Sound and Its Notation

Music is, by a common definition, organized sound. Music notation records this organization. However, sound has many aspects--too many for us to record easily in a written notation. As a result, musical notations record only those aspects of the sound most rigidly organized by the composer, or those of most interest to the performer.


Most objects possess elasticity, the ability to spring back into shape after being displaced or stretched by some force. For example, a violin string being moved when drawing a violin bow. Elasticity allows the string to not only return to equilibrium (its point of rest), but to pass through equilibrium in the other direction. As long as the bow continues pulling on the string, it will continue to oscillate or vibrate around equilibrium. One cycle consists of the initial displacement (+), the motion back through equilibrium, the continuation of the motion (-), and the motion back to equilibrium. The frequency of the sound is the number of cycles per second. Vibrating objects cause a chain reaction to take place in the air, molecules are pushed together (compressions) and stretched apart (rarifactions). The distance between peak compressions is called the wave-length.

  • Pitch. When all the wave-lengths are the same it is considered to be periodic, and a periodic wave has a frequency that falls somewhere between 20 and 12,000 cycles per second we call the sound a pitch. (Frequently, a musical sound is referred to as a "note" or "tone." However, pitch is the correct term and the term that we will use here.)
  • Noise. If the wave-lengths are of irregular length (aperiodic) we consider the sound to be a noise. High and low are metaphors for shorter and longer wave-lengths.
  • Amplitude is the intensity of the compressions, usually proportionate to the magnitude of the displacement of the vibrating body. We experience amplitude as volume.
  • Timbre. Not to be confused with pitch; tone, timbre, or sound-color is produced primarily by sympathetic resonances in the body of the instrument, whether it be a violin or a human voice. We would not recognize either of these instruments if we listened to their "vibrators" outside of their resonating bodies! We call the frequencies that comprise the entire resonating system the sound's spectrum, (pl. spectra).


Distinguishing One Sound from Another


We hear or perceive the sound when the wave-train of compressions and rarifactions reaches our ears and is processed by our nervous systems. We distinguish sounds from one another if their is a significant difference in pitch, volume, and/or timbre.

As far as our brains are concerned, distinguishing one sound from another is very much like distinguishing the difference between visual images. Light-spectra of sufficiently contrasting wave-lengths produce the edge-boundaries between images, and sound-spectra of sufficiently contrasting wave-length (contrasting pitches and timbres) produce the edge-boundaries that help use hear the difference between the end of one sound and the beginning of another.

The elapsed time between the beginning and ending of a sound (or a silence) is its duration. We will refer to the method of representing durations in hours, minutes, seconds, and milliseconds as clock-time measurements. Psychological studies have shown that when even professional musicians are asked to recall rhythmic durations their rhythmic memories are often very inaccurate when compared to clock-time measurements. However, when they represent their recollections as proportional relationships (twice as long, half as long), they are much more accurate. No wonder music notation evolved as a system of relative rhythmic proportions.

Pitch Notation


It is doubtful that any person can accurately identify the difference between two pitches in cycles per second. When we want to speak or write about the difference between two pitches we have no alternative but to refer to their notational representations. Our notational system profoundly shapes the ways in which we hear, imagine, classify, and subclassify musical phenomena. In fact, it is impossible to distinguish between our "unmediated" and "mediated" perceptions of the world. By mediated perceptions we mean those perceptions we consider to be shaped and filtered by the influences of others and our graphical systems of representation (for example written language and geometry). Our notational system consists of many different elements, but the elements most related to pitch are the note, the staff and ledger lines.

The Note


The most important element of Western musical notation is the note. A note is the written symbol that represents a sound. A note may have three parts. The body of a note is a small ellipse, either hollow or filled in, called the note head. We call the vertical line that either ascends or descends from the note head the stem. Often, a flag is attached to the stem.



THE STAFF


he placement of the note head on the staff depicts relative pitch. To show relative pitch (that is, relative highness or lowness), we place note heads on a fixed series of five horizontal lines called the staff or, rarely, a stave (pl. staves). We can place a note head on a line or in between two lines--that is, in a space.



We can extend the staff indefinitely in either direction. To write a note above the space on top of the staff or below the space at the bottom of the staff, we use ledger lines (sometimes spelled leger lines). We can add as many ledger lines as we need.



PITCH INTERVALS


A pitch interval is the difference between the notational representations of two pitches. Pitch-intervals allow us to notate and speak about two pitches in a context sensitive manner. There are three basic interval categories, unisons, steps, and skips. Each is the by-product of our notational system. Two noteheads written on the same line or space produce the interval of a unison. Two note-heads written on an adjacent line and space is a step; and two note heads separated by one or more spaces is a skip.



