The last chapter showed the correlation between what we had previously learned about rhythm and meter, and traditional rhythmic notation. This chapter will transfer what we know about pitch into its own traditional form of notation.
Letter Names
For a very long time, musicians have been using letters instead of scale degree numbers (or syllables) to represent pitches. For our system of Western music notation, we use the letters A through G. For this chapter, we will let ! correspond to the letter C. The other scale degrees and letters will then line up as follows:
The Development of Staves and Clefs
In order indicate pitches and use the rhythmic symbols we learned in the previous chapter, we could combine scale degrees or letter names with rhythms this way:
But musicians long ago developed means of indicating pitch by placing symbols in different vertical locations on a fixed background. Although the system developed and changed over many centuries, the basic principle was (and is) to place notes on the page, with lower positions on the page representing lower pitches and higher positions on the page representing higher pitches. At first, symbols were written in campo aperto (“in the open field”) — without any reference points at all.
Here’s an example from an eleventh-century manuscript (Paris B.N.776), which uses just such a system:
Some musicians then began to include a single horizontal line that could serve as a reference point. Here is some music from a twelfth-century manuscript notated with a horizontal reference line:
Neither of these schemes gives reliable information about exactly how high or low any particular leap should go, nor do they indicate exactly where in the gamut of pitches these notes should be placed.
Guido of Arezzo, an eleventh-century monk and music theorist, promoted the idea of using a series of alternating lines and spaces, each standing for a single letter name, mapping the ascending pitch letters from low to high on the page. Here is an example of music written near the end of the eleventh century (Benevento 34), in which each line or space denotes a different pitch:
A series of lines and spaces, each representing a unique letter name, is called a STAFF. Guido’s approach was adopted rather quickly across Europe, and the staff has remained the standard way to represent pitch in Western music ever since.
In order to indicate precisely which pitches are represented by which lines, musicians placed letters at the beginning of certain lines. Look again at the example immediately above, and note the F and C written on the left. Those symbols directly mark those two pitches. Any symbol that indicates the letter names of the lines and spaces is called a CLEF.
This gives us way to unlock the names of all the lines and spaces in this excerpt — we can figure that the lowest line is D, the space above it is E, and so on. Therefore, the lines and spaces, from bottom to top, represent these pitches: D – E – F – G – A – B – C.
The choice to mark F and C was not an arbitrary one. As we learned in Unit 3, our gamut of pitches is comprised of a series of whole steps punctuated by half steps in certain spots. In our major scale, those half steps occur between 3 and 4, and between 7 and 1. Look back to the letter-name chart at the beginning of this Unit, and you’ll see that 3–4 corresponds to E–F, and 7–1 corresponds to B–C. Medieval musicians marked F and C because they were the upper notes of each half step.
Modern Staves
It’s possible to extend this system of lines and spaces so that it covers a wide range of pitches, from rather low, to quite high:
However, such a large staff would be difficult to work with, and it would be easy to get lost reading it — especially in the middle of the page and the middle of the staff. To avoid this problem, musicians decided to use only a handful of the lines at any time. By the seventeenth century, showing five lines and four spaces at a time became a standard practice.
In fact, if we simply eliminate the middle line in the system above, we’re left with two five-line staves:
The higher staff covers what is called the TREBLE register; the lower staff covers the BASS register.
Modern Clefs
We can indicate the pitches of the treble staff by placing a G on the second line, like this:
And we can indicate the pitches of the bass staff by placing an F on the fourth line, like this:
Over the years, the G became stylized:
As did the F:
A G CLEF curls around the line for G. When the G clef is printed on a staff placing G on the second line from the bottom, the staff is then referred to as the TREBLE CLEF STAFF and the clef is often called the TREBLE CLEF.
An F clef has two dots that surround the line for F. When the F clef is printed on a staff placing F on the fourth line from the bottom, the staff is then referred to as the BASS CLEF STAFF and the clef is often called the BASS CLEF.
The treble clef staff may also be joined to the bass clef staff. The C-line — originally in between the two staves — is not a part of either clef, and is therefore not written.
Notice the gap in between the two staves where the C-line used to be. Also notice that the two staves have been joined by a vertical line. When the treble and bass clef staves have been joined in this manner, the whole system is called the GRAND STAFF.
The C in between the two staves can be written on a LEDGER LINE (a small segment of a staff line), as can other notes above or below the staves. We call the C in between the staves MIDDLE C because of its position in the middle of the grand staff, and near the middle of the piano keyboard.
Here are the letter names, scale degrees, and syllables of the lines and spaces of the grand staff, beginning on C two ledger lines below the bass clef staff and ending on C two ledger lines above the treble clef staff:
We will also encounter one variation on the treble clef. This variation indicates that all pitches are to be performed one octave lower than in the regular treble clef (usually to be sung by the tenor voice). We will call this the “vocal tenor clef.” It may be written in any of several ways:
Without a clef, a staff is meaningless. You must place a clef at the beginning of each staff you use, or the lines and spaces will have no names.
Naming Lines and Spaces
The lines and spaces of a staff are numbered from the bottom up:
For example, the 3rd line in the treble clef staff is B:
Whereas the fourth space in the bass clef staff is G:
Octave Designations
When speaking or writing about pitches without using staff notation, there is a special problem involving just which A, B, etc. one is referring to. Most musicians deal with this problem by dividing the pitch continuum into discreet octaves, each new octave beginning on each C. However, musicians have used several different methods of designating these different octaves. This book uses the method adopted by the International Standards Organization, the Acoustical Society of America, the Society for Music Theory, and many other important organizations and publications. This method works like this:
Start with C four octaves below middle C (a convenient starting point, since this pitch is at the lowest limits of hearing for most humans). Call that pitch C0 (pronounced “C-zero”). Number the next higher pitch D0, the next E0, and so on, thorough B0. Call the next pitch C1 (the C an octave above C0). Continue with D1, E1, and so on. Number each new octave starting with C2, C3, and so on. As a point of reference, it is helpful to remember that middle C is C4.
