Matthew Saunders’ Blog

An excerpt from Chapter 7 of my book Music: Notation and Practice in Past and Present, now in press with National Social Science Press.

The issue of how to accurately tune a musical instrument, especially one which depends on a number of independent strings, has long been a source of concern for musicians and mathematicians.  One of the earliest documents of Western music is a stone tablet written in Babylonian cuneiform that has been interpreted as a set of directions for the proper tuning of a seven-string harp or lyre.

The question, then, of what tuning is and what it means to be “in tune” is central to the understanding of music and to the training of musicians.  Simply put, two pitches are considered to be in tune if they have the same fundamental frequency, or if their fundamental frequencies are related to each other by a low whole-number ratio.  Because human beings are by nature somewhat imprecise, both in perception and in manipulation of pitch, the practical meaning of being “in tune” is somewhat more complex.  Because various cultures have accepted differing musical intervals as sounding “correct,” intonation for human ears is highly dependent on training and cultural norms, at least beyond the tuning of perfect unisons or octaves.  The practice of accurately producing a desired pitch is known as intonation, and the ability to play with good intonation is a skill that takes many musicians years to master.

A useful approach may be to examine the experience of various musicians with regard to tuning in order to understand what role intonation and tuning play in the practice of music.  To begin, consider a vocalist who may perform with or without accompaniment.  An accomplished singer will have practiced many years to develop his “ear,” that is, his inner sense of intonation, which is usually based on an understanding of scales, keys and the relationships between notes in those keys.  Most musicians do not possess the set of abilities collectively referred to as absolute pitch, also known as perfect pitch.  Absolute pitch is the ability to identify a pitch by note name when it is heard or to accurately produce a requested pitch without reference to a standard.  A great deal of research has been done in this area to determine just how absolute pitch is developed and expressed, and what its limitations are.  It is somewhat ironic that many—if not most—musicians are unable to identify the basic materials of their art without reference to some known standard, as if a painter were able to relate colors to each other within the context of a painting, but not be able to certainly identify red as red without reference to a color wheel.  A singer’s tuning and intonation, then, rely on constant comparison of notes to each other and to outside reference pitches, such as might be found in an instrumental accompaniment.  It is quite possible for a person to possess an exquisite vocal instrument but to utterly lack the ability to control intonation, whether through a lack of training or a simple lack of musical aptitude.[1]  Conversely, a person may possess an inner ear, or ability to audiate musical sound, that is without peer, but be unable to control the vocal apparatus sufficiently to communicate music to others, whether through physiological structure, lack of kinesthetic ability or auditory dysfunction.

A performer on a brass instrument, then, faces a similar set of dilemmas to a vocalist, but with the additional challenge of making music using a device outside the body.[2]  The brass player relies on her training and internal ear to audiate pitches prior to playing them, but also on her knowledge of the tendencies of her instrument.  Professional brass players must spend many years becoming comfortable with their personal instrument, as every trumpet, for example, is subtly different from every other trumpet, even those by the same manufacturer.  The intonation tendencies of various pitches and groups of pitches are basic knowledge for a brass player.  When playing in an ensemble setting, in a brass section of an orchestra, perhaps, the brass player will also be aware of the pitches played by other players and adjust her own pitch accordingly.  To play a pitch in tune requires first that a player anticipate the fine adjustments that will be required, but also the ability to detect several acoustical phenomena.

For unison and octave pitches, most musicians, including brass players, utilize a technique known as beatless tuning.  When two pitches are very close to one another (or close to being a perfect octave apart), the crests and troughs of their waveforms become very closely aligned, and reinforce or cancel each other in predictable patterns, resulting in beats.  The closer to each other two pitches are, the slower these beats sound, and when a player detects beats, she knows to make adjustments in order to eliminate them.

