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I'm aware why E and B sharp don't exist but apparently they exist in music theory because of functional differences that may occur. If they don't exist on instruments, why do they exist in theory? Why can't I just mess around F instead of E#?

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    Don’t forget F flat and C flat! Aug 30, 2022 at 16:19
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    Well, technically, no letter names "exist on instruments" (unless they literally have them written on them, like maybe an autoharp). Instruments can vibrate at certain frequencies, like 440 Hz. It's up to us what we call them. (Also, while an equal-tempered piano makes the exact same sound for "E#" as for "F", instruments that can change their intonation, like voice, violin, oboe, etc., can make intonational differences for the different contexts that call for one or the other.) Aug 30, 2022 at 16:19
  • @AndyBonner almost all unequally tempered keyboards make the same sound for E sharp and F, too.
    – phoog
    Aug 30, 2022 at 18:42
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    @phoog Well, there is an oddity near me with some "split" black keys! Aug 30, 2022 at 20:28
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    Have you even stopped to consider naming notes in the key of F# major? Aug 31, 2022 at 17:57

6 Answers 6

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I'm aware why E and B sharp don't exist...

Of course they exist.

For tonics of F# and C# the leading tones are E# and B#. If you want to see examples of those tonics with their leading tones, without the mess of enharmonic keys like Db versus C# major, just look at the minor keys: F# minor and C# minor.

There is something called a theoretical key which is the kind of purely theoretical thing that I think you had in mind.

Why do such things exist in theory? I suppose the answer is because you can infinitely transpose (like transposing up/down a perfect fifth) and if you do that you eventually get into double, triple, etc. sharps/flats and enharmonic equivalents.

If you meant to ask about theoretical keys of E sharp major and B sharp major, you should make that clear. E♯ is a pitch. E♯ major is still ambiguous. It could mean a chord or key. "Key of E# major" is clear.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Doktor Mayhem
    Aug 31, 2022 at 22:49
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For simplicity of writing in any key, each of the 7 notes diatonic to that key is deigned to have a separate letter name - chosen from A B C D E F and G.

That in itself necessitates there being E♯ in C♯ key, and B♯ in C♯ key also. (Not forgetting F♭ and C♭ in another key). At least that way, written music will have each line and each space dedicated to a specific letter name.

There's also the fact that certain chords, to be written properly, need to be as such. Take, for example, the chord of E+ (E augmented). It has the 5th sharpened. Standard E comprises E G♯B. So E+ will have to be E G♯ B♯. Writing it as E G♯ C is plain wrong!

All this presumes 12tet - as other tuning systems (temperaments) will actually have B♯ and C as (slightly) different pitches.

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    Most historical unequal temperaments are 12-tone temperaments (or even more-than-12-tone temperaments) in which B♯ and C are necessarily the same pitch (but it might be better tuned for use as C than as B♯).
    – phoog
    Aug 30, 2022 at 21:01
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They exist because the spelling of notes matter. One very simple example is a C major chord consist of the notes C, E, G. All a 3rd apart as that's how chords are spelled. When you build a C♯ major chord you then have C♯, E♯, G♯.

I'd also like to point out things like double sharps and flats that extend the range of notes even more so something like D♭♭ would be equivalent to a C, it's spelled that way for a reason.

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The fact that they have functional differences is exactly why they exist in theory. The purpose of theory is to describe why "F" functions differently in C# major than it does in C major.

Historically it is also the case that notes like C# and Db were actually two different pitches, thus the distinction existed before the theory came about.

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    "Historically" like last night, in fact.
    – phoog
    Aug 30, 2022 at 18:44
  • Also "the distinction existed before the theory came about" is kind of backwards. The functional distinction existed first; tuning considerations came later.
    – phoog
    Aug 30, 2022 at 20:54
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They exist because ANY note can be sharpened or flatted (flattened?), even if there is no accidental note between them. The most fundamental example is if you have studied the cycle of 5ths you will know that when you get to 7 sharps (C#) or 7 flats (Cb) every note is either sharp or flat. The key of F#, or 6 sharps contains an E# and Gb, or 6 flats contains a Cb. This is necessary because keys must contain every letter with no repetitions in their makeup, you can not have one letter repeated even if they are different notes, for example F to F# must be E# to F#.

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  • And I assume the reason why the "no repetitions" rule exist is because sheet music would look weird if you had to explicitly mark every F♯ and F♮ in a key that had both.
    – dan04
    Aug 31, 2022 at 17:21
  • @dan04 Even beyond that is the fact that every scale tone and chord that is built on those scale tones has a specific numerical name and theoretical function. For example if you are in the key of F# the leading tone must be ^7, E#, not ^b1, F. To show the upwards movement in the staff and the ^7-^1 movement. Aug 31, 2022 at 17:48
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Well for me E#, B#, etc exist both in theory and practice, and they can be very useful as well.

I'm a string player, and I find it very useful, when I'm in the middle of some sequence of modulations, to get this kind of (partial) cue or reminder, about what part my coming note is playing in the harmony. It can furnish a cue about suitable adjustment or 'bending' of the pitch either up or down.

Of course it's only a partial cue, it doesn't tell the whole story about the upcoming harmony, but it's a useful part of the tradition that I wouldn't like to see eliminated.

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