E Sharp?

[SHall1000]

It’s enough to drive you insane.

Sums up my attitude to music theory.

[shantus]

I think this has to do with the possible contexts in which this e# would function. I can't find the example but there is a piano sonata by Brahms where there is this important moment where an F# in the melody carries over into a new harmony where it has the role of Gb. Apparently it's a popular example used in music theory, maybe to encourage people to not just approach it in terms of chord-sequences.

[jamcat]

It helps to think of musical notes in terms of a continuous pure-pitched system like a violin, instead of a fixed-note compromise system such as a piano or guitar.

If you play a scale on a violin then move up one pure tone and play the scale again, you’d see that the notes don’t line up exactly. A in one scale is a different frequency than A in another scale. The same goes for G♯ and A♭, or E♯ and F♮. But on a keyboard or fretted neck, the notes are poked and prodded into conformity to simplify the instrument construction. Such is equal-temperament.

[mystran]

If you play a scale on a violin then move up one pure tone and play the scale again, you’d see that the notes don’t line up exactly. A in one scale is a different frequency than A in another scale.

Really with a violin the ("ideal") frequency of any given note, say A, can vary a little bit even in a single scale depending on the surrounding notes and perhaps what other instruments are playing concurrently and which other instruments you are playing with. If you were to pick a single fixed frequency for each note of the scale, you'd be similarly "always out of tune" as say a piano.

In practice though, even if you take say equal temperament as "ground truth" that doesn't really change the fact that classically each scale is a repeating sequence of ABCDEFG where we can pick any letter as the starting point, rotating the whole thing and then we add a bunch of flats and sharps to get the major/minor/whatever scale we want... and whether or not E# and F are actually a different frequency, it still makes sense to think about them logically as two different notes, because this makes it a lot more clear which scale you're actually working with and if we were to say have E and E# in the same piece of music, this immediately signals that there is some sort of modulation or at least "out of scale" notes going on... so it's a mental tool more than anything.

[jamcat]

Really with a violin the ("ideal") frequency of any given note, say A, can vary a little bit even in a single scale depending on the surrounding notes and perhaps what other instruments are playing concurrently and which other instruments you are playing with.

Yes, this is true too. Harmony will be Just intonation which is dynamically tuned relative to the note of the melodic lead for consonance. Tuning for each chord is treated as though it is the tonic, with perfect intervals. And even the tuning of the lead will change depending on context. For example, with Expressive tuning, minor thirds will be flat, and just how flat will depend on the mood of the moment.

[XNOR]

This is called enharmony. Although earlier in music history C# would be slightly higher than Db, the harpsichord had 2 black keys in between!

[BKSchatzki]

Unless you get into the weeds of the actual mathematical ratios, the main answer to the question I'm pretty sure you're asking is that classical music theory uses these terms because, as others have mentioned before, there are conventions in musical spelling. Think about triads.

C Major: C d E f G, right?
C Minor: C d E(b) f G. The main point is that we build it with a third, and another third. We couldn't do the following: C D(#) e f G. This would be a second, then a forth, making the chord a... C-sharp-9-no-3rd?

This also shows up when using chromatic voice leading and modal mixture. Imagine you're in C#m, but you want the five chord to have a major 3rd, making a leading tone pulling up to C#. Well, C doesn't pull to C#. Generally, you want to read a B# before the C#. It is more meaningful to read the harmonic and melodic intention when you see that this is the note below the tonic.

This is the difference between a dominant 7th chord and a German augmented 6th chord:
Dominant 7th: G B D F, where the F wants to "collapse down" to the E.
German Augmented 6th: G B D E#, where the E# wants to "ascend to" the F#. Also, the G wants to collapse down to the F#. This is why the Augmented 6th chords have an "expansionary" voice leading, and dominant 7th chords have a "contractionary" voice leading.

Anyway, do whatever you want. But people who know theory are going to be annoyed when you spell your F# major chord F# Bb C#, and if you actually commit this to sheet music, it will be needlessly difficult to read according to convention. Triads should "stack" in sheet music, and a F# Bb C# wouldn't stack properly.

[jancivil]

BertKoor is right. There's not much call for E#, because "the key of F#" is pretty much always given as "the key of Gb," so it's not too common to think of it that way.

Bert Koor was right in that basic explanation for the note's existence, but he didn't weigh in on a preference for flats over sharps, did he.

Pretty much always what, exactly, though? Flat keys are a preference for a musician whose instrument is pitched from a fundamental like Eb, no doubt. It means pretty much nothing for a guitarist, and the fingerings on a keyboard are going to be the same.

The fingerings for [single notes] D# and Eb on an [Eb] alto saxophone are identical, as they are enharmonic equivalents. However, there are some differences to consider {NB: keys =}:
D# (Concert F#) Uses more complex fingerings with multiple side keys
Typically involves more "forked" or cross fingerings
Eb (Concert Gb) Generally uses simpler, more straightforward fingerings;
can involve fewer keys pressed simultaneously.

The transposing instrument here means if the concert key is F# we're writing (or the instrumentalist is transposing at sight from) it in D#: D# E# Fx G# A# B# Cx. The composer or arranger will avoid doing this, in favor of a cleaner look, besides the above.

In objective or abstract terms, key of F# has six sharps in its key signature. Key of Gb has six flats in its signature. Six of one, half dozen of another.

[AlainGeneva]

Scales have exact names. If the major game is I II III IV V VI VII, each degree need to have a different name. In this case, f# is the one, then the "f" is token, thus the VII have to be be E#.

[jancivil]

Asked and answered to begin with.
it's simpler to just observe that a seven-note scale is named according to the alphabet, sharps/flats notwithstanding.
C D E F G A B for "C major";
Cb Db Eb Fb Gb Ab Bb for "Cb major";
C# D# E# F# G# A# B# for "C# major".

FYI: The convention, Roman numerals for scale degree indicates the triadic harmony on that degree. No reason for it otherwise.

[digitalboytn]

'E's a very sharp guy.....