Other intervals require a different approach to intonation.[3]  Beats are one aspect of an acoustical phenomenon known as difference tones.  The frequency in Herz of the beats between two pitches is the arithmetic difference between the frequencies of the two pitches.  Thus, when a tone is played at 440Hz simultaneously with a tone at 444Hz, the beats, or difference tones, will sound at a rate of 4Hz.  When pitches are in small whole-number ratios to each other, difference tones can become quite prominent, especially to listeners in close proximity to the sound sources.  For example, when two brass players play pitches a major third apart, say, A4 and C#4, when the pitches are in tune with each other, they will produce a tone reflecting the difference between their frequencies, 440 Hz and 550 Hz, respectively, for a low additional pitch of 110 Hz, or A2.  Most musicians perceive this as a “buzz” that indicates that the chords have been “locked-in.”  A similar phenomenon that is exploited by musicians is the summation tone, which is heard as a tone with a frequency that is the sum of the two component frequencies.  In the example given above, the summation tone for 440 Hz and 550 Hz would be 990Hz, or B5.  As intervals are added to each other to become chords, the achievement of summation and difference tones becomes crucial to good intonation.

At times, passagework on a brass instrument becomes too rapid for the tuning of each individual chord or interval, and a player must fall back on her experience and technique on the instrument to ensure good intonation.  This comes about through years of practice and preparation, especially work on scales, arpeggios, or chords played one note at a time, and etudes, or music that incorporates common patterns or technical difficulties and is intended mainly for the practice room.  Effective practice for many musicians does not mean solely the preparation of music that is to later be played in public, but rather the development of a daily routine that emphasizes the technical fundamentals for the performer’s instrument in order to be prepared for whatever music may appear in the future.

In contrast to the emphasis that vocalists or brass players must place on intonation, some instruments offer the player very little control over intonation or even none at all.  The piano, for example, while certainly tunable by any musician with the proper equipment, is generally tuned prior to performance or more likely only periodically, leaving the pianist with a fixed set of pitches at his disposal.  The tuning of pianos, then, is frequently left to specialized piano tuners, who may or may not be accomplished pianists, while pianists of any skill level are fairly unlikely to be skilled piano tuners.

In the era before the commercial availability of first analog and then digital tuners, piano tuning was a skill acquired only through great effort and refined through extensive experience.  At one time, visually-impaired persons were frequently trained as piano tuners because it was assumed, often correctly, that the other sensory organs acquired greater acuity in those lacking the visual sense.  With perfect vision not required, and the piano at one time enjoying the place in middle class homes now given over to the television, piano tuning was a logical career for persons in this situation.[4]  The difficulty in tuning a piano lies in that instrument’s use of equal temperament, in which only the octaves are tuned to the precise frequencies generated by the harmonic series.  In addition, the lower strings of a piano are often tuned deliberately low, while the higher strings are tuned deliberately high, meaning that the instrument as a whole has a certain inharmonicity that has become the preferred norm in many parts of society.   A final challenge is that most of the pitches on the modern piano involve not just one string but two or three, meaning that every note must be in tune with itself before it can be in tune with the rest of the instrument.  Thus, while the performer at a piano may think little of intonation—except perhaps to notice that the instrument is in need of a tuning, or to notice intonation deficiencies in the performers with whom he collaborates—the process of tuning a piano is very complex and can be very time-consuming.[5]

Other musicians are responsible for calibrating their own instruments.  A common example in this regard is the guitar, either in acoustic or electric forms.  Before a guitarist can play, she must tune the strings of the instrument, which on six-string models are tuned to six different pitches at varying intervals from each other.  In addition, basic guitar technique often involves various alternate tunings to allow the guitarist to play certain music more easily.  A guitarist will begin by tuning one string to a reference pitch, and then tune other strings, one at a time, to the first string.  The frets on the neck of the guitar guarantee that one string can be tuned to another fairly easily, and many guitarists also make use of harmonics to check strings even more closely.  Once the guitar is in tune, the guitarist can begin to play with relatively little attention to intonation, but she must continually listen to her instrument to insure that it hasn’t gone out of tune, and make adjustments as needed.

Both the piano and the guitar have had turns as mass-produced, popular instruments, with the piano’s heyday occurring in the 19^th century, and the guitar taking the piano’s place in the late-20^th century.  These instruments have the advantage of being instruments that can supply complete musical textures, but can also be played while singing.  A very basic technique on either instrument can supply needed accompaniment to vocal music, and both were brought into the economic reach of the European and American middle class by mass production and the rise in living standards that followed the Industrial Revolution.  The piano and guitar, however, were not the only instruments to benefit from the advantages listed above.  What they seem to have in common that other instruments lack is a relatively simple approach to intonation.  A piano that is once tuned by a specialist and then kept within reasonable limits of temperature and humidity will remain relatively in tune for quite some time, perhaps six months or more.  The guitar is easily tuned at the beginning of a session, and with high-quality strings and only minor adjustments, will remain in tune for a performance without the guitarist having to constantly worry about intonation in the manner of a brass player or violinist.  This approach to intonation has certainly contributed to the intense popularity of both of these instruments.