If you’re curious, C0 would appear here in the bass clef staff:
For the most part, we’ll be dealing with only a few ledger lines (not nine, as for C0 above).
Here are the pitches of the lines and spaces of the grand staff, beginning on C two ledger lines below the bass clef staff and ending on C two ledger lines above the treble clef staff:
Here are the pitches of the lines and spaces of the grand staff, beginning on C two ledger lines below the bass clef staff and ending on C two ledger lines above the treble clef staff:
The Structure of the Scale and the Structure of the Staff
The intervals between the lines and spaces of these staves are a product of the pitches they represent. For example, the interval between the first line in the bass clef (G) and the space above it (A) is one whole step. But the distance from the second line (B) to the following space (C) is only a half step. In this way, the musical staff is an irregular or inconsistent system. At first glance, all vertical distances between lines and spaces look the same, but they’re not.
Among the pitches we’ve discussed so far, the only half steps occur between E and F, and between B and C. It is very important to memorize the location of these “natural” half-steps. They occur in these places:
All other steps in the staff are whole steps.
Keyboard Instruments
For more than a thousand years, Western musicians have built keyboard instruments. These instruments connect a series of keys to devices that produce pitches — for example, pipes (in acoustic organs), strings (in harpsichords and pianos), and even electronic oscillators (in synthesizers).
The earliest keyboard instruments were constructed with keys corresponding to the pitches of what would eventually become our C-major scale (although, at the time, these pitches were used in successions and manners different from our modern major and minor scales). This yielded a series of seven unique keys, each of which produced one of the pitches of the scale, and that pattern of keys could repeat in each new octave.
But as we have seen, some of the adjacent pitches in the scale are a half step apart, whereas others form a whole step. This means that between any two scale degrees separated by a whole step it is possible to insert a new pitch — a half step in between the two. Thus, musicians inserted keys in the following whole-step adjacencies: C–D, D–E, F–G, G–A, and A–B.4 (Note that, in this approach, the E–F and B–C pairs don’t allow for an “in-between” pitch because they are already a half step from one another.)
To help performers keep a visual and tactile distinction between the original pitches (C–D–E–F–G–A–B) and these new “in-between” pitches, instrument builders constructed keyboards so that the original pitches were larger, lower, and closer to the performer than the others. Conversely, the “in-between” pitches were smaller, raised, and slightly further away from the performer. Most builders also used color as a way to distinguish between these keys. By far the most common color scheme is white for the original pitches and black for the “in- between” ones. Here is a schematic drawing of this kind of keyboard, with each of the white keys labeled with the letter name of its pitch:
And here is a photograph of a Roland EXR-3 synthesizer keyboard, which better illustrates the relative shape and position of the two types of keys:
It is important to keep in mind the fact that both the musical staff and the keyboard grew out of the structure of the letter-named pitches that existed long before either the staff or the keyboard were created. This means that the white- key/black-key structure of the keyboard is a product of the whole and half steps musicians had already been imagining, singing, and playing for a long time.
Here is a graphic that shows the relationship between the pitches (down the middle), the keyboard, (on the left), and the grand staff (on the right):
“Pulling Apart” the Grand Staff
Up until now, we’ve been showing the grand staff in a way that leaves exactly enough vertical space between the treble and bass clef staves to correspond to the B, C, and D that fall between them. In practice, however, musicians print the grand staff with much more space between the staves. This is a convenience, which allows for notating certain notes above the bass clef and others below the treble clef. This is particularly helpful in printing keyboard music, in which the bass clef staff generally represents notes to be played by the left hand and the treble clef staff represents notes for the right hand. Thus, one hand can play notes that enter into the other register simply by reading pitches on ledger lines between the staves. In addition, it allows room to print other symbols between the staves.
However, putting greater distance between the staves can cause some confusion because this distorts the relationship between pitch space and the space on the page. For example, look at the middle Cs in the second and third measures of the following excerpt. Those in the bass-clef staff look “lower” than those in the treble clef staff, but they are in fact the same pitch:
Other Clefs
The treble and bass clefs are actually part of a larger system of clefs. Older music (particularly music printed before the middle of the nineteenth century) made us of many different clef-staff combinations. Two of these have survived into the twenty-first century, and are worth mentioning here.
The C clef we saw on page 3 in this unit also developed into a modern clef. It marks the position of middle C, and looks like this (if you look right in the middle, you can still see the remnants of a stylized “C”):
Because it marks the position of middle C, this clef is called a C CLEF. When the C clef is centered on the third line, we call it the ALTO CLEF. When the C clef is centered on the fourth line, we call it the TENOR CLEF. Some modern scores still use these clefs.
Reading Pitches on the Staff
There are several ways to learn to read fluently in both the treble and bass clef (and C-clef) staves. One of the best is to practice reading in each clef on an instrument. Another is to practice reciting the names of pitches aloud. Your goal should be to be able to name any pitch in either clef without hesitation. This takes lots of practice.
In addition to the exercises that follow here, you might also want to practice using some online pitch-identification drills. Here are a few suggestions:
- http://www.musictheory.net/exercises
- http://musicards.net/music_flash_cards/music_note_flashcards.html?type=treblenoledgernatural
This material corresponds to the UMass OWL Homework 4