21

I understand that the key signature indicates what are the exact notes represented on the staff lines and spaces and thus tells us the diatonic scale in which the music is composed, which in turns gives us a clue about which key the music is composed in.

E.g a key signature with two sharps tells me that the music will probably mainly use the notes of the D major scale (D E F♯ G A B C♯) so the music will probably be in the key of D or one of its related modes.

Now, I can imagine that back in those days, it would have been very cumbersome for a composer to have to write four or more accidentals with a quill and ink on every row of the staff.

Yet, it seems to me that unconventional key signatures are hardly used (I've never come across one personally) so a key signature of four sharps will always be the same set of four notes, to the point that all musicians have to memorize the "order of sharps" and the "order of flats".

My question is: why was the key signature notation never simplified?. Why did we never decide to use symbols instead of listing accidentals, e.g just write "4♭" instead of actually writing the four flats?

  • 2
    Look in the Real/Fake books, and see that the key sigs are often written only on the first lines. – Tim Nov 23 '19 at 13:53
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    If there are 4 sharps in the key sig, writing those 4 sharps once on each line was probably less than all the times they appeared in the music so it was actually a time saver. – b3ko Nov 23 '19 at 14:08
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    Not sure I understand the question. To use computer programming terminology : You want a compiler to open out (compile) the key-signature into the score inline — Right? – Rusi Nov 23 '19 at 15:27
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    So what if we are in F minor. Do we write F minor in the same way we would have written A♭ ? If so do we assume that the E is flat or natural? – JimM Nov 23 '19 at 15:37
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    F minor has a key signature of four flats. But non-diatonic notes, particularly the sharpened 7th, are even more common in minor keys than in major ones. (And they're pretty common in major keys!) – Laurence Payne Nov 23 '19 at 16:58
38

Actually, it seems to me that designating the key by a letter instead of the arrangement of sharps or flats is not simplifying the process. Simply stating the intended key by letter and accidental ignores the need for information that many less advanced musicians need to know in order to make sense of what is written in the sheet music. I can look at a key signature and quickly understand which notes need to be sharped or flatted without even considering the name of the key, but knowing which notes are sharped or flatted can tell me the name of the key so this is the method generally used to identify the key. Otherwise a less skilled musician would need to look up the sharps and flats of a given key in order to know how to play the piece. The point that strikes me as most important when playing music, is knowing where the accidentals appear, more important than actually knowing the name of the key itself. Thanks for the question.

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  • Another hurdle: instruments are tuned to different keys, so the set of accidentals associated with (for example) the key of D is different for a trombone that it is for an oboe. This is a significant increase in cognitive load for an instrumentalist, particularly one that plays multiple instruments. – bta Nov 25 '19 at 20:18
  • @bta That's actually less of an issue. A given key will have the same arrangement of sharps or flats. Different instruments, however, will be told to play in different keys. For example, the pianist would be told to play in the key of A, while the trumpet player will be told to play in the key of B. That's effectively what already happens, though we get told the arrangement of the sharps and flats, rather than just the key. – fyrepenguin Nov 26 '19 at 13:05
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    @bta You are correct that for a given key for a song (for the pianist), the other instruments will have to play in a different key, but speaking as one who played an instrument other than a C instrument, we didn't really consider anything other than the key that our music was in. (Key of G for a Bb instrument still only has 1 sharp, even though it sounds like we are playing in the key of F, with 1 flat). Sorry if I misunderstood what you said, but the whole transposing thing is important to me; I used to sight-transpose off of the piano/SATB music, so lots of dealing with keys/transposition – fyrepenguin Nov 26 '19 at 13:08
19

I believe it's not simplified for some reasons:

1st: Music notation is an orthodox practice which has kept its standardization globally for common understanding. The Boethian notation (alphabet notes A, B, C, D...) was developed as early as the 6th century, but key signature as we known today was developed in the 16th century. Musicians could have chosen to use the Boethian notation instead accidentals at the start of the piece, as you suggest, but they didn't. Why? I think the 2nd reason justifies it.

2nd: When we are reading a score, it's sometimes helpful to check the accidentals at the beginning of the stave row. We may known by heart that the key of E major has 4 accidentals, but how fast do we remember the order (F#, C#, G#, D#) while we are reading at first sight? Sometimes a quick look at the accidental on the staff line helps us to remember, it's helpful to have those accidental cues. And how about chromatic passing notes where we have to signalise natural accidents, then back to sharps/flats, etc? Wouldn't it become confusing, especially in late Romanticism? So I think this notation has been designed for facilitating the musical reading.

