Key Signatures: Why is there an E#?

I think it's to do with notation. A scale should only contain one of each letter name so take C Major for instance.. C D E F G A B. If you go up a semitone the notes would become C# D# E# F# G# A# B#.

If you decided to skip the use of E# then you would end up with a F and F# which will cause obvious problems, you wouldn't be able to write it on the key signature so every F would end up needing a sharp or natural sign next to it.

For this reason Db would be the better choice. As for why the key of C# should ever be needed (if ever) then I haven't a clue.

Lee

You only want one note for each letter name - that way in standar notation you don't need too many accidentals in the measures.

Although E# in a key signature is rare, appearing only in the keys of F# and C# (and the oddball signatures with double sharps that you'll only see in academic texts), the do happen all the time in minor keys.

Take the relative minor of A - the key of F# minor. We often use the harmonic minor form of the scale, which raises the seventh note - E - by a half step. Even though E# is the same tone as F, you wouldn't want to write it as F natural, because F# is the key note - you'll probably have a lot of them in the piece.

So the F# harmonic minor scale ends up being:

F#-G#-A-B-C#-D-E#-F#

Ok, got it, thanks!

As for why the key of C# should ever be needed (if ever) then I haven't a clue.

You'll find C# fairly often in some works from the 1800s. Publishers tended to emphasize the root note (at least in the antique music I've got here), so if a piece went from major to tonic minor, you'd end up with C# - a key signature might go from seven sharps (C#) to four sharps (C#m).

The alternative would have been to show five flats (Db) and eight flats (Dbm - with a double flatted F note)

Publishing conventions have changed, and now most publishers will assume you know it's the enharmonic tonic minor when the signature moves from five flats (Db) to four sharps (C#m)

EDIT: Whoops, I took too long typing, so what I've said may have been covered. But this is a sort of overview of what I think I understand (!) about the reasons why we have all that sharp and flat stuff at all...)

Lee N is right, it's all about how the music is written on the staff. :)

We're trying to squeeze 12 notes into 7 named spaces.

There is no real reason why the 12 notes couldn't be called A, B, C, D...through to J, K, L. Over the years several people have come up with other ways of representing the notes, but they've never caught on. :o

However, you'd need a much wider staff to fit all the notes on if you had a line for each note. So the staff we use is a way of compressing it into a smaller space by only giving 7 of the notes their own line. The other 5 "share".

Back when this stuff was all being thrashed out they really LOVED the C major scale (I think is was to doing with the church people of the day, who had a lot of control over music, and reading and writing in general. I think they thought it was more "heavenly" or something.) So the C major scale got all the best names. :wink:

So, basically you have 12 notes sharing 7 spaces.

The notes "in between" are not inferior, or weaker in any way - all 12 are a semi-tone apart from each other - but they just don't happen to be part of the C major scale.

So when a piece is in another key, the "in between" notes just "borrow" the staff line of whichever Cmajor note is closest.

Now sometimes the line below is "free" so you can call the note C# for instance (the note between C and D). However, if the scale already has a C in it, it's too clumsy to have the same line trying to represent two different notes (as Lee said, it can be done but it get messy). :shock:

So you borrow the line above and call it D flat instead (sometimes written Db). But it's the SAME note (the one betwen C and D) whether you call it C#or Db. :)

Some people think it would be easier just to have 12 note letters, and a bigger staff - but it's OK once you get the hang of it.

I hope that made sense. :?

It all seems rather weird until the penny drops...

Thanks Tom, I had to read it a couple of times to understand it but I got the point in the end. :)

Lee

Yep the whole thing should be decimalised. :lol:
Sharps and flats my arse. ABCDEFGHIJKL sounds good to me.

Errrm why is their no accidental note between BC and EF anyway. Unless of course as given in the reasons above, i.e its better to have the note named E as oppossed to F just to make the key/scale look nice and tidy. :lol:

Yep the whole thing should be decimalised. :lol:
Sharps and flats my arse. ABCDEFGHIJKL sounds good to me.

It has been decimalised. :shock:

Have a read of this, if you don't mind risking your brain suddenly going POP!

Click to go to the Cypher Sytem website

He uses numbers 1 - 12 and certain symbols, but I wasn't kidding about some people thinking that A to L would be dandy too. :D

Ironically, reading Roger Blumberg's explanation of what he thought was wrong with the traditional notation (on The Cypher site) helped me understand it better, and feel more comfortable about learning it! :lol:

That's actually the original notation system - the ancient Greeks used a letter of the alphabet for each note.

They had 7 tones per octave, and the range of the instruments was two octaves, so they used 15 letters - octaves had different names, so tone L would be an octave above tone E (using the English alphabet)

That system got changed around 500 AD, when octaves were recognized as pretty much the same thing. So now we had only letters A-G to deal with. That A-G system got pretty ingrained over the next thousand years... so when people started using notes in between those pitches with regularity, around 1500 or so, the altered them with sharps and flats to avoid having to re-learn the whole letter scheme.

:D

Thanks very much for the historical background NoteBoat.

I've been trying to find out a bit more about this subject. Do you know any good websites or books I could check out?

I'd read about the Greek system with the fifteen letter system, but I'm still a bity hazy about the actual notes being used.