A very few instruments are impossible to tune once manufactured and have a fixed pitch.  An example of this would be so-called keyboard percussion instruments such as the xylophone, which consists of a set of hardwood or synthetic bars in graduated sizes which are struck with mallets.  While it would conceivably be possible to shorten these bars, and thus raise their pitch, this is rarely done, and it would be patently impossible to lengthen the bars to lower their pitch.  Thus, the percussionist can exercise no control whatsoever over intonation and is completely dependent on the skill of the manufacturer and the quality of the materials and design, which hopefully will be only minimally susceptible to changes in temperature and humidity.  It is likely that other musicians will find it necessary to adjust their intonation to these instruments.

All serious musicians, and most amateurs, are able to calibrate their own instruments, with the exception of those who play piano, organ or other instruments that rely on specialists for tuning or which cannot be adjusted.  When a musician performs as a soloist, with no accompaniment, all tuning and intonation can be done internally, with only the musician’s internal ear to guide the performance.  A more likely situation, however, is that of the ensemble performance, in which instruments must not only be played with good intonation, but must be calibrated to each other.  Since the 19^th century, the international standard for ensemble performance in Western music has been to tune A4 to 440Hz, sometimes referred to as A440.[6]  Tuning forks, pitch pipes and analog and digital tuners have all come to be manufactured to this standard, as have fixed-pitch instruments, such as the keyboard percussion mentioned above.[7]  A musical ensemble, then, must develop a procedure—a ritual, even—for this calibration.  The ritual calibration for an American orchestra is almost a cliché—the principal oboist, usually with the aid of a digital tuner, sounds A4, providing a standard to which the other musicians of the orchestra will then adjust their own instruments.[8]  By contrast, in Europe, orchestras do not tune onstage, with the result that if the temperature onstage is different than that offstage, the first part of the first piece to be performed may be grossly out of tune until the musicians can make the necessary tuning adjustments.

An excerpt from Chapter 5 of my book Music: Notation and Practice in Past and Present, currently in press.

The conception of the staff as a form of the xy-coordinate plane is adequate for an understanding of the notation of pitch events and their temporal relationships.  However, music is far more subtle than the four elements of melody, harmony, tempo and rhythm that can be described in this way.  In fact, staff notation as we have studied it ignores the musical element that frequently gives the first and most basic aural cues to listeners:  timbre.  Many listeners who fail to be excited by the use of unique scales, obscure keys, unorthodox meters or complex chords are instantly enthralled by the sound of familiar or favorite instruments or the specific timbral qualities of the voice of a beloved singer.  The system of musical notation simply cannot be considered complete without a means for indicating timbre.

For centuries, though, there were no such indications in Western musical notation.  While the earliest forms of what would become modern notation date back to the 10^th century A.D., no composer indicated what instruments were to play the specific parts in a score until Giovanni Gabrieli (c. 1554/1557-1612) published his Symphoniae Sacrae (1597, 1601), which indicated timbre by naming the desired instrument to the left of each staff in a system, or group of staves.  For music prior to that time, performers and musicologists must often rely on other clues left by the compositional process.  The inclusion of poetic text, for example, indicates that a composition was likely for voices, although it is always possible that instrumentalists would double the vocal parts, as continues to be the case in much music written to this day.  This practice is prevalent in Protestant hymnody, where it was traditional for the music to be written in four vocal parts (soprano, alto, tenor and bass), but doubled on a keyboard instrument such as piano or organ.  Specific melodic or harmonic figurations may indicate that a composition was intended for a specific instrument, such as a keyboard instrument or a fretted string instrument.  In general, however, during much of the history of music, music, whether notated or not was performed by the available forces at any given moment.  It is remarkable that the first composer to call for specific instrument worked in Venice, one of the most prosperous cities at the time, where he supervised the music for St. Mark’s Cathedral, the central church of the city.  The musical forces available to Gabrielli were likely some of the most reliable, professional and well-paid in Europe, and it has typically been in environments such as this that musical experimentation thrives and new standards are set that eventually become adopted throughout a culture.