3rd: How about modulation? We could notate the music is in E major, but it could soon change to its relative (C# minor). Perhaps it would be misleading to have something affirming the tonality to be E major. Then this becomes a harmonic matter.

These are only suggestions, but I hope it makes sense.

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  • 4
    In addition to these reasons: (4) Not all music is written in the major/minor system. For example, both ancient music and some modern jazz use other modes. In the OP's suggested system, we would need a different notation for every mode. (5) Music can have obscure clefs and movable clefs, and an orchestral score can have a whole bunch of transposing instruments. Given the key signature for the part, it's always easy to locate the tonic. – Ben Crowell Nov 23 '19 at 22:56
  • @BenCrowell well, in practice, pieces in e.g. D-Dorian are very often still written with a ♭ in the signature (even if that requires putting a ♮ before every B note). So, having only systems for every major and every minor key (and accidentals) would be sufficient, albeit not necessarily as convenient. – leftaroundabout Nov 24 '19 at 10:47
  • @BenCrowell it would be perfectly possible to simply key signatures without regard to mode. Key signatures already suffer from a complete lack of information about mode, so a simplified system that failed to indicate mode would not detract from the system we have today. For example, you could replace the current system with a single integer plus a flat or sharp sign, so that (for example) 2♯ means D major or B minor. Or you could institute a system that does convey more information, by writing (for example) DM or Bm or Ed for a key signature of two sharps. – phoog Nov 25 '19 at 2:52
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    Isn't this a misuse of the term "accidental'? "In music, an accidental is a note of a pitch (or pitch class) that is not a member of the scale or mode indicated by the most recently applied key signature." So the sharps or flats in the key signature are not accidentals. Or is it a reference to this usage? "Sometimes the black keys on a musical keyboard are called accidentals (i.e., sharps or flats), and the white keys are called naturals." – nasch Nov 25 '19 at 18:02
7

The traditional style of key signatures is pretty close to optimal for the music written from about 1700 to 2000 or so. During the 1700-1800 (give or take a few decades), it was traditional style was to use 1 less sharp or flat than the piece would now call for. Thus Bach's "Dorian Fugue" is really in D minor with all the Bbs accidentally notated.

Bartok experimented with mixed sharps and flats for notating Eastern European modes. In general, remembering the (generally one-off) key signature wasn't easier than reading a few extra accidentals.

Several articles have suggested using two flats and a sharp for pieces in a minor mode. However, other articles counted the number of accidentals needed using the traditional notation (using the key signature of the relative major) and using two flats and one sharp (on steps 3,6, and 7 respectively) wasn't much different. The minor mode is basically 5 notes (steps 1,2,3,4,5 normal and steps 6 and 7 mutable) so it doesn't seem to matter much which notation was used. The number of raised 6th and 7th steps is about the same as the number of lowered sixth and seventh steps. As many pieces (from the 1600 onward) did modulate from minor to its relative major and vice versa quite a bit, the traditional notation (relative major's key signature) works well overall.

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  • The first paragraph is surely incorrect (or incomplete). The Dorian mode on D has B naturals, so if a B-flat is required it would be indicated as an accidental. The piece might actually be in D minor, but only because of the accidentals (and as they are accidentals, and not part of the key signature, it's not in D minor). – Andrew Leach Nov 24 '19 at 14:33
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    A lot of questions get posted about why musical notation has not been simplified to remove irregularities and redundant information. And the answer is almost always this - because the traditional system is pretty close to optimal. It is the irregularities and redundancies that allow experienced musicians to navigate quickly and accurately without losing their place. – Ian Goldby Nov 25 '19 at 12:56
  • I think that's right. The traditional system has been simplified (or at least modified) towards optimality. One problem is that there are several criteria for optimality (economy, precision, ease of reading, ease of writing or printing, etc.), and in general, optimizing one does not yield good results for the others. – ttw Nov 25 '19 at 14:30
  • @AndrewLeach This is the "Dorian notation" for (what we would now call) minor keys with flats. Bach actually switches from Dorian notation into Aeolian/modern notation between the fantasia and the fugue sections of the Chromatic Fantasia & Fugue BWV 903. – Michaelyus Nov 25 '19 at 16:54
  • What changed in 2000? – Beanluc Nov 25 '19 at 19:22
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I think the basic answer is that the vast majority of classical music used notes beyond the diatonic scale, and even in pop music today it's still pretty frequent to have chromatic notes.