My reading of it is that the 12 note scale that we use now is 'relatively' recent, in terms of the 'equal' spacing between all the notes as far as ..umm not sure of the right terms are here... as far as sounds, wavelengths etc are concerned (??)

I've read that other system (such as Indian music) divide their octaves into many more subdivisions, and also that some earlier western tunings (or rather 'temperaments') used different spacings from note to note.

So my question is:

Did the 7 note A to G system correspond with our modern notes named A to G - with our 'sharps' just not used? Or was it a different way of dividing an octave into 7 instead of 12 divisions?

Perhaps I should ask in the Theory forum instead of hijacking this thread - but NoteBoat's answer was very informative and ...tempting.. :D

It has been decimalised. :shock:

The Structure of Atonal Music is the usual reference for this.

Personally, I think it's a very GOOD idea to move away from the A-G+accidental system of thinking about music. While it has been the basis of a great deal of very good music. The fact remains that since the advent of well-tempered tunings, our instruments don't have seperate notes for C# and Db. The old musical notation system doesn't accurately reflect the music as played.

That said, there's virtually no traction for that idea, and as such there's no real reason to expect that we'd be moving anywhere anytime soon.

Advances in notation seem to follow advances in music practice by roughly 150-200 years, so I'll be communing with the universe before I see a good system for 12-tone notation (coming to a music stand near you in the next century or so)

Chris, we really don't know what notes the Greeks used, only that they named the range using the first 15 letters of their alphabet, and that their lyre had four strings tuned to different notes - we draw the term 'tetrachord' from their four-note tunings. Unfortunately, the Greeks didn't develop recording technology, so a lot of music history research is pretty speculative.

Most books treat the notation history aspects as sidebars - a decent one is John Castellini's "Rudiments of Music", copyright 1962 and no doubt out of print... it's got sidebars on the development of the piano, the various minor scales, etc. I'm not aware of a good book devoted to the topic; I've picked it up in bits and pieces over the years from various sources.

The 12 note scale is pretty recent. Heck, sharps and flats didn't really get going until people started writing for more than one voice at a time - a bit less than a thousand years ago. If you stay in one key, that means the 7th note harmonizes into an ugly interval, so they needed something different... so the development of harmony preceeded (and spurred) the notation. Once we had sharps and flats for every note - they actually developed one at a time- by around 1500AD, that opened up the whole idea of a system of keys, fully exploited by Bach with his Well Tempered Clavier books.

Non-western music often uses more than 12 discrete notes, but systems like Arabic music (with 24 tones per octave) or Indian music (with 22 as I recall) don't use more than 7 at a time - so it's sort of like our scales, but they have more starting notes to choose from. Once you pick your scale, you don't have quarter-step accidentals, you only have notes in the scale. Modern notation systems have developed to cope with half-sharps and flats, and quarter-sharps and flats, but we'll no doubt do better in another 75 years or so. Realistically, you'd need about 70+ divisions within an octave to accurately notate all the different world musics out there.

Temperment is a whole 'nother ball game. If you use the Pythagorean system, where intervals have a strict frequency ratio of 3:2, 5:4, etc, you get a different scale than we use today. You also get nice little features like the fact that F# and Gb are different notes, and octaves don't sit quite right - Google 'Pythagorean comma' and you'll no doubt find resources in that line of inquiry.

Some instruments could handle the different keys quite easily, like violins - they just move their finger a tad, since it's fretless - and other instrumentalists relied on instruments built specifically for the key. A horn player in 1600 might need four or five horns to play in the different keys required, since some might do F# and others Gb. When keyboards developed, they had split black keys, so you could choose F# or Gb and stay in tune.

With the development of the piano just over 300 years ago, there was a keyboard instrument of orchestral prominence for the first time. Something had to give, and the search was on for a tempering system that would allow F# to equal Gb. We didn't settle on a winner until the 1800s, and that's the system we still use today.

The early (pre-1000 AD) 7 note A-G systems did correspond to our A-G today, although we can't be certain if the pitch was the same. Early choirs used 7-string harps to settle on a common pitch, and A was considered the lowest note... but it's likely that A in France didn't match A in Italy. The common thread there is A=lowest; we didn't settle on the idea of 'middle C' and fixing pitch frequency for several hundred more years.

See the wikipedia article http://en.wikipedia.org/wiki/Pythagorean_tuning for an auditory explanation on why the pythagorean tuning gave way to equal temperament. There are two audio filed posted there showing how the "stacked" harmonic intervals can create a perceptibly out of tune interval that could drive you mad. If you listen to that "wolf interval" enough times you'll understand why JS Bach felt passionate enough about getting away from pythagorean tuning to write preludes and fugues in all 24 keys for a "well tempered clavier".

Wow!

I go away for a few hours, and some excellent replies have appeared. Thanks to you all for taking your time to share that knowledge. It still blows me away how much of their time that some people are prepared to donate to help total strangers. :D :D

I'm a bit sad to hear about the Greeks failing to develop a decent Hi-Fi system though - and I'd been so impressed with their other achievements. :?

It's a bit like medieval language pronounciations I suppose, lots of guesswork but not much hard evidence.

Sometimes these things have been partly pieced together through clever detective work. I quite enjoy books/articles about etymology and it's amazing how much they know (or think they know :wink: ) about word pronunciation from the past based on things like the rhymes and rhythms used in poetry.