What is meant by a "sharp" note?

Not sure how technical a response you’re looking for. Basically, in the traditional ABCDEFG scheme of music notation, if you walk your fingers up the white keys of a piano, you’ll be hitting only these “normal” notes. But our tonal language recognizes the existence of intermediate notes between most of these “steps” in the scale. These are the black keys on the piano.

These black keys can be thought of as being either the “sharp” of the key below them or the flat of the key above them. Either is true. F-sharp is the same note as G-flat.

Some pairs of notes don’t have such an intermediate step. That’s why there are gaps in the row of black keys on the key board. So there is no such thing as F-flat; that’s the space occupied by E.

But every note is just a particular frequency. Of course there are infinite frequencies between any two frequencies. So what’s so special about “sharp” and “flat” notes between the “normal” notes? That’s what I don’t get. Why not just letter the notes all consecutively without calling some “sharp” and “flat?”

And why are do B and E have no “sharp” variants? What’s so special about them? Again, they’re just particular frequencies.

Simply put, the exact frequencies are determined by harmonies, i.e. how the note sounds when played with other notes. Harmonious chords can be played with white keys alone, but it’s also possible to mix black keys into the chord and still produce a harmonious chord. If you were to change the frequency of one of those black keys, tweaking it a little in either direction without changing any of the other keys, you’d find that you could never use it in any chord without producing a disharmony.

There is no frequency between B and C, or between E and F, that is capable of producing a harmonious chord with any other note on the keyboard.

Okay. But can you define “harmonious” technically? Or is it just subjective as to what sounds nice?

A sharped note is half a step higher than the original note. B sharp is the same as C. E sharp is the same as F. A double sharped note is a whole step higher.

When tuning, you want to play a pitch that is right on key. If it is sharp, it means it is a higher frequency—anywhere from an sixteenth of a step on up. I’m not sure what the minimum difference is that we can detect. Tuning machines are not necessarily more sensitive than the human ear.

Personally, I can always hear when two pitches do not match, but I can’t always tell which pitch is sharper.

I still don’t get it. If a sharped note is half a step higher, then B sharp should be halfway between B and C. And if that’s the case, why not just delineate twice the number of notes in an octave and do away with the concept of sharps and flats? (And if some of those notes aren’t “harmonious” [like B# and E#] then so be it.)

@HungryGuy Here you’re getting into physics. Harmony is a function of how acoustic waves of different frequencies interact. Wave frequencies whose ratios are simple fractions of each other (e.g. ⅔) will mesh together without cancelling each other out. If the two frequencies are close to this fractional relationship, but not quite, then periodically, the peak of one wave will cancel out the valley of another wave. This creates a pulse effect that is perceived by the ear as an annoying dissonance.

Yes, that’s what I want to understand: the physics.

So if the ratios of the distance in frequency are the same for each pair of consecutive notes (is that a true assumption?), shouldn’t the dissonance (or lack thereof) of a “flat” to its “base” note be the same for every note? Again, what’s unique about the specific frequencies that have been labelled “B” and “E”?

No, there is only a half step between a B and a C, or between an E and a F.

This is because a major scale has a specific set of distances between the notes. There are two whole steps and a half step, three whole steps and a half step. That’s the major scale sequence. The C major scale is the one you can see on the piano. If you follow the sequence of white and black keys; playing only the white keys, you can actually see the whole and half steps.

Scales don’t sound right in Western music if they are whole tone scales. They sound weird to most people’s ears. Of course, there are many scale sequences. Minor scales, and then all the scales have a number of modalities, which change the sequences. In Indian music, they use quarter tone scales.

You can not understand this as a matter of math. This can only be understood as a matter of music—of pitches and pitch sequences that people think sound good. What we think sounds good is culturally determined. It is not mathematically determined.

You are asking about music theory, and I would like to know why you want to know about music theory? Is there something you need theory in order to understand? Are you trying to see how music is constructed? Do you need to compose?