It is likely that an experienced musician, presented with an unlabelled instrumental part for a standard instrument, could identify the instrument being called for by investigating certain factors.  Instrumental range is a possible clue, as all instruments have at least an absolute lowest pitch, and while their range may theoretically extend upward to infinity, there is usually a generally-accepted upper limit to the pitches that a standard instrument can play.  For example, the modern flute can play no lower than B3, and only to C4 on some student models[1].  Its upper range extends to approximately C7 for professional players.  In addition, as with all woodwind instruments, it is common to write trills, in which a player rapidly alternates between two notes a step apart, for flute.  However, some notes are more easily trilled than others, and an astute composer will avoid the difficult trills while utilizing the more convenient ones.  If the hypothetical mystery part, then, had no notes below C4, but a range extending up to B$6, all the while treading delicately around the more tricky trills (such as that between C4 and D$4), it would be reasonable to conclude that it was music for the flute.  This music would be said to be written idiomatically for the flute.

Idiomatic writing for an instrument or voice is crucial to successful composing and arranging.  While more basic music is generally playable on any instrument if transposed into the correct range, more complex and difficult music can quickly overwhelm the abilities of even a professional performer if utmost consideration is not given to the unique properties of an instrument or voice.  For vocal music, it is even reasonable to compose with a specific performer in mind, as human voices are as wondrously varied as human faces.  For example, British composer Benjamin Britten (1913-1976) had a life-long collaboration—both personally and professionally—with tenor Peter Pears (1910-1986), resulting in several sets of songs, operatic roles and the incomparable Serenade for Tenor, Horn and Strings (1943) being composed with Pears’ somewhat unremarkable voice in mind.  These works reflect the limitations and advantages of Pears’ instrument and, like others composed for specific performers, they must be approached with this in mind.  The Britten-Pears collaboration has been the subject of much musicological study, and is a prime example of the ways in which a composer’s life can impact his work and vice versa.

Composers also write for specific instrumentalists.  For example, Aaron Copland (1900-1990) composed his Clarinet Concerto (1947-9) on a commission from clarinetist Benny Goodman (1909-1986).  Goodman, better known for his jazz improvisations than his classical performances, felt a responsibility to add to the repertoire for his instrument, despite his own feelings of inadequacy about his ability as a classical performer and admitted discomfort with notated music.  Copland’s concerto, then, is scrupulously notated and, while not in a jazz idiom, works very closely with what is natural to the clarinet while at the same time providing a piece worthy of Goodman’s substantial technical prowess.  Goodman has not been the only performer to feel compelled to contribute to the repertoire for his instrument.  In the 19^th century, virtuoso violinist Niccolo Paganini (1782-1840) not only composed music for himself but commissioned others, with the result that Paganini’s revolutionary technical skills, many of which were innovative developments for the instrument, became standard violin technique within a few generations.  In the late-20^th and early-21^st century, a generation of gifted trombone players, such as Swedish virtuoso Christian Lindberg (b. 1958) and the American Joseph Alessi (b. 1959), has been creating a repertoire for their instrument by commissioning and performing new music.  These new pieces will impact the study of the trombone for generations to come as students begin to view these new works as the standard aims of serious study on the instrument.

Similarly, a performer may possess unique or innovative abilities that a composer wishes to exploit in a musical composition, or that a performer may employ in his own music.  Vocalist Bobby McFerrin (b. 1950) possesses a miraculous instrument capable of an enormous variety of vocalizations that he has employed in jazz, popular and classical-style compositions.  Similarly, soprano and composer Cathy Berberian (1925-1983) possessed a vocal instrument whose range, expressiveness and accuracy inspired not only her own compositions, but also those of her husband Lucciano Berio (1925-2003) and many other composers.  The ongoing collaboration between composer and performer can be as vital and important as that between two actors or an actor and a director with onscreen chemistry (Tom Hanks and Meg Ryan, for example, or Jack Lemmon and Walter Mathau, or Jimmy Stewart and Alfred Hitchcock), and it can define careers and musical legacy, as is currently being seen in the collaborations of composer Osvaldo Golijov (b. 1960) and soprano Dawn Upshaw (b. 1960), or composer Magnus Lindberg’s (b. 1958) on-going work as Composer-in-Residence with the New York Philharmonic.  For this author, who is trained as a composer, collaboration with a performer who gives significant practice time to a new piece is a joy.  When a performer becomes as emotionally involved as the composer with the new piece, however, the experience is as thrilling—and absorbing—as a new love affair.[2]

