favorite]

There's also a certain elegance to the relationship between the number of accidentals in a key and the circle of fifths. C major, no accidentals. Go up a fifth to G major, one sharp. Go up another fifth to D major, two sharps, and so on. Go down a fifth from C to F major, one flat. Down another fifth to B♭for two flats, and so on.
posted by shadow vector at 4:49 AM on June 27, 2008

When I play F major and F sharp major on the violin, the B flat (in F maj) and the A sharp (in F# maj) are different - the A # is slightly higher than the B flat.

Uh, what? That's not possible. A#=Bb, all the time. They are the same note, period.
posted by dirtynumbangelboy at 5:11 AM on June 27, 2008 [1 favorite]

Uh, what? That's not possible. A#=B♭, all the time. They are the same note, period.

Not true. Well, on a piano, maybe. On a stringed, unfretted instrument however, how a note gets played has a lot to do with where it is in the movement of the melodic line.
posted by god hates math at 5:28 AM on June 27, 2008 [2 favorites]

Well, on a piano, maybe.

Or most of the time on a clarinet, or a tuba, or a guitar, or pretty much everyone except you crazy guys in the strings section. Don't get me wrong, I greatly admire your refusal to give in to equal temperament, but you're understating its influence a little, here. The wind section in a good orchestra might sometimes go along with it to the extent they can, but it's not exactly that common I think.

For those still confused by this, here's one explanation including mp3 comparison of just and equal temperament, and my personal favourite as a keyboard player, Werckmeister.
posted by sfenders at 6:05 AM on June 27, 2008 [2 favorites]

As a flutist I was trained to do what god hates math is talking about (it's done by altering the angle and speed of the airstream). Most wind instruments have a lot of control over pitch beyond just the fingering and professional musicians use it to make the pitch more accurately fit the melodic line.
posted by hydropsyche at 6:26 AM on June 27, 2008

Are you sure you're talking about changing the pitch and not the "voice" or tone of the note, or maybe a form of pitch bending? Because to my ear, flat is flat whether it's on purpose or not...
posted by gjc at 6:38 AM on June 27, 2008

Fingerings--not just altering the airstream--will occasionally change on some wind instruments, depending on the key you're playing in and the tone you're after. When playing the saxophone, an A# is not always a Bb, even though you'd think they should be precisely the same: it's not a perfectly tuned instrument. As a result, there are slight variations in tone, brought about through different fingerings, that just sound better on wind instruments when playing in certain keys. This is a more in depth fingering chart for the saxophone though, to be fair, there's a fair bit to learn before you get to alternate fingerings!
posted by lumiere at 6:40 AM on June 27, 2008

Uh, what? That's not possible. A#=Bb, all the time. They are the same note, period.

Um, what? What you say is not true. Period. On some instruments they have to be, but not on all.
posted by altolinguistic at 6:59 AM on June 27, 2008

yes, gjc, they're talking about the tone, roughly. Concert A is 440 cycles/second, no matter where you are, and all notes (incl sharps and flats) progress in a very orderly mathematic progression up and down from there. Musicians--especially string musicians (and, btw, my instrument was viola for nine years)--may fiddle with the tone slightly for stylistic purposes, but A# and Bb are the same note expressed in cycles per second.
posted by dirtynumbangelboy at 7:00 AM on June 27, 2008 [1 favorite]

Um, what? What you say is not true. Period. On some instruments they have to be, but not on all.

No, sorry. See above.
posted by dirtynumbangelboy at 7:05 AM on June 27, 2008

Here's a related AskMe question. It appears from one of the answers there that if you're using just temperament (not the more common equal temperament that dirtynumbangelboy is talking about, which makes it easier for different instruments to play "in tune" with one another), not only does an A# not always equal a Bb, an A# doesn't necessarily equal another A# in a different scale. The human voice, for example, is infinitely tuneable, and not restrained by the limitations of equal temperament. Barbershop singers, for example, regularly make extremely small adjustments to the pitch of the notes they are singing to perfectly align the frequencies of the notes in a chord, which reinforces the harmonic structure of the chord and creates overtones. You can't do that using equal temperament.
posted by Balonious Assault at 7:14 AM on June 27, 2008

Another violist here, and, dirtynumbangelboy, you are wrong. This is as good an explanation as anything else I found.
posted by QIbHom at 7:17 AM on June 27, 2008

dirtynumbangelboy, how does your theory account for different temperaments (i.e. well-tempered, equal tempered, etc.). I suggest you stop commenting in this thread until you've done some more research.
posted by knave at 7:19 AM on June 27, 2008

Saying A# and Bb are the same note is like saying caught and cot are the same word. I happen to pronounce them identically, but not everyone does, and they have different meanings.

dirtynumbangelboy, you're obviously musically schooled enough to know that the assertion that A# and Bb are exactly the same thing is overstating the case, so I don't know if you just like arguing or what. Everyone in the debate seems to know in what contexts they are the same or different, so I'm not sure why anyone is bothering (including me, you could say, but I'm just trying to point out that the argument is pointless except for "SOMEONE ON THE INTERNET IS WRONG" sort of fun).
posted by dfan at 7:32 AM on June 27, 2008

It's simply a convention of music theory.