There are two ways to after music. One is intuitively, using your ear. The other is by understanding the theory behind what sounds good. If you want to understand theory, I recommend you learn to play an instrument. Learn to play some scales. Get a ukulele or a guitar or a recorder. Something simple to learn. Take a few lessons with someone who is willing to teach theory as well as chords and technique.

Music theory, in my opinion, must be done in conjunction with music, and preferably with a piano. It is easiest to see on a piano. I am a trumpet player, and I’m not that dumb, but I couldn’t understand theory until I was in my 40s and I had my kids start learning piano. Then, all of a sudden, things started to make sense. I could see it on the keyboard. A trumpet just isn’t as visual, although it kind of is.

One valve makes notes a half step lower. One valve makes them a whole step lower. The third valve makes them a step and a half lower. This, in conjunction with the overtone series, makes it possible to play all notes in a Western 8 tone scale and the associated chromatic scale. A chromatic scale is made up of half steps only.

Confused yet? ;-)

I think that’s the problem, ”...You can not understand this as a matter of math…” But I think in terms of math and science, not in what “sounds good.”

If you don’t recognize what sounds good, the math will make no sense. The math is there, and it is a pattern, but it all has to do with what sounds good to our ears. Otherwise, looking at the math will be like looking at random patterns. Why are they there, you will wonder? The answer lies in your ear. It can only be explained by human preference. And the preferences differ by culture.

Ah yes, culture. Is that why Indian music sounds off-key to western ears?

We’re now out of the scope of what can be easily handled in a discussion format. The best I can do is refer you to a good treatment of the physics (see especially the “beats” and “scales” links).

@HungryGuy Yes. They have developed quarter tone scales. It comes from the meditative mode of sound, where you stick with one foundation pitch and modulate that within a narrow—quarter pitch range. Then all the other pitches relate to that one, but they play around with pitches in order to give them a more haunting, meditative feeling.

This is a response to environment—both physical and social. It has to do with technology and many other factors.

In the west, technology moved differently, and the construction of piano-fortes and previous instruments helped solidify our predilection for the western major and minor scales.

In Southeast asia, technology militated the pentatonic scales such as we hear in gamelon, as well as the reedy, nasal sounds produced by Eastern stringed instruments that also ended up being used in the pentatonic scales an awful lot.

Technology and environment push human preference. We can get used to just about anything, I believe. People love and hate rap. They love and hate Eastern music. There can’t be anything mathematical to this. It has to be preferences born of random chance.

I have played in many of these modalities and I play music that is influenced by everything I have heard. I feel comfortable moving around between many different styles. I feel like I understand or can understand just about all musics. But my entrance to the music is always through experience and intuition first. I must close my eyes and sing and find out where the music is coming from. Later on, I can analyze it. But without understanding it from inside, I don’t think it’ll ever make sense from the scientific perspective.

Oh well. I get what you’re saying, but if I can’t relate to it mathematically, then resistance is futile :-p

You can relate to it through math, but it will make more sense if you relate to it through your ear first. You do relate to it through your ear. You would never have noticed Indian music sounds off key to you if you weren’t relating by ear.

Pay attention to what you hear, and then try to explain the relationships between the notes mathematically. It doesn’t work the other way around, I don’t think. Not usually, anyway. You can use the math and try to order your ear to make sense of it, but I don’t think you’ll be successful. Better to use math to explain your ear. To do that, you have to pay attention to your ear as carefully as you can.

Then you can try to apply the jargon. Like what is a sharp. A sharp makes the desired pitch go up half a step.

Scales are made of whole steps and half steps because that’s what sounds right, not because math dictates it.

Okay, we’re at least getting close to the specific answer to my question: “A sharp makes the desired pitch go up half a step.” Is that the definition of “sharp” at all times?

yes, as an accidental sign (#) in written music. It is always used to indicate the note should be played a half pitch higher.

k. That answers my question :-) Thanks!

So even though musicians don’t recognize such a thing as a B# or E#, I could play them anyway simply by playing B or E half a pitch higher than normal (even if they would sound horrid to the ear and serve no useful purpose in making music)...

