Hoooo booooy. Good luck with this rabbit hole. It has to do, in part, with sytems of tuning. You (most likely given the forum) play a banjo in tempered tuning where mathematically the ratios between note intervals are a compromise. This is different from just tunings which use different mathematical approaches to define intervals.

Bottom line, the enharmonic notes you look at right now as being "the same" were not the same during the time of Renaissance composers who used different tuning methods. The minute differences between the intervals created happier and sadder sounding music, especially in stringed instruments with no frets.

Have fun diving into this quagmire, Quagmire.

A scale must use each letter only once.

The G scale must contain G A B C D E F.
So the F must be F# and not Gb.

The F scale must contain F G A B C D E.
So the B must be Bb and not A#.

The circle of fifths adds sharps clockwise and adds flats counter-clockwise. At the bottom of the circle you have 3 keys each with 2 names: Db/C#, Gb/F# and B/Cb. C# has seven sharps and Cb has seven flats. All the keys above these have one name because the second name would have more than 7 sharps or flats in a 7 note scale.

So which name do you choose for Db/C#?

Almost all classical songs change key several times. If you start out in a heavy sharp key like E you
would choose C#. If you start out in a heavy flat key like Ab you would choose Db. If your music doesn't change key you would
choose Db because it has less sharps/flats and thus is easier to read.

Whether you use the sharp name or the flat name for a particular key has to do with the avoidance of the need for a double sharp and to use the least amount of accidentals (sharps and flats) as possible. Using your example of the enharmonius Db and C#.

C# major = C#D#E#F#G#A#B# = 7 sharps
Db major - DbEbFGbAbBbC = 5 flats

Sometimes you will see C# instead of Db used even though it has more accidentals. If there is a modulation from a sharp key, you usually will stick with the same, ie a modulation from F# to C#. Also, sometimes it is easier for a player to think in C# instead of Db due to its relation to C Major. C# Major (all sharps) is all notes 1/2 step up from C Major (no sharps)

Using the chromatic scale it is common to use sharps ascending and flats decending like B,C,C#,D as opposed to B,C,Db,D and D,Db,C,B as opposed to D,C#,C,B.

The above answers are correct and excellent for why notes in a scale are named sharps and flats when they have to be a half step away from their natural.

These don't answer why the occasional out-of-scale accidental is called by its sharp or enharmonic flat letter name.

And I don't know why. But I thought I'd raise this as what Quagmire might really have been asking, since in his question he said he'd read "the general guidance on whether or not a note is designated sharp or flat is supposed to be according to its placement in a descending scale (flat) or ascending scale (sharp) in a given musical passage."

So, while its true that key construction requires using each note letter A to G exactly once, requiring some of those notes to be sharp or flat, that doesn't answer the question of what to call the middle note in the chromatic passage: C C#/Db - D does it? How do you choose which to call it? Does it depend on whether you're already in a sharp or flat key?

Again, I don't know. But I think Quaqmire was asking about choosing sharp or flat for out-of-scale notes, when either could apply.

@250gibson is correct that for chromatic passages, you'd typically use sharps if ascending and flats if descending. This is less of a theory issue and more of a writing convention. The problem with doing it the opposite way is that you then have to use natural symbols, which makes the notation busier and harder to read.

Example (@ = natural symbol, just use your imagination):

C Db D@ Eb E@ F
vs.
C C# D D# E F

However, outside of chromatic passages, the choice of sharp or flat depends on what scale degree is being altered.

C D E F# G A
vs.
C D E F Gb A

F# and Gb are the same pitch, but in the first example, we are raising F (the 4th scale degree), and in the second, we are lowering G (the 5th scale degree). This is true regardless of whether the passage is ascending or descending.

Keys add another layer of complexity in that some notes are raised or lowered by default, but this all still works the same way.

I thought a C# and a Db are a quarter step apart. But thanks to justified temperament there's only one key on the piano.

If you were tuning your string instrument to a key with Dd in it, you can freely tune it to perfect fifths temperament. My digital tuner, I noticed, only indicates sharp accidentals. But most can hear perfect fifths as they ring when they come in tune.