It also makes it possible to look at written music and know what key it is written in.
posted by konolia at 7:43 AM on June 27, 2008

Okay. A major scale is made up of the following steps between the notes:

whole whole half whole whole whole half

So in F major this is: F (whole) G (whole) A (half) Bb (whole) C (whole) D (whole) E (half) F

This explains the sharps in D major as well: D (whole) E (whole) F# (half) G (whole) A (whole) B (whole) C# (half) D.

By "steps" I refer to either a major or a minor 2nd interval between the notes. "Whole" referring to a Major second, and "half" referring to a Minor second.
posted by frecklefaerie at 7:55 AM on June 27, 2008

A major second is supposed to be 9/8. A minor second is supposed to be 16/15.

So lets start multiplying those up. We have five major seconds - that's (9/8)⁵, and two minor seconds - that's (16/15)². Multiply them all out and you get
15116544/7372800
which is
6561/3200, or 2 161/3200, 2.05. It's supposed to be an octave. It's supposed to be exactly 2.

The major scale isn't made up of those major and minor second steps, that's just the approximation of equal temperament that dfan and others are trying to point out.
posted by edd at 8:04 AM on June 27, 2008

Edd, we can get into actual pitch and what not, but that doesn't answer the question.
posted by frecklefaerie at 8:28 AM on June 27, 2008

The answer to the question is that every diatonic scale has one pitch for each letter. It's simpler and easier to read that way.

And dirtynumbangelboy is incorrect. A# can be slightly higher than Bb, as it will tend to resolve upwards while Bb will resolve downwards.
posted by ludwig_van at 8:33 AM on June 27, 2008

Generally speaking, the sharped & flatted notes in any given key are assigned sharps or flats (i.e. A# vs Bb) depending on the accidentals used to build the key signature.

Plus, dirtynumbangelboy is WRONNNNNNGGGGGGG! Any violin player with perfect pitch can demonstrate that A# is clearly not the same as Bb.
posted by Aquaman at 8:35 AM on June 27, 2008

I didn't read all the answers here, but anyway: This is called 'note spelling'. This isn't such a big deal when we're in simple, non-chromatic F major. Indeed the only problem that exists is the B-flat and it's notated as such because of the preceding A (it looks untidy and confusing to have to correct the note in a simple key.

This gets much more confusing when chromaticism occours hence the rule that when you're in a flat key everything is flat (and conversely for a sharp key). This is why chromatic yet tonal music has double sharps and double flats. This serves to keep everything looking the same and to avoid confusion (even though double sharps/flats are actually quite difficult to read.) When this does not occur in tonal music for whatever reason, this is called a 'false relation' and there are numerous examples in the literature, especially in Baroque music, of false relations between parts (i.e. a b natural in one part that is 'corrected' by a b flat in another part in the same bar). This is a coloristic device.

Things get really complicated in fully chromatic, or atonal (or whatever else you want to call it) music, and note spellling is a huge issue there, but the basic rule is to make everything agree within the bar (although sometimes this rule has to be broken otherwise things look ridiculous.)

The last thing to say is that it's interesting to look at sharp and flat composers, that is to say composers that naturally write in sharp keys and those that naturally write in flat keys. Tchaikovsky is a great example of a flat composer, hey often favors flat keys. This links to what others have been saying about the difference between b-flat and a-sharp on string instruments, and I feel that a little part (albeit an important part) of Tchaikovsky's sound is the very flat keys being played by the strings. Anyway, I've written way too much and have gone off on a few tangents, but actually this is an interesting question. Next week: why 4/4 and not 4/8?!!!
posted by ob at 8:42 AM on June 27, 2008

This is why chromatic yet tonal music has double sharps and double flats. This serves to keep everything looking the same and to avoid confusion (even though double sharps/flats are actually quite difficult to read.)

