Difference between flat/sharp

Nowadays for most western instruments, they are the same, but that wasn't always the case. A# and Bb (and all the others) were slightly different, which led to problems of trying to build instruments capable of playing all those notes. So a compromise solution was reached, in which, rather than having two slightly different notes, just have one, which is neither an exact A# or Bb but somewhere between the two. Not perfect, but close enough that most of us can put up with the imperfection. That compromise system is called equal temperament which came in a couple of hundred years ago.

As for getting rid of the double names. That has already been done in some kinds of modern classical music, where only sharps are used.

But the reason that most music still uses both sharps and flats is that the system we use (the diatonic/chromatic system) predates equal temperament and all our scales chords, keys etc have been worked out to fit that system. And having learned that system, we rely on it to keep us aware of what's happening musically. For example, if I'm reading music in the key of C and I see the note F#, I can predict (with a great deal of certainty) how the music will proceed. If the note is written as Gb instead of F#, I can predict it will go another way. If it's written as one but should have been written as the other, I'll be left confused about what's happening musically, which may show either as notes played hesitantly, or an expression of panic on my face - or both. :?

It's true that the notation can help predict where the melody is going, but that's almost coincidental... the biggest reason we use a sharp in one instance and a flat in another is to make music easy to read.

Accidentals - sharps or flats contained within one measure of music - last until the next bar line. The bar line is the "reset switch", and all notes go back to being naturals (or whatever the key signature says is the default for the note written on that line/space)*

If you want to reset a note early, you need to use a natural sign. Since the natural sign is also an accidental, it lasts until the bar line... or until the next accidental is applied to the same note.

So let's say you've got a melody that goes back and forth between F and the note a half step higher, and it does that eight times in a measure. If you call the second note F#, you need to reset for each F natural, and you end up with seven accidentals in the measure:

F-F#-FN (natural)-F#-FN-F#-FN-F#

If you call the note Gb instead, you only need one:

F-Gb-F-G-F-G-F-G

because all the G notes that follow the first Gb will be Gb notes - until/unless you reach a natural or a bar line.

* - there's one instrument that doesn't follow this convention: the harp. Harps are constructed diatonically - one string for each letter name piano - and they have a pedal for each letter name; moving the pedal up or down will sharp or flat ALL the strings with that letter name. Since it would take a lot of memory to remember which pedals you'd altered in each measure, a sharp or flat in harp music isn't cancelled by a bar line; it lasts until the next accidental, even if that's four pages later in the music. That leads to some quirks... if a harp changes a note from Gb to G#, the G# has TWO accidentals: a natural followed by a sharp - to tell the harpist it goes up two notches instead of one.

It's true that the notation can help predict where the melody is going, but that's almost coincidental... the biggest reason we use a sharp in one instance and a flat in another is to make music easy to read.

No it's not at all a matter of coincidence, it's a matter of conformity. You're right that the main concern is to make the music easy to read, but being easy to read doesn't just mean keeping the page clean by reducing accidentals. It means naming notes in such a way that the underlying diatonic structure is revealed. A D major chord, for example, should never be shown with the note Gb instead of an F#, whatever the context.
So, if your example had a passage repeatedly alternating between D major and D minor within a single measure, calling D major's third, Gb instead of F#, just to make the page cleaner, does everyone a disservice by obscuring the true structure of the music. It would achieve the opposite aim and actually make it harder to read - or at least, harder to read with understanding. And music played without understanding is music played without conviction, however clean the page.

In contexts where the music's diatonic structure won't be compromised by reducing the number of accidentals, then that's fine, otherwise it's not.

I'll stand by what I said: the way a note is written will often coincide with the harmonic structure (making the motion easy to predict), but it's still coincidental.

I didn't have to look too far to find something nearly identical to the example you gave- in Beethoven's Piano Sonata #7 (Op. 10, No.3) there's a series of chords in measures 278-281 that go major/minor/major. In each case, the third is written as a raised second - when the chord is A major, the A minor is written using B#, etc. This preserves notational clarity by using fewer accents.

There are (usually) two hands in the pot here: a composer, who wishes harmonic clarity, and a publisher, who wants scores with clearly understood notation. Some composers, like Wagner, have raised fits over the changes publishers made, but for the most part the publishers have the final say - so if there's a disagreement between harmonic intent and notational clarity, notation almost always wins.

I don't think that creates a situation where the harmonic intent isn't understood. If you're playing the piece for the first time at sight, sure it can lead to momentary confusion... but your ears quickly tell you what's going on, because there's no mistaking the alteration of major/minor chords.

The Beethoven example conforms with the harmonic direction. The note is written as B#, not to cut down on accidentals, but because the interval it forms with the chord's root is intended to be heard as an augmented second, rather than a minor third. We can know that because it behaves like an augmented second in the way it rises back to the major third. It's not a true major-minor-major progression, but a major chord decorated with an auxiliary aug 2 note momentarily displacing the third. The fact that writing it that way also cuts down on accidentals is where the coincidence would appear to lie. But actually, it's no coincidence at all given that the notation system has evolved to represent the diatonic system.
To be fair, I should apply the same reasoning to my own example D - Dm - D. In a similar context to the Beethoven example, the D minor would have an E# instead of an F and wouldn't be a true D minor at all.
In both examples, however, it's the harmonic structure that should determine the notation. When reading, I don't want my eyes and ears telling me different things. I take your point though that the publishers have the final say, and will often choose notational clarity over musical clarity.

But to get back to Forkof's original question, along the lines of "Does it matter whether we call a note C# or Db?". With no musical context - it matters not at all. With musical context, it matters a great deal 'most of the time'.

Most of this went so far over my head I'd need the Hubble telescope to even see it - but one question does raise its head...

A# is a slightly different note from Bb, but for various reasons they're treated the same....can the human ear distinguish between a pure A# and a pure Bb, is there much difference between them? Or is it just a well-trained ear that can tell?

And if they're treated the same, although there's a slight difference - is this why sometimes a guitar can sound (especially distorted) slightly out of tune, when the tuner says everything's perfect?

Just curious....

:D :D :D

Vic

Yes Vic - the difference can be quite easily heard, to the extent that, one or the other would sound out of tune, depending on which key you were in.
It's mostly academic now because you can't easily play those notes. Guitars are fretted to produce the compromise A#/Bb which is neither one nor the other.

Guitar tuners are also designed for those 'tempered' notes. The 'out of tune' dissonance you sometimes hear, especially when distortion is present could be caused by (among other things) the difference between the tempered fretted notes and the still relatively pure 'untempered' natural harmonics that each string produces.

A Flash Animation describing the difference between Pythagorean tuning and Equal Temperament can be found Here

It explains things from a mathematical point of view... Which may help if your that way inclined (like me)

Josh

Excellent explanation, thanks for the link.