Is it fair to say the treble clef is optimized for piano?

Question

When playing the piano, I find that staff notation with the treble clef makes sense.

However when moving to string instruments, specifically the guitar and violin (in my case), I find the notation a lot less intuitive. After some consideration I have identified why, but I'd like to be sure that:

1. I'm correct in my assertions, and:
2. I'm not going to mislead myself with them.

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Here's the notes of the treble clef, overlaid on a staff where the lines have been expanded to the same width as the spaces:

I have used used (#) to denote the positions in which it is legal to put a sharp.

At this point I'd like to make my first assersion:

The Wikipedia page on staff positions states:

The vertical position of the notehead on the staff indicates which note to play: higher-pitched notes are marked higher on the staff.

I don't believe this is true, since a note with a sharp accidental will be higher-pitched that its natural counter part, but it won't appear higher on the staff.

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Given that it's possible to have multiple pitches represented in a single staff position (through the use of accidentals), I'd propose that the staff is in some sense, not to scale (pun semi-intended).

To make this clear, I present a to scale version of the treble clef, which forms my second assertion:

I propose that this with this version of the staff, we no longer need the sharp accent, and that the Wikipedia quote above would now hold true.

Also we can see that embedded within the widths of the lines and spaces, is the tone/semitone scale of the clef.

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As mentioned at the top of the post, my questions here are:

1. Are my assertions correct (i.e. am I missing anything)?
2. Is this 'dangerous thinking' (i.e. am I misleading myself)?

Answer 1

The staff is not optimized for piano, nor vice versa. Both the staff and the keyboard are optimized towards playing diatonic scales. A diatonic scale is a 7-note scale containing exactly one note of each letter type, and which contains a mixture of whole and half steps. By far, the vast majority of western music (from Renaissance and Classical, to Pop and Rock) is written in diatonic scales. These 7 notes form your "palette", if you will. If you sing a simple scale (do, re, mi, fa, so, la, ti, do) you are singing a diatonic scale. Because the notes in this scale are perceived as adjacent, it makes sense, to aid in sight reading, to represent them as adjacent in a staff notation, or in a keyboard layout.

However when moving to string instruments, specifically the guitar and violin (in my case), I find the notation a lot less intuitive.

This is because, due to the nature of those instruments, a note's position on a string must be related exactly to its physical frequency, and cannot be related to perceptions of adjacency. This exposes the gaps in the diatonic scale, and prevents the instrument from being optimized for playing diatonically (unlike a piano, where the keys can be arranged in whatever pattern one pleases).

I have used used (#) to denote the positions in which it is legal to put a sharp.

Others have already pointed this out, but this statement is in error. Sharps and flats can be added to any note. To check out previous questions about this, see:

• If between E and F is a halftone, why can F not be an E♯
• What does this note - B# - mean?
• Why do notes have multiple names?
• Why are notes named the way they are?

The Wikipedia page on staff positions states:

The vertical position of the notehead on the staff indicates which note to play: higher-pitched notes are marked higher on the staff.

I don't believe this is true, since a note with a sharp accidental will be higher-pitched that its natural counter part, but it won't appear higher on the staff.

Again, the staff is optimized towards diatonic scales, which have exactly one note of each letter type. In the staff, "some form" of A will always be written below "some form" of B, which will always be written below "some form" of C. It is true that a staff position can represent multiple pitches, but in a diatonic scale, only one of them will be used at any given time. Key signatures (and accidentals) will tell you which form of each letter to use, and will guarantee that these notes are properly ordered.

Technically, it could be possible to write, for example, an A♯ and a B%flat; at the same time, which would represent the same pitch in two different staff positions. You could even write a C♭ and a B♯ which would have a pitch relationship inverted to their staff position. But practically speaking, you will likely never see this. It's similar to the English sentence "This sentence is false," -- it may follow the rules of grammar and syntax, but it has no meaningful semantic content.

So the notes in the staff will be ordered. But they will not be regularly spaced. Two adjacent notes on a staff will be separated by either a half step or a whole step. Once again, this is deliberate, and goes back to the shape of the diatonic scale that the staff represents.

To make this clear, I present a to scale version of the treble clef, which forms my second assertion

Your proposal is based on the equally-spaced chromatic scale, and as such, it actually obscures the nature of the diatonic scale. You certainly aren't the first to propose a staff system based on a chromatic scale rather than a diatonic one. Here's a website that collects such alternative notation ideas -- might as well add yours to the mix. Or see if there's one there that you like better. These systems might seem logical at first, and could even be useful to someone doing atonal music, but for people working in tonal diatonic systems (like 99.99+% of western music) using a notation system that ignores the diatonic scale is likely to prove more difficult. For example, notes that sound adjacent in the scale (or that "feel" adjacent to a singer) are now visually separated by a gap, causing you to lose a sense of continuity.

If the only reason for making this change is to correspond better to the physical layout of string instruments, I'd point out that we already have a notation called tablature which does a better job of meeting this purpose.

Are my assertions correct (i.e. am I missing anything)?