The Harmonic Series, Pitch Class & Octave Perception


Understanding the frequency relationships within the timbre or spectrum of a single pitch will help us understand why the members of some pitch-intervals are more closely related than the members of other pitch-intervals.

The Harmonic Series


The spectrum of a pitch consists of many different frequencies called partials. The lowest partial is called the fundamental and all the others are called overtones. They are related to the fundamental by integral multiples (1:2:3:4 etc.). If the fundamental is 100 cycles per second (c.p.s.), then the spectra would consist of the frequencies 200, 300, 400, and on up into infinity. Spectra of this type are called harmonic and the series of ratios between their frequencies is called the harmonic series.

Generally speaking, the amplitude of a partial is inversely proportionate to its frequency; in other words, the higher the partial the lower its amplitude. We hear the sound as a single pitch instead of a cluster of different frequencies specifically because the relationships between the frequencies are harmonically "simple" and their amplitudes favor the lowest most simple relationships of all (1:2:3:4), by far the most prominent frequencies in pitched sounds.

Pitch Classes and The Octave


The arousal patterns of the nerves in our inner ears and the neurons on the auditory cortexes of our brains have so often "mapped" these most prominent relationships that when we hear two entirely different pitches, one being twice the frequency of the other, we are tempted to think that they are merely different versions of the same thing. Compare listening example A to example B and I think you will be able to tell which one best illustrates this phenomenon.

In Western Europe the staff system, instrument design, and music theory evolved in a way that lead to the use of 7 basic pitch-classes. They constitute the seven basic note-names: A, B, C, D, E, F, and G.



THE KEYBOARD


The arrangement of white and black keys on a piano or similar instrument is the keyboard. The white keys of the keyboard bear the seven note names mentioned above.



The interval between two members of the same pitch class (two A's, for example), is an octave. Octave means "eight," and two successive A's are eight white keys apart. Notice that successive white notes are notated as steps.

Half Steps and Whole Steps


Technicians tune the piano so that the twelve white and black keys within the octave--any octave--divide the octave into twelve equal parts.



The above example shows that two different-sized steps separate adjacent white keys. The distance between any two adjoining keys--that is, any two keys, black or white, with no key between--is a half step (or semitone). The distance between any two keys separated by one other key (black or white) is a whole step. Sometimes both half steps and whole steps are referred to simply as steps.

The White Keys


Any seven successive white keys run through all seven letter names. A is the name of the class of white keys found between the two upper (that is, farthest right) members of the cluster of three black keys. Going to the right of A--that is, "upward" or to pitches of higher frequency--we come successively to B, C, D, E, F, and G. Then the cycle repeats itself with the next A, and so on.

The Black Keys


Note the asymmetric arrangement of the black keys: two black keys, then three then two again. Two intervening white keys separate each group of black keys from the next. This pattern repeats itself in each succeeding octave. Thus any key, black or white, has exactly the same position within the black-white pattern immediately surrounding it as does tat key an octave above it or below it. The black keys do not have simple letter names, but are considered altered versions of the white keys that they adjoin. Thus we can refer to the black key between A and B as either A[insert 1a] (pronounced "A-sharp") or B[insert 1b] (pronounced "B-flat"). The sharp raises the pitch by a half step. The flat lowers the pitch by a half step. Context determines which of the two terms or spellings we use. In general, if the pitch pulls up toward B, we call it A-sharp. If it pulls down toward A, we call it B-flat. (We will consider the factors that provide this sense of "pull" in succeeding chapters.) We refer to an unaltered white note simply as "A" or "A-natural." The sign [insert 1c] before a note head, stands for "natural."



Enharmonic Equivalence


As we saw above, each black key has two different names. We can think of the black key between C and D, for instance, as C-sharp (C raised by a half step) or D-flat (D lowered by a half step).

C-sharp and D-flat stand for the same pitch (that is, are produced by the same key on the keyboard). Any two notes that we spell differently but that stand for the same pitch are enharmonically equivalent.

CLEFS


To know which pitch class a note head on the staff represents, we must first order the staff. A clef (French for "key") placed at the left of each staff shows which pitch classes are represented by which lines and which spaces. There are three commonly used clefs: the treble clef (G clef), the bass clef (F clef), and the C clef.



  • Middle C. We call that C found in the middle of the piano keyboard (usually beneath the piano maker's name) middle C. Each clef orders the staff in relation to middle C.

  • The Treble Clef. The treble clef tells us that the second line from the bottom of the staff is the G above middle C (a). For this reason, we sometimes call it the "G clef." When we add this clef to a staff, we call the staff the treble staff. Traditionally, students learn the treble staff by remembering the sentence: Every Good Boy Does Fine. (The first letters of the words give the letter names of the lines, bottom to top, of the treble staff--E, G, B, D, F.)