Tangential, but there's a little more to that explanation. Double flats and double sharps are used in chord spelling to preserve proper generic intervals, which makes chords easier to read. For instance, a Cdim7 chord is spelled C Eb Gb Bbb. If you wrote C Eb Gb A on the staff instead, the notes would be enharmonically equivalent and would sound the same on a piano, but it wouldn't look like a diminished 7th chord built from thirds. C to Bbb is a diminished seventh while C to A is a major sixth, and those two intervals are usually handled in different ways.
posted by ludwig_van at 9:05 AM on June 27, 2008

Mod note: few comments removed - go to metatalk
posted by jessamyn (staff) at 9:34 AM on June 27, 2008

You might be interested to know that a long time ago, A sharp and B flat were not the same note. They were close, but not identical. This is before the development of the equal-tempered 12-tone scale, where the notes are equal logarithmic steps apart.

There are early keyboard instruments to be found where there are two keys where we would expect a single black key.
posted by Class Goat at 10:13 AM on June 27, 2008

Mod note: Seriously, take it to email or metatalk pronto. This continues to be pretty argue-y for askme.
posted by cortex (staff) at 11:01 AM on June 27, 2008

"Concert A is 440 cycles/second, no matter where you are"

This is overstating in the same way that "A flat and B sharp are always the same" is overstating. Concert A is A440, but "concert pitch" means "A440" and nothing more, so that's just saying "In A440, A is 440Hz." And that's why there's disagreement here. Yes, modern western music uses 440Hz A, and equal temperament, but not all the music played in the West in 2008 is modern western music.

Specifically, period Baroque music is often at A415 or A392 -- a semitone and full tone flat, respectively -- and "period church" is a semitone sharper than modern at A466. And it's still going up, too; Moeck makes A442 recorders.

And for the same reason, period music often uses temperament or tuning systems that aren't equal temperament, because equal temperament wasn't in common use when the pieces being performed were written. And in many of those systems, A sharp is not B flat.
posted by mendel at 6:36 PM on June 27, 2008 [1 favorite]

If you're wondering about how such a seemingly simple and innocuous question could lead to such a bunch of confusion and argument, it's because the question of "what is a note?" is not such a simple one to answer.

A "note" is a slightly concept different depending on whether you are talking about the name of a key on a particular instrument (like the piano), notes as used in musical notation, or sounds as produced by a singer or instrument.

For instance, on a piano, A# and Bb are both the same key. So in that case you could say they are the same and there is no real difference.

But in musical notation, there is a drastic and important difference between A# and Bb. Some of the reason for that is outlined above, but the complete explanation has to do with how the whole system of music notation works and the ideas and conventions behind it. But, for example, if you were to take a piece written in the key of F major and randomly notate Bb or A# whenever you come to that note, any musician or music publisher would immediately notice that as "wrong" and extraordinarily confusing and difficult to read.

Interestingly enough, that is true even when the music is written for an instrument like the piano, where you push the same button for A# as you do for Bb.

But (I'm sorry to report) the situation for actual music as performed is even more complex. In any ensemble where the members can bend or move the pitch of the note (so groups including vocalists, stringed instruments, wind instruments, etc.) and where the members are taught to listen to an automatically adjust for intonation, the pitch of any particular note can vary quite a lot, depending on the context.

So not only is the pitch of an A# generally lower than that of Bb, but there is variation of the pitch of Bb (or any other note) depending on its melodic and harmonic context.

For instance, the pitch of a Bb will vary depending on whether it is the root of a Bb major chord, the 3rd of a g minor chord, or the 5th of an Eb major chord, the 7th of a C7 chord, and so on.

You can work out mathematically why this is so, but the reality is that musicians performing in groups like this learn to listen and automatically adjust for intonation in the various harmonic contexts. So in simplest terms, and assuming we are tuning to A-440 concert pitch, we might think of the "note" Bb as the pitch represented by 466.164 Hertz. But in reality Bb is a cluster of pitches near this standard reference pitch, which can and are adjusted depending on the musical context.

Relevant to your question, though, is the fact that the notes written as Bb will tend to be performed at a slightly higher pitch than those written as A#, but even that is an oversimplification, because the "cloud" of pitches that represent Bb overlaps with the cloud of pitches that represent A#.

So, for instance, if you were playing A# within an F#-A#-C# chord, but were placing your pitch rather high--more within the usual range of Bb--the comment you'd likely get from your fellow musicians wouldn't be "Hey, dummy, you're playing Bb there instead of A#!"

Much more likely it would be, "Tune that A#--it's way sharp!"

The range of pitches that the ear accepts as A# and the range for Bb have considerable overlap. So the secret of tunings like well temperament and equal temperament--which make keyboard instruments like the organ and piano practical--is that you can choose a pitch in this area of overlap between A# and Bb and let it do double duty as both pitches.

And that's why you'll hear some people say that yes, A# and Bb are all one and the same and others will say, no--they're really quite different.
posted by flug at 4:40 PM on June 28, 2008