It is likely that most composers in the era before 1600 simply knew their performers personally, never intended to distribute their music widely and wrote for the individual at hand.  In our technological, text-saturated world, duplication of the written word (or composed note) is cheap and easy.  A composer can write a piece today that will be played, sung or heard  by thousands tomorrow, making it impossible for the composer to know every performer—or potential performer—personally.  Every musician’s abilities are different, and every musician’s musical language is slightly different.   This is the challenge that the composer of music for a specific timbre faces, then, and the answers to this challenge are highly varied, and often quite subtle.

An excerpt from Chapter 4 of my forthcoming book, Music: Notation and Practice in Past and Present:

There is an unfortunate tendency among music readers to view rhythmic notation as defining points of sound that occur at discrete moments.  On certain instruments, this is effectively true.  For example, once some percussion instruments are struck, there is very little the performer can do to alter the resulting sound, which at any rate, has a relatively short duration.  This is certainly the case for some drums, such as the snare drum, and for some of the idiophones such as the claves, woodblock or anvil.  For nearly every other instrument, though, including the piano, guitar and the human voice, a note indicates not only an attack, or the start of the sound, but also a release, or an endpoint.  In addition, performers may have some control over a sustaining, or continuous middle portion, of a tone, or the decay of a sound, the resonance that continues after a release point.  While some aspects of these envelopes are inherent in the timbre of an instrument, others can be effected through developed instrumental or vocal technique.  For example, the timbre of the piano has very little sustaining quality—as soon as a note is struck, the sound begins to decay.  But through the use of the damper pedal (found on the right on modern pianos), the decay can be allowed to persist instead of being cut off when the key is allowed to return to its original position.  This ability has largely defined the sound of piano music for the last two centuries, and a piano without a functioning damper pedal is not a functioning instrument any more than a car without brakes is a functioning vehicle.

The act of shaping the attack, sustain, decay and release of notes is known as articulation, and the art of articulation varies to a greater or lesser degree on every instrument.  It is crucial for an aspiring musician to study and understand the technique of articulation on her chosen instrument, and within various styles.  Much of what constitutes a style is often a tacit agreement on how to apply articulations to written or improvised music.

Despite the differences in articulation technique between instruments, a reasonably standard set of symbols has developed in written music to allow the composer some control over certain aspects of the shape of notes.  These symbols really alter any of several different musical elements—most often rhythm or dynamics, other times melody, and occasionally timbre.  Their meanings vary slightly between instruments and styles, but some generalizations about each symbol can be made.

The slur is a symbol with several different meanings, depending on the instrument or voice for which music is written.  Its first use was with notes in vocal music that employed melisma, the technique in which a single syllable is sung over two or more notes.  In this case, as in Figure 29, the slur indicates exactly which notes are involved in the melisma, and does so more precisely than the lyrics below the notes can do.

 

Figure 29: Indication of melisma in a vocal part using a slur.  The notes will be sung with the words “A melisma,” with the melisma occuring on the syllable mel.

Woodwind and brass players, whose approach to phrasing and articulation is similar to singing in many respects, also use slurs to group notes into unbroken (or slightly-broken) streams of sound.  In Figure 30, a passage for clarinet, the first note under each slur is given a relatively pointed attack with the tongue.  For the subsequent notes, the air continues to move through the instrument without interference, while the fingers work keys and cover or uncover holes to change the pitch.  At the end of the last note, either the tongue or the breathing apparatus may be used to stop the air.



 

Figure 30: A passage for a wind instrument employing slurs.  Only the first and seventh notes would have tongued attacks.

