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Why do we need key signatures such as E♯, B♯, C♭, and F♭? Take a look at the scales for E♯ and B♯:

enter image description here enter image description here

E♯ has 4 sharps and 4 double sharps. The key of F is exactly the same, and it only has one accidental in the key signature (B♭). I understand why it's sometimes necessary to use the note E♯, but using the E♯ key signature seems like it makes things more confusing.

B♯ has 3 sharps and 5 double sharps, while C major has no accidentals in the key signature at all! Which do you think is easier to understand?

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They're just extreme versions of enharmonic scales-that is, scales that exist in an identical sounding key but are spelled differently. It simply has to do with the fact that we have to have as many keys as possible to allow correct spellings of chords and whatnot. For example, A# minor is the relative minor of C# major (they share all the same notes). Now, the key of E# major is ridiculous on its own, but E# is the dominant of A# minor, and should we be writing a sonata in an old style, then we would need E# available to us as it is a necessity to writing in A# minor for any length of time. Like I said, these are kind of extreme keys: they exist primarily for theoretical reasons (and because theory teachers and professors say they have to exist) as opposed to everyday use and practical ones.

  • A nice "practical" illustration is the E flat minor prelude and D sharp minor fugue in book one of Bach''s "48" (BWV 853). The prelude has a climax about 3/4 of the way through, on the "Neapolitan 2nd" chord of F flat major (i.e. 9 flats). The fugue has a set of entries in the dominant-of-the domimant key of E sharp minor (i.e. 9 sharps).. – user19146 Mar 31 '15 at 20:57
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Regarding key signatures, you'd be hard pressed to find a musical work which has a key signature in either of those keys you've mentioned. The screenshot of your examples are even without any key signature; it's difficult for a staff to accommodate that that many accidentals and they were likely never intended to be able to encompass every possible key signature. Your example instead illustrates major scales based upon them. This is likely done as an exercise for a student of music theory in order for them to engage with pitches not commonly found in music, and a major scale is a convenient means of summarizing several of them. As you said yourself, notes like E# are sometimes necessary. The same goes for each of the other pitches found in your example.

C-major and F-major scales are undoubtedly more readable than the same sort beginning on B# or E#, but musicians should nevertheless become comfortable with reading pitches of double sharps, flats, et al, despite their infrequency. Modal mixture, altered chords, and composers that avoid enharmonic spellings spring to mind as a few reasons to be exposed to these sorts of pitches.

  • It's possible (and not uncommon) to have a major scale passage within a section of music that has a different key signature. If a piece of music in C# major (with sharps F#, C#, G#,D#, A#, E#, B#) has a scale passage starting on a note a four half-steps above the key note, notating that as (E# F## G## A# B# C## D## E#) would require accidentals on four notes (since E#, A# and B# are in they key signature). Notating it as (F G A Bb C D E F) would require accidentals on all seven notes. Even notating it as E# G A A# B# D E E# to exploit the sharps in the key signature would still... – supercat Dec 17 '17 at 18:34
  • ...likely require putting accidentals on more notes than would be needed using double sharps, since the Anat and Enat would cancel ut the A# and E# in the key signature, making it necessary to restate them on the next note. – supercat Dec 17 '17 at 18:36
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Another issue not yet mentioned is that, especially when using a computer to edit music, one may want to perform a sequence of transposing operations that create weird key signatures, but only normalize key signatures after performing all the steps. If one transposes a piece of music up, and then transposes a portion of it down by the same amount, it will often be desirable that the downward transposition should precisely cancel the effect of the upward transposition. If key signatures are normalized between the two operations, however, the operations might not cancel.

For example, if a piece of music had section which switched a few times between B major (five sharps) and B minor (two sharps) and was transposed up a major third, that would yield key signatures of D# major (nine sharps) and D# minor (six sharps). If the D# major portion were normalized to Eb (three sharps) and then the section was transposed back down, the result would be a mixture of Cb major (seven flats) and B minor (two sharps), with a consequence that matching notes in the major and minor key would appear at different staff positions.

One would generally want to normalize key signatures before printing them out for purposes of performance, but being able to have unusual key signatures during the editing process can allow computers to maintain distinctions during editing (e.g. the difference between Cb major and B major).

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These scales logically exist but, you're right, it's hard to imagine a circumstance where we'd need them! Occasionally it's appropriate to use a scale outside the scope of key-signatures (they only go as far as 7 sharps or 7 flats, we don't use double sharps or flats in key-signatures). G# major is not ridiculous.

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off drpylon's A#m example:

Without this "strange" enharmonic notation, the chord built on the 4th degree would be notated as: natural F, G#, natural C. Looking at this on a score would not look right; I read somewhere that the one of the purposes of enharmonic notation is to allow the writer (and reader) the ability to visually see what appears to be a normal chord at first glance, such as while sight reading.

In other words, it would be easier to sight read e#, g#, b#, rather than natural f, g#, natural c, hence an actual advantage of this strange enharmonic notation.

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Once you start talking about keys and scales you're basically ticking the box that says 'I agree never to use the same letter name consecutively'. Practical considerations, such as ease of reading, do not trump this. For better or worse, this proscription of consecutive letter names lies so far back in the musical theory genome that to upset it would lead to a period of chaos; so we persist.

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There are no key signatures of E# or B#! But there are B# and E# in REAL key signatures (and Cb and Fb too). For example, C# Maj has all notes sharped, so that is the easiest example. NO real key signatures have double sharps and these keys are NOT needed. Yes some music had double sharps, just NOT in the key signature. There are 7 sharps and 7 flat and one all natural (C Maj) key signature. That is all! It is important to note that there used to be a note between B and C and between E and F to facilitate different tunings to make the music more harmonious, on Harpsichords and I believe Clavichords, where the player would choose one or the other to fit with the remaining notes being played. Different tunings (temperaments such as even and equal etc) have compromised the notes enough so as to prevent this need. I think the old kind was "Just temperament" and "Pythagorean" or other tunings. Hope this makes sense...

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