Thus, if you're playing in the key of D major, and there's a C-natural, you need to write C♮ with the natural sign. If this continues for several measures (as sometimes happens with a temporary modulation), it's helpful to have a reminder at the beginning of each staff system that says, "Oh, yeah, C♯ is still the default." The more chromatic music gets, the harder it can become to remember what the "default" sharps and flats are in the key signature, so having a periodic reminder is helpful.

Also, even if you're in one key, the notation can be harder to understand for music beginners, who may not make immediate connections between the sharps and flats notated on each line and the key of a piece. This is particularly problematic in minor, where the 6th and 7th scale degrees also tend to move about and can contain various accidentals. Beginners in music are often taught about "natural minor" and "melodic minor" and "harmonic minor," but actual minor key music tends to use a lot of accidentals on those 6th and 7th degrees. Again, having a visual reminder on each staff of the accepted defaults can be helpful.

And it's often visually more helpful to see those sharps or flats on the lines and spaces where they actually occur (and can sometimes be cancelled with naturals or added to with additional accidentals). In fact, it was still accepted practice at times even in the 18th century (and later) to include those key signature sharps and flats on every place in the staff that they'd occur -- for example, a piece in D major in treble clef might mark the F♯ both on the top line of the staff and in the bottom space. In that sense, modern notation has simplified key signature notation a bit.

(Just as a historical note, part of the reason for that previous practice was because clefs were not particularly fixed in their staff positions until some point in the seventeenth century. It was quite common for clefs to move up or down by a line or more, even multiple times in the same piece. Performers reading a score needed to be able to immediately reorient themselves on every line of a score to where the clef was and therefore where the notes were. So having default sharps and flats marked on each staff line or space was also helpful in orienting to each staff line. We've dispensed with some of the other notational practices needed back then, such as the custos, a symbol that often looked a bit like a checkmark and appeared at the end of each staff system to tell the performer which note was the first note at the beginning of the next system. Again, this was needed at a time when clefs could move about freely, and performers needed to immediately know how the notes from one line of music connected to those on the next line.)

All of that said, modern practice is inconsistent. Sometimes things like fake book lead sheets will dispense with the practice of writing the key signature on every line, merely giving it once at the beginning. (Often they also omit the clef except for the first line.)

It really all depends on how much consistency you have. In a mostly diatonic piece of music that remains in one key, I agree that one could easily just write "D major" on the top line and everything should be clear. However, the more chromaticism, key changes, etc. that occur, the more it is helpful to have visual reminders of what the current default sharps and flats are.

On the other extreme, many 20th century composers who began to write highly chromatic and atonal music sometimes dispensed with key signatures altogether, instead preferring merely to note all accidentals when they occur. If you really wanted to simplify music notation, that practice would actually be most helpful, I think -- any note without an accidental is assumed to be natural, and when sharps or flats occur, they must be written before every note. That would make music notation more accessible to beginners and be consistent across styles of music that are diatonic, highly chromatic, or even atonal. However, that practice would require even more notated sharps and flats than our current practice of putting key signatures on every system, so it's unlikely to be adopted anytime soon.

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    An observation, not a criticism. Those # and b at the beginning of each line aren't accidentals - they're there on purpose! They unfortunately do get called accidentals, but they simply constitute the key signature. Accidentals are all the extra ones needed to cancel that pesky key signature (and other accidentals...)! – Tim Nov 23 '19 at 16:14
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    @Tim: yes, you're right. I used the word "accidental" as a shortcut, since there's no concise term for "default sharps or flats included in a key signature." I thought about that as I was writing and decided not to worry about it, but I'll edit to be clearer. – Athanasius Nov 23 '19 at 19:11
  • The custos was never needed; it's really just a courtesy. Granted, it is more useful when the clef is changing, but whether the clef changes or not it helps by visually identifying the interval between the last note of one line and the first of the next. I frequently write them into my scores. – phoog Nov 25 '19 at 2:55
  • @phoog - If you haven't, I'd encourage you to try to sing chant from 12th century notation without a custos. Then try to reach a 15th-century vocal part in original mensural notation without custodes. I've done some of both. When clefs are jumping all around on each line, they are incredibly helpful, albeit (I agree) strictly not necessary. (I find it odd to think of it as "identifying the interval between the last note of one line and the first of the next" - it literally is showing you what the next note is. Thinking of it as an "interval" is a rather modern perspective.) – Athanasius Nov 25 '19 at 19:22
  • @Athanasius I've done those things. And as I've said, I find the custos helpful even in modern notation. But what's the point of showing the next note when you can simply look at the next line? The benefit of the custos has always struck me as showing the interval, that is, the distance from the previous note to the next, which is far less obvious across staves (again, even if they use the same clef). The concept of intervals is hardly modern. It permeates Guido's work, so it's not a stretch to imagine that reading intervals as such was an important part of the benefit of his system. – phoog Nov 25 '19 at 19:42
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Actually, for your 4 sharps example, the key doesn't have to be E major. It could be C♯ minor, or any other mode.