To summarize:

• Your assertion about permissible sharps was wrong
• Your assertion about wikipedia being wrong was wrong, since a proper application of key signatures and accidentals will guarantee that the pitches remain in order with the staff (higher pitches are written higher on the staff), however...
• Your assertion that the staff is not scaled one-to-one with pitch is correct -- but this is by design. It is scaled to the diatonic scale.
• Your "second assertion" is actually just a proposal, and cannot be true or false (but it is true that in such a system, or any of the similar ones that I linked, sharps or flats wouldn't be needed; this is not necessarily an improvement).

Is this 'dangerous thinking' (i.e. am I misleading myself)?

Depends on whether you want to write/play atonal music. If that is not your goal, then thinking that a notation system can be improved by disregarding the diatonic scale used by the music it represents shows a lack of understanding.

Answer 2

The layout of the clefs and staves, the placement of the pitches on the staff, and all the other elements of music notation, are the way that they are because they have evolved to be that way as a result of many centuries of usage and refinement by all the musicians in the world. They are the best way to represent the notes.

Also, the piano's sheet music is represented on the grand staff, which is a treble clef and staff together with a bass clef and staff connected by a bracket. The piano does not use the treble clef and staff alone.

At this stage I suspect that you are only beginning to study music. Initially these concepts may seem daunting or counter-intuitive, but that is only because you know very little at this point. The more you learn, the more sense it will make to you.

Answer 3

What happens in your version of the staff when you start tossing in flats and sharps and double-flats and double-sharps and such? Is the bottom of the D space now Db and the top of the D space a D natural, then when you use a sharp, it suddenly switches around and the natural is on the bottom?

This is just the first most obvious problem with your variable line system.

One aspect of staff notation is that serves two masters: first and foremost it gives the musician the notes to play and the duration to play them. Secondly, and arguably as important, it reveals the harmonic relationships.

By means of a contrasting example, I suggest you look at guitar tabulature (tab). It tells the player where to put his fingers, but reveals NOTHING about the harmonic structure and tonality. TAB is an example of a positional notation system that if anything obfuscates what's actually going on in the music.

So what happens in your notation when you have a sloppy transcriber? What about ledger lines? What happens when the tempo is very fast, and the reader has to differentiate between twelve different locations instead of 9? In standard notation, we have a key signature that tells us up front which are the "default" sharps and flats. When reading music that has a key signature, the accidentals "fall out" of the staff and we don't really have to think about them...In fact, because sharps and flats in the staff only indicate places where we're jumping out of key, they are the exception, and fairly rare, and we can then see very clearly and easily that some exceptional transition is coming up. By contrast, in your notataion ALL of the accidentals are special...which means none are special.

What you're trying to do is interesting, but it can be characterized as trying to "pivot on the wrong axis in the data." Imagine, if you will, a hardware store nut-and-bolt shelf. How is it organized? Almost universally, it is organized by function/type as the primary sorting, and by size as the secondary sorting. You walk in there knowing you need a lag bolt, and when you get to the lag bolts you easily find the 3 inch bolt. Why isn't it organized the other way around, by size THEN by type? Because 250 years of usability testing has shown that function.type.size is the natural sort order for people needing fasteners.

So here in this new staff system of yours, you're doing much the same thing. You're taking a note that was primarily categorized in terms of function, and recategorizing it in terms of size. That simply doesn't conform to the way people USE the notes.

One thing that jumps right out when one observes an experienced sight reader going through music, is that it's far too difficult and frenetic to try to literally read every note. The experienced adept reader doesn't try to do that. Instead, they tend to quickly parse RELATIONSHIPS from one note pattern to the next. They don't necessarily say, "aha! I see a G natural after this C!" Instead, they see the distinctive PATTERN in the notes of a fifth interval IN THE KEY and play that.

Answer 4

It's more like the piano is optimized for the diatonic scales with a tonal center of C major that staff notation is trying to do justice.

Now if we are talking about the treble clef in particular, it is a violin clef (which has reasonably nice spacing for a violin's open strings, with the violin range for typical positions extending similar amounts beyond both top and bottom of the staff) without a particular relation to the piano. The traditional singers' clefs are all C clefs, basically what is used these days for a viola, shifted in position. The bass clef (as opposed to the bariton clef) was an F clef, also used for instruments.

It turns out that violin and bass clef combined reasonably nicely into a musically useful two-hand range, with just a single (and thus unambiguous) ledger line in between. From keyboard reductions and scores (most useful for conductors), those clefs then invaded the singers' scores.

The starting proposition of the staff system, even before accidentals became widespread, was to reflect a system of diatonic scales. The first widespread system of that kind was the four-line square note notation for chant.

It is not just the piano keyboard (used in a number of instruments) which reflects a setup focused on diatonic scales: wind instruments with key flaps (like flutes, saxophones, clarinets, bassons) loosely also work with a "white" and "black" key system, though not all of them based on the C major scale. Where they are based on a different scale, it is customary to notate them in "transposing keys" reflecting them back to C major.