Sometimes the choice of sharp or flat depends on the note's context within a chord. For example, if you play the bluegrass song "The Old Home Place" in the key of G, the second chord is a B. If you write that chord out, the notes are B, D#, and F#. (Most likely the F# won't be explicitly sharped right there, because the written music will have indicated that in the key signature, right at the start of the piece.) People who understand theory will look at that on the staff and immediately recognize it as a B-major chord.

But if you write it as B-Eb-F#, the immediate reaction of the experienced reader will be, "Huh? What the heck is that?" Calling the note Eb instead D# results in a weird-looking cluster on the page that doesn't LOOK like a major chord. It's like having misleading signs on the highway that make drivers wonder whether they need to take this exit or not. They may slow down while they figure out what the sign meant, or make an abrupt lane change once they do figure it out, and the result could get--uh--messy.

You go with what shows as clearly as possible what the chord in question really is.

(BTW, note that in casual conversations like the one we're having here, you can use a lower-case "b" instead of a flat symbol. In context, people will understand what you mean.)

quote:

---

Originally posted by Ira Gitlin

Sometimes the choice of sharp or flat depends on the note's context within a chord. For example, if you play the bluegrass song "The Old Home Place" in the key of G, the second chord is a B. If you write that chord out, the notes are B, D#, and F#. (Most likely the F# won't be explicitly sharped right there, because the written music will have indicated that in the key signature, right at the start of the piece.) People who understand theory will look at that on the staff and immediately recognize it as a B-major chord.

But if you write it as B-Eb-F#, the immediate reaction of the experienced reader will be, "Huh? What the heck is that?" Calling the note Eb instead D# results in a weird-looking cluster on the page that doesn't LOOK like a major chord. It's like having misleading signs on the highway that make drivers wonder whether they need to take this exit or not. They may slow down while they figure out what the sign meant, or make an abrupt lane change once they do figure it out, and the result could get--uh--messy.

You go with what shows as clearly as possible what the chord in question really is.

(BTW, note that in casual conversations like the one we're having here, you can use a lower-case "b" instead of a flat symbol. In context, people will understand what you mean.)

---

So if a sharp or flat is expressed in the key signature, that isn't actually an accidental, is it?

quote:

---

Originally posted by Nopix

quote:

---

Originally posted by Ira Gitlin

Sometimes the choice of sharp or flat depends on the note's context within a chord. For example, if you play the bluegrass song "The Old Home Place" in the key of G, the second chord is a B. If you write that chord out, the notes are B, D#, and F#. (Most likely the F# won't be explicitly sharped right there, because the written music will have indicated that in the key signature, right at the start of the piece.) People who understand theory will look at that on the staff and immediately recognize it as a B-major chord.

But if you write it as B-Eb-F#, the immediate reaction of the experienced reader will be, "Huh? What the heck is that?" Calling the note Eb instead D# results in a weird-looking cluster on the page that doesn't LOOK like a major chord. It's like having misleading signs on the highway that make drivers wonder whether they need to take this exit or not. They may slow down while they figure out what the sign meant, or make an abrupt lane change once they do figure it out, and the result could get--uh--messy.

You go with what shows as clearly as possible what the chord in question really is.

(BTW, note that in casual conversations like the one we're having here, you can use a lower-case "b" instead of a flat symbol. In context, people will understand what you mean.)

---

So if a sharp or flat is expressed in the key signature, that isn't actually an accidental, is it?

---

No, it would not be an accidental, as I understand it.

quote:

---

Originally posted by Nopix

I thought a C# and a Db are a quarter step apart. But thanks to justified temperament there's only one key on the piano.

If you were tuning your string instrument to a key with Dd in it, you can freely tune it to perfect fifths temperament. My digital tuner, I noticed, only indicates sharp accidentals. But most can hear perfect fifths as they ring when they come in tune.

---

The difference between C# and Db in pure fifths (AKA Pythagorean) tuning is only 23 cents, which is more like an eighth tone. 

Some digital tuners (like those aimed at guitarists) only display sharps. Others will show a flat note if your intonation is low and a sharp note if your intonation is high. This doesn't have anything to do with how notes are written in practice, which is context-dependent (on key and scale degree).