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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#?

Aaron
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anotherstranger
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    Don’t forget F flat and C flat! – John Belzaguy Aug 30 '22 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.) – Andy Bonner Aug 30 '22 at 16:19
  • @AndyBonner almost all unequally tempered keyboards make the same sound for E sharp and F, too. – phoog Aug 30 '22 at 18:42
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    @phoog Well, there is an oddity near me with some "split" black keys! – Andy Bonner Aug 30 '22 at 20:28
  • @AndyBonner if I'm reading that correctly, they've got a broken octave in the bass and an ahistorical mechanism to have distinct D sharp/E flat and G sharp/A flat without splitting the keys. But since we're talking about E sharp, there are very few split-key keyboards that support it. Most but not all limit themselves to splitting the black notes (and usually only a subset thereof, as noted in your link). – phoog Aug 30 '22 at 20:51
  • Observe how some musicians apply the same reasoning to notes overall - "why mess around with note names when I can just say {fret} {string}?" ^^ Music is a language, and certain concepts need E#/B#/Cb/Fb (and Bbb, and so forth...) to be conveyed. – moonwave99 Aug 31 '22 at 11:36
  • @moonwave99 - there is an awful lot of musos - guitarists in particular, who would disagree with calling A Bbb, not understanding the reasons why it should technically be Bbb. Those who are ignorant still get by, to the chagrin of us purists. After all, both notes live on the same fret/string, so why not use the more simple name..? Admission - for years I thought the dim7 note from Cdim 7 was A. Well, it looks that way - and I've seen it on staves that way too. – Tim Aug 31 '22 at 11:54
  • @Tim that's the exact example I was referring to! ^^ – moonwave99 Aug 31 '22 at 13:28
  • Isn't the issue really whether your read notation for common practice harmony? The point is to maintain the familiar, and correct, intervals of the moving lines, the voice leading. In F minor F♮ F♯ isn't used for a leading tone motion, because it's so horridly unreadable compared to correct E♯ F♯. Double sharps/flats seem a bit different than the B/C E/F enharmonics, but I consider than my personal weakness is reading skill. – Michael Curtis Aug 31 '22 at 14:00
  • @MichaelCurtis - yes, it's basically a reading thing. If one doesn't read, or doesn't read well, it really doesn't make much difference. And if one is not steeped in theory, unlike what we are, apparently it doesn't matter much either... – Tim Aug 31 '22 at 14:52
  • I don't think someone needs to be steeped in theory to encounter some of these enharmonics. You just need to read/play a bit beyond F/C/G major. F# and C# minor just aren't unusual enough to say these things happen only in obscure harmony. – Michael Curtis Aug 31 '22 at 15:57
  • On keyboard instruments E# and F are the same key, but voices, strings, and some wind and brass instruments can produce infinite variation of pitch. If you write a C# major chord moving to F# major for a string quartet or choir, the musicians will raise the E# as they ascend to F#. They will sing or play a higher frequency than the F/E# key produces on an equal-tempered keyboard. – musarithmia Aug 31 '22 at 16:10
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    Have you even stopped to consider naming notes in the key of F# major? – Carl Witthoft Aug 31 '22 at 17:57

6 Answers6

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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.

Michael Curtis
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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.

Tim
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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 '22 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.

Dom
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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.

Aaron
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    "Historically" like last night, in fact. – phoog Aug 30 '22 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 '22 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#.

John Belzaguy
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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 '22 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. – John Belzaguy Aug 31 '22 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.

terry-s
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