For bowed stringed instruments, slurs indicate the use of the bow rather than the tongue or airstream.  All notes under a slur will be played without changing bow direction.  In Figure 31, for violin, the player would play the first four notes without changing direction, then reverse course for the next five notes.  String players often use the Π and V symbols for downbow and upbow, respectively, in which the right (bow) hand moves in the stated direction, adding further control over attack and sustain envelopes.  In addition, other articulation symbols may be used in combination with the slur in writing for strings, often indicating the degree to which the bow should stay on or bounce off of the string at the end of each note.[1]

 

Figure 31:  A slurred passage for a bowed string instrument.  The bow would change direction on the first, fifth, tenth, twelfth, 14th, 16th, 17th and 18th notes.

Some instruments, such as piano, guitar and many percussion instruments, have little control over the sustaining power of their notes.  The result is that slurs for these instruments are most removed (although not completely separate) from their meaning for the voice.  For guitar, a slur indicates that the performer is to pluck the string for the first note with the right hand, and then either “hammer on” (articulate the second note by pressing a higher left-hand finger onto the same string), or “pull off” (change to the second note by lifting up a finger to lengthen the string).  The ability to slur on guitar, then, is much more limited than on most instruments.

In music for the piano, which also has limited sustaining power, a slur generally indicates a legato approach to the notes under the slur, meaning that the release of a note is delayed until the finger playing the next note can be put down, usually with a sense of heaviness in the wrist that allows one note to effectively blend into the next.

Slurs for most percussion instruments have only the most basic meaning, but one that is really at the core of the idea of the slur.  In its most basic form, a slur indicates musical phrasing, that is, it shows a player that a group of notes is meant to be a single musical idea.  This type of slur is frequently combined with the other types for all instruments, and it is typical of many styles to modify the tempo at the beginnings and ends of slurs to allow performers to breathe.[2]

Figure 32 shows the notational difference between the slur and the tie.  Several visual cues can be used identify which symbol is being used, notably that the tie always connects two adjacent notes that are on the same line or space on the staff, while the slur may connect any number of notes.  There are also slight engraving differences, namely that the ends of a tie are closer to the heads of the affected notes, and the overall depth of the curve is shallower.  Slurs generally point to the heads of the first and last notes, and are found on opposite sides of the note from the stem.  Two important exceptions, however, should be noted:  When a slurred passage begins with a stem-up note and ends with a stem-down note (or vice-versa), the slur is drawn above the notes.  And when two voices appear on a single staff, any slurs will connect stems instead of noteheads.

 

Figure 32: Slurs vs. ties.  In each measure, the first two notes are slurred while the second two notes are tied.

Several other standard articulation symbols appear in contemporary notation, each with a slightly different meaning on every instrument.  A good instrumental teacher will be able to couch their meaning in terms of instrumental technique rather than precise rhythmic practice, but in each case, the effect is relatively the same.  An additional differing factor is how each articulation is treated in any given style, even down to the expectations of an individual composer.

The staccato dot (.), which appears either directly above or below a notehead, opposite the stem, originally instructed players to perform the note at half its value, with a rest on the second half.   While this interpretation holds true for many styles, there is a fair amount of variation in the meaning of this symbol, even among performances of the same piece.  Many performers will tailor their interpretation of staccato in some passages to the acoustics of the room in which they sing or play, as the reverberation times of musical sound can vary greatly in live performance spaces.  Other composers had the opportunity to let their desires be known, as in the case of Igor Stravinsky, who generally insisted that his staccato markings indicated that the note was to be played “as short as possible.”

The tenuto symbol (–) is an indication to play a note for full value, but no more, in other words, to let a note take up its entire allotted space, but to also keep it separate from the next note.  Like the staccato dot, the tenuto symbol is written either above or below the notehead, opposite the stem.  While this symbol may seem redundant, it is highly useful as a clarifying symbol in a complex passage, or in unfamiliar styles.  The author, in his role as a composer, advises contemporary composers to use articulation symbols liberally in their music.  While most classically-trained performers could supply a reasonably acceptable performance of a piece by Mozart without any written articulations, and indeed frequently do so with the music by Bach, which has few, if any of these symbols, contemporary composers cannot rely on performers’ being able to make these assumptions, and thus should be as specific as possible.