  • The Bass Clef. The bass clef tells us that the second line from the top of the staff (the line between the two dots) is the F below middle C (b). We sometimes call it the "F clef." When we add the bass clef to a staff we create a bass staff. The first letter of each word in the following sentence recalls the spaces, bottom to top, of the bass staff: A, C, E, G.: All Cows Eat Grass.

  • The C clefs. The several C clefs simply tell us where middle C is. The alto clef places middle C at the center line (c), and the tenor clef places middle C at the second line from the top (d). Of these two surviving C clefs, the alto clef is the most common.

  • The Grand Staff. Often we join the treble staff and bass staff with a brace. We write middle C on the treble staff as the note one ledger line below the staff. We write middle C on the bass staff as the note one ledger line above the staff. These joined staves are called the grand staff.




The "Horizontal" and the "Vertical"


Simultaneously sounding pitches are written one on top of the other, or vertically, on the staff. As a rule, we call two pitches sounding together an interval. However, when more than two pitches sound together we use the term chord or sonority (or, less frequently, simultaneity). When dealing with chords, or the vertical aspect of music, we are dealing with harmony. Pitches that sound in succession are written one after the other from left to right, or horizontally, along the staff. We call such a succession a melody or tune--or, more abstractly, a line or voice. When dealing with melody, we are dealing with the linear, melodic, or horizontal aspect of music. As we shall repeatedly discover, Western music binds the vertical and the horizontal tightly together. Although it is possible to concentrate on one or the other from time to time, we cannot meaningfully separate the two.

Timbral Notation


Traditionally, Western musicians notate (and seek to control) three aspects of timbre. First, we represent the sound source by providing each instrument its own staff. Second, we represent the relative loudness or softness of a sound using dynamic marks. Third, we control how individual notes are played with articulation marks.

Dynamics


The relative loudness or softness of a sound is its dynamic. The words, letters, and symbols that depict relative dynamics are dynamic marks.
  • Basic Dynamic Marks. The Italian terms piano (soft, abbreviated p) and forte (strong or loud, abbreviated f) are the basic dynamic values. Most others derive from these two. For example, pianissimo (pp) means "very soft, softer than piano." Fortissimo (ff) means "very loud, louder than forte."

  • Other Dynamic Marks. Crescendo (abbreviated cresc.) tells us to get gradually louder. Decrescendo or diminuendo (abbreviated decresc. and dim.) tell us to get gradually softer. We represent a crescendo or decrescendo graphically with what is popularly called a hair-pin: [insert 1d] A [insert 1e] represents a crescendo, and a [insert 1f] represents a decrescendo or diminuendo.


Articulation


Articulation marks tell the performer how to begin a note, how to sustain it, and how to connect it to other notes. Articulation is suggested in three ways.
  • Articulation Marks. Articulation marks (for example, [insert 1g], [insert 1h], or ^) affect the way in which the performer is to attack and sustain a note.
  • Phrasing Marks. A dependent division of a melody is called a phrase. It is like a clause in prose. Phrasing marks demarcate these divisions and instruct the performer on how to connect one note to another.
  • Descriptive words. Finally, composers use descriptive words--such as legato (smoothly connected), espressivo (expressively), or tenuto (held, sustained)--to suggest a gneral manner of articulation and performance.



Summary


A musical sound has three qualities: pitch, duration, and timbre. Western musical notation precisely records all three. The primary symbol is the note. A note can have three parts: a note head, a stem, and a flag.
The placement of the note head on a five-line staff depicts relative pitch. The clef orders the staff, allowing a note to specify a particular pitch. We join the treble staff and bass staff to form the grand staff.
The type of note head (hollow or filled in) and the presence or absence of a stem, flag or flags represent the relative duration of a note.
We accord every instrument its own staff. Articulation marks tell us how to begin, sustain, and connect notes to one another.


For Additional Study

  • Bamberger, Jeanne Shapiro, and Howard Brofsky. The Art of Listening: Developing Music Perception. 5th ed. New York: Harper & Row, 1988. Chapter 1.
  • Mitchell, William J. Elementary Harmony. 2d ed. Englewood Cliffs, NJ: Prentice-Hall, 1948. Chapter 1.
  • Piston, Walter. Harmony. 5th ed. Revised and expanded by Mark DeVoto. New York: W. W. Norton & Company, Inc. 1987. Chapter 1.
  • Westergaard, Peter. An Introduction to Tonal Thery. New York: Norton, 1975. Chapters 1-2.
  • Williams, Edgar. Harmony and Voice Leading. New York: HarperCollins, 1992. Chapter 1.