Key signatures don't actually specify the tonal center of a piece. They simply define a set of seven pitch classes that are going to be written without accidentals. I've got no evidence that this is historically why they never simplified it, but if I had to argue right now against specifying the tonal center within the key signature, this is what I'd write.

The key signature is better left as is because tonal centers are often ambiguous or poorly defined, and it is much more efficient to specify a set of basic diatonic notes than to try to define the subjective tonal center of a piece of music.

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The only real reason is "convention changes slowly, if it changes at all".

For example, consider how much worse are the flaws of time signatures: time signatures are misleading to beginners (6/8 usually has two beats in a bar, not six), and fundamentally ambiguous in many cases (7/8 could be two or three beats arranged in any order of longs-and-shorts). There are well-known solutions to both of these problems that have been used in widely-published music (2/♩. and 3+2+2/♪); despite this, 6/8 and 7/8 are still the standards, because despite their flaws, they mostly work. You only need to tell a student once, "no, sorry, 6/8 is two dotted crotchet beats"; and note grouping conventions convey beats in unusual time signatures.

Key signatures are very easily readable, and very flexible (as you say, the freedom to notate unusual key signatures is very rarely used -- but it is used). They may be slightly inefficient to write, but the flaw is not enough to sway people away from a notation that they are used to reading. It is not surprising, given how slowly time signatures evolve, that key signature notation has also been relatively static.

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Perhaps a better alternative to writing 'A-flat' would be '4 flats', the point being that at least for a long time in the history of music, 4-flats always meant B-flat, E-flat, A-flat, D-flat. So when you look at the key signature you just see that there are 4 flats, you don't actually need to see which lines and spaces are indicated, because they are always the same. However 4-flats doesn't necessarily mean A-flat major, it could mean f-minor, so that is a reason to prefer '4 flats' over 'A-flat'. The question here is - over the few centuries when 4 flats always meant the same 4 notes being flatted, why wasn't the convention adopted of just saying '4 flats' - this would have been a convenience for the composer and copyist, if not particularly for the performer. I agree with Peter Smith above that probably the answer is just conservatism; the advantages of adopting a different notation were not that great, and everyone was used to the existing system.

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As you suggested in your question the reason is historical. A very long time ago the only "key signature" was a single flat. That was back in the modal system, the Medieval period. As harmony developed into the major/minor system, the notion of "key" and key signatures developed.

Obviously key signatures work most clearly when the harmony is diatonic. The more music becomes chromatic the more accidentals and/or key signature changes are needed. Getting into modern harmony some music simply dispenses with key signatures and all sharps and flats are written throughout a score.

...My question is: why was the key signature notation never simplified? e.g just write « A♭ » instead of four flats?

So, this...

enter image description here

...versus this...

enter image description here

What problem does that solve?

It seems to only trade one "problem" for another.

Writing Ab tells me the tonic, so I don't have to wonder if the tonality of four flats means Ab major, F minor, Bb Dorian, etc. But it doesn't tell me the specific tones that get the flats (Bb, Eb, Ab, Db.)

Writing the four flats on staff for the key signature tells us the specific tones, but it doesn't tell us the tonic.

...unconventional key signatures are hardly used

Well, if they are unconventionally they wouldn't be used often. But occasionally you can see them, like this for a Freygish scale...

enter image description here

The reason key signatures are still used is lots of music is still fundamentally diatonic and the chromaticism typically encountered isn't that much of a strain on the system.

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2

Let's suppose that notation was changed at some point in the past. But at that point 100% of sheet music already out there was still in the old notation. So musicians would have had to learn the old notation too, anyway. Even decades or centuries later, until the old sheets were completely replaced, people would have had to learn and use both notations.

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  • That is generally a good argument for “why change isn't done”, however in case of signatures it doesn't really carry much weight. It would be feasible to have a different notation and teach that to beginners. Then later, just memorising a translation table for what the old notation means in terms of the one the student is already familiar with would be easy enough (it's literally just discrete replacements in an “alphabet” of ~10 symbols). In comparison, switching between e.g. notation and guitar-tabulature is highly nontrivial, still many teachers will teach both. – leftaroundabout Nov 24 '19 at 23:55

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