The accent mark (>) always appears above a note, whether the stem is up or down, in order to be somewhat more visible.  This mark indicates that a more forceful attack, often in contrast to the tendency of the meter, should be made on that note.  The mechanics of this attack vary from instrument to instrument, and among styles, composers and individual performers, but the effect generally results in a more forceful attack at a slightly stronger dynamic level than the surrounding notes.

A cousin of the accent mark is the martellato accent (Λ), which is frequently understood as a combination of the staccato and accent.  It is not appropriate in some styles, but is ubiquitous in jazz, where it is often placed above beat-length notes.  Experienced jazz brass and woodwind players emphasize not only the attack but the release of notes with this symbol, and often describe the result with the word “daht” in the vernacular (and often highly personal) rhythmic solfege syllables that are used to communicate information about “swung” rhythms.

The notation of rhythm, meter and tempo, whether in the form of individual rhythmic patterns, metric notation, or articulations defining attack and release, is the key to the higher-level organization of notated music.  Ironically, it is the aspect of Western notation that came later (although not last), as the music originally notated (Medieval plainchant) was rhythmically formulaic to the point where only pitch and text required notation.  Precision of rhythmic notation, and accuracy in reading rhythm, are crucial skills for any musician that will allow the development of true music reading skill.  Rhythmic notation can be confusing, and must be read in real-time, but a focus on learning specific rhythmic patterns will yield relatively quick results for most students, and a degree of comfort and familiarity that will allow exploration of a great deal of written music can be developed by regular practice.  It is crucial that the goal of an aspiring musician in the Western tradition be to understand musical notation at sight without assistance from a teacher or director.  This is the first step toward a firsthand experience of the body of work that is the musical inheritance of a civilization.

An excerpt from Chapter 3: The Notation of Melody and Harmony of my forthcoming book Music: Notation and Practice in Past and Present:

Modern Western musical notation has its beginnings in the liturgical music of the Roman Catholic Church.  By ca. 800 C.E., a common repertory of plainchant had solidified for use in the vast array of worship services performed throughout Western Europe.  A plainchant is an unaccompanied vocal setting of Latin or Greek prayers or hymns, sung at specific dates and times through the rotating calendar of the Catholic Church.  Plainchant is assumed to have developed from Greek, Byzantine and Jewish antecedents, just as Christian worship evolved from Jewish Temple and synagogue traditions of the early Common Era.  During Late Antiquity and the Early Middle Ages, there were many forms of plainchant, some of which continue in use alongside other forms of worship to this day[1].  With the rise in importance of the Pope (i.e., the Bishop of Rome) in governance in the Western church, however, worship practices became standardized.  Pope Gregory (dates) is often wrongly credited with inventing the system of notation that would become our modern system, but his role was actually to instigate a cataloguing and standardization of plainchant throughout the church year.  Nonetheless, the term Gregorian chant is often used synonymously (and technically incorrectly) to refer to plainchant.

The key difference between Western musical notation and earlier systems is that the earlier methods generally relied on an alphabetic approach to notation in which every note available was assigned a specific symbol, just as an alphabetic writing system assigns a specific symbol to each phoneme in a language.  An example of this type of system can be found in ancient Greece, where by the early Common Era, both a vocal and an instrumental set of symbols had developed on this principle.  The system appears to have been fairly well-known, and used in a variety of settings, from the theatre (scraps of papyri give musical notation for lines from plays by Euripedes), to religious settings (the Delphic hymns), to funereal memorials, such as the Epitaph of Seikilos, found carved on a tombstone.  In the Greek vocal system, symbols for individual pitches were simply written above or below the corresponding words.  The Jewish Psalter, the hymnal for worship at the Temple in Jerusalem, used a simpler set of diacritical marks to indicate musical cues within the Hebrew text of the Psalms.

While music is often referred to as a “language,” especially by writers and speakers who gush over its emotional properties and spiritual meaning, the truth is that it is not.  There are similarities between music and spoken language, but there are also great differences.  Music alone cannot convey precise meaning.  It cannot give directions or specific instructions.  It cannot describe historical events in unambiguous detail.  It can tell stories, but only in vague ways that often rely on a written or spoken description, or a preexisting understanding of the story being told.