A microcosm of the adaption of semitones can be seen with diatonic bellows instruments: starting from a purely diatonic one-row accordion, the first accidentals came into being by adding a second row with a different tonic, and then adding additional semitones one by one in a third helper row ("club harmonica") or haphazardly ("bandonion").

Most of them lead to individual notation systems not useful to other instruments (basically, instrument-specific "tablatures" reflecting the finger action more than the musical relations).

In contrast, the "chromatic button accordion" did away with both bisonoric (different notes on push and pull) and diatonic setup and arranged the notes in a regular pattern of semitones. Now this actually is a keyboard arrangement that would be amenable to your notation ideas. It turns out that no tablatures, namely instrument-specific notations rather than the established diatonic notation system also used for piano, were able to make enough of an impression to become relevant.

It also turns out that singers are reasonably comfortable thinking in diatonic scales so the traditional staff system with its irregularly spaced semitones actually matches their manner of thinking better concerning most music than a regularly spaced system without similarly focused relation to a tonic would.

If you take a look at idiomatic music composed specifically for the equi-spaced chromatic button accordion, French musette music comes to mind. It is placed strictly in a diatonic framework, but one somewhat noticeable element is that embellishments work with more chromatic runs and figures than often seen in other folk music.

So the notation systems rooted in diatonic scales do not root as much in the piano as they do in our traditional Western systems of music, and the piano follows those systems rather than leads them.

Answer 5

1. It is definitely legal to put Sharps on E and B!

Depending on the context. For example in a piece of F# major, you would always see E# instead of F♮ (natural), makes it easier for us to read, because we would automatically assume F as the leading note in F# major.

2. The quote from wiki is actually correct.

Yea it is true that say, if I have a G#, and above it I place a A♭♭ (double flat, which means G now). So now I will have a note marked higher, but actually lower pitch. Then that quote doesn't hold true anymore. BUT, this is not the usual convention we would see in all the music sheets! Music sheets were meant to written in a way that a player can read it fast and easily. (Hence my first point).

Answer 6

I think what you aren't appreciating enough is all the extra information you're getting in staff notation, especially regarding tonality. I.e. being able to identify the key of the piece, the hierarchical position of the notes within the key, notes borrowed of other keys, modulations,... Staff notation conveys meaning other systems, like tablature, aren't able to convey so easily. It's this information which makes classical musicians playing string instruments prefer staff notation to other systems. It helps them to see tonal structure and interpretation of a piece.

Systems like the one you are proposing could be useful in music with a more atonal character. And I wouldn't be surprised if there are experimental systems, akin to yours, in atonal music bringing all pitches on the same hierarchical status, also in it's graphical notation.

To answer your questions:

1) No, staff notation isn't developed for piano. It was developed for tonal music, much in the same way the layout of the keys of a piano was developed for tonal music. Also staff notation existed before the piano was invented.

2) Thinking is never dangerous, but when you advance in your musical career you will see that there are upsides to staff notation. Don't be stuborn and dismiss it for being not adapted to your instrument, because probably it isn't.

Answer 7

Violin works comparatively well with the violin clef as its empty notes are in reasonably recognizable places in the staff and its range maps reasonably well to the range of the staff as well. Western music is generally organized into scales, and the strict fifth ordering of the strings mean that the fingering patterns on successive strings are very much related, making position play where the wrist retains place for extended periods of time reasonably natural. Also if we are not talking about Bach solo pieces, the violin is usually played monotonically, one note at a time.

As a consequence, its playing is governed by managing scales and note progressions one note at a time: forming patterns like with a guitar is not necessary.

For guitar, things are quite harder: the positions of empty strings in the staff are in less exposed places, the strings are more and not entirely regularly tuned, and the basic mode of play is polyphonic, making the patterns of the scales on the strings correspond much weaker with the fingering action.

Consequently, tablature saves quite a bit of mental effort and has been customary since the time of lutes.

Similarly, getting along fine with standard scores on a chromatic button accordion (which never established something akin to tablature and has a chromatic arrangement of buttons which wraps to the next column every three rows) takes quite longer than with a piano accordion's diatonic key orientation.

While tablature-like arrangements offer learning and sightreading benefits, the tonality of the music becomes much less obvious when not actually playing since Western music is fundamentally based on diatonic scales and the way intervals are warped when moving them across the scale.

Answer 8

To chime in: I (as a composer, not as a performer) like to view the western musical pitch system as relative. It isn't presented relative in notation - which is precisely reason for your confusion - but it is.

This means (as you have mention) it's the intervals between the notes that's important when talking about scales. The movable Do system takes advantage of this and I would argue is a more intuitive way to think about music and perhaps even notate it.

But we don't use movable Do, we use a system with arbitrary letters assigned to pitches. We said: 'Hey, major C is our reference point and anything that differs from it will have to use sharps and flats.' I'm no historian, but I'm guessing we did that because we wrote diatonic music and we had to pick some scale as a baseline.

If we picked another scale as baseline, your version of the staff would look different.

The entire problem arises because we map a relative system onto an absolute notation system. And as other users mentioned, like with any language, 'that's just how it evolved.'