@HungryGuy If you play B or E a “half a pitch” higher, you will be playing either C or F, consecutively.

I think you probably already know this, but here are the fixed note options in Western music:

A
A sharp = B flat
B
C = (B sharp)
C sharp = D flat
D
D sharp = E flat
E
F (= E sharp)
F sharp = G flat
G
G sharp = A flat

In western music, the major scale is made up of a set pattern of tones (T) and semitones (S). That pattern is T T S T T T S.

In the scale of C major, that is equivalent to all the “normal” notes. (For the sake of technicality, a note that is neither sharp nor flat is called “natural”.)

So: C D E F G A B C
C to D is a tone, D to E is a tone, E to F is a semitone, F to G is a tone, G to A is a tone, A to B is a tone, and B to C is a semitone.

If you want a different major scale, the flats or sharps enable you to do that, whilst still using each letter name. For example, the scale of F major is: F G A B-flat C D E F.

F to G is a tone, G to A is a tone, A to B-flat is a semitone, B-flat to C is a tone, C to D is a tone, D to E is a tone, E to F is a semitone.

Interestingly, in the UK, an A natural is at 440 hz. In Germany, an A natural is at 444 hz.

@harple – Thanks! That helps :-) Now if you could point me to a page that shows, for each note, the frequency (or wavelength) that it represents. Maybe that way I could wrap my mathematical mind around this “sharp” and “flat” business. Then simply regard each note as a particular frequency (UK norm preferably, else USA) and call it a day…

Try this one, (though it means very little to me)... What this table does point out, which I had failed to mention, is that the A natural at 440 hz which I mention above is an A natural in a particular octave. In this table you’ll see it at A4. It is the A that orchestras tune to, and is also known as the A above middle C.

This probably isn’t the time to introduce that fact that A sharp and B flat didn’t used to be quite exactly the same note a few centuries back, pre “tempering”. Keyboards, however, brought about the requirement for them to be the same, hence Bach’s the well-tempered clavier.

That’s very helpful…I think. It looks like D is a multiple of 1.22 times C, and E is a multiple of 1.22 times D, but then the pattern breaks because the next multiple of 1.22 is F#.

I’ll need to do a little analysis….

But thanks for that! :-D

Musicians do recognize B# and E#. They are the same pitch as C and F, but they fit in different key signatures. So the key of C# has an E# in it, not an F. They are they same note, pitchwise, but labeled differently because of the key signature you are in.

In the common western scale it’s a logorithmic progression.
Each octave doubles the frequency.
There are 12 notes in an octave (includes all white and black notes on the piano, which are evenly spaced).

For any given note with frequency f the next note up (sharp) is f * 2**(1/12).
The note below (flat) is f * 2**(-1/12).
Generalized the note that is x steps above or below will have the frequency f * 2**(x/12).

A sharp is ½ step up the scale. An A sharp is ½ step up the scale from an A.

The definition of sharp, in relation to scales, is indeed, a note ½ step higher. the terms sharp and flat are also used in intonation. If a player or singer is slightly off the tone, they are playing (or singing) sharp if they are playing above the tone, or flat if below.

To get really technical, when we are talking about a tempered tuning versus a ‘just’ tuning, here is an article and a chart that shows that there are differences from note to note depending on the tuning. For the equal temperament scale (also known as the “tempered ” scale, generally used by most western musicians), the frequency of each note in the chromatic scale is related to the frequency of the notes next to it by a factor of the twelfth root of 2. For the Just scale, the notes are related to the fundamental or tonic by rational numbers and the semitones are not equally spaced. So you can see by the chart that in a “Just” scale, the ratio of the frequency of the 5th to the tonic (Unison) is 1.5, whereas the ratio of the frequency of the same notes in a tempered scale is 1.49831. If the tonic is an “A” at a frequency of 440 hz (a standard tuning in most US music organizations) the “Just” frequency of the 5th (E) would be 660 hz, and the “tempered” frequency would be 655.6 hz. That would make the E on the “Just” scale sharp compared to the E on the tempered scale.