At the same time, language is not music.  Our ear for language is somewhat forgiving, as evidenced by our ability to understand each other despite individual variations in pitch, rhythm and articulation.  It may be difficult to understand a speaker using our native tongue with a strong accent, but we still comprehend the same words.  If a musical composition were changed by the same amount in the same aspects, we might be forced to understand it as a variation on the original piece, if not a completely different piece.

The alphabetical approach to musical notation, then, while a clear borrowing of a wondrous invention, leaves some things to be desired.  The Greek and Hebrew systems did not have any way of showing duration, for the most part.  Duration, in the form of tempo, rhythm and meter, is crucial to musical expression and to the reproduction of a musical idea, which is the purpose of notation in the first place.  When notation using a musical alphabet is added to written language, the result is that a performer must either use both as simple mnemonic devices or attempt to simultaneously read both lines flawlessly.

For written language, the process of fluent reading depends on chunking—the mental grouping of characters into recognizable patterns.[2]  Fluent readers chunk on the word and phrase level, often making assumptions about the identity of a word based on its shape and first and last letters rather than perceiving every symbol.  In music, this sort of chunking might be useful to a certain degree, especially in styles that abound in melodic cliché, but the ability to simultaneously perform this mental operation in two different alphabets would likely be very difficult to develop.  Whether this is a reason that the Greek system never became as ubiquitous as our modern system of notation is debatable.  More likely, in a largely illiterate society, the need for musical notation was simply not all that great.

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[1] Over the last 400 years, the Roman Catholic Church has increasingly left behind plainchant, and music derived from it, as the regular mode of worship.  Unaccompanied singing was appropriate in times and places where sustenance and survival were uncertain, but as Europe became more prosperous, the music used in worship became more complex.  The Second Vatican Council of the 1960s introduced the most sweeping changes in Catholic worship by mandating worship in vernacular languages rather than Latin.  With this shift, musical styles in worship also shifted to reflect folk and popular styles.  Plainchant continues to be used in some religious communities and on certain occasions in worship, but its interest is now primarily historical for most listeners.

[2] Another example of chunking in everyday life is the splitting of phone numbers into groups of two, three or four digits, thus making them easy to remember.  The American convention, for example, uses the three-digit area code, followed by a three-digit exchange, followed by the four-digit extension.  To the switching computers at the telephone company, these groupings are irrelevant, but they are extremely useful for humans who wish to remember a phone number.  Four digits seems to be an upward limit, and children often have to remember the last four digits of a phone number two digits at a time.

An excerpt from Chapter 2 of my forthcoming book, Music: Notation and Practice in Past and Present.

What is the fate, then, of popular music in the twenty-first century?  This question will be examined in-depth later in this book, but a brief consideration is appropriate here.  The culture industry was predicated on the idea that most individuals could not afford to record and distribute their music.  As a result, the music that was recorded was calculated to appeal to large numbers so that the sale and broadcast of that music would pay the greatest possible dividends.  In the era of the Internet, with its cheap and easy distribution models, coupled with the ability of many musicians to afford their own home recording studios, the recording industry has gone into a precipitous decline, with annual album sales falling by more than 50% by 2009 from their all-time high of nearly 800 million units in 2000.[1]  While there will always be popular music, the consequences for the popular music industry would seem to be dire, and it is doubtful that the current model of mass-market popular music can survive.  Various authors have put forward theories of what 21^st-century popular music will look like.  Here are some possibilities:

• There will increasingly be no truly popular music, as it becomes less and less possible for musicians to make a living providing a service that can largely be had for free.
• There will increasingly be no music that has a broad public appeal, as the variety of music available on the Internet allows listeners to consume only that music that fits their very specific tastes, and the eclecticism of, say, 1970s FM radio disappears.
• Popular music will become folk music, as more and more musicians make music for their own entertainment, releasing it to the Internet for the enjoyment of friends, family and a few die-hard fans, who may be scattered throughout the world.
• New music will involve fewer and fewer live musicians, as more and more relatively untrained (in the traditional sense) composers create “mashups” of historical styles using home recording technology.  The future will sound like the past in a blender.
• As recorded popular music becomes more of a free commodity, musicians will return to live performance as their primary means of making a living, and have as their goal a contract with a national concert promoter rather than one with a large recording company. 
• As the popular music of the past becomes ossified into a “canon” that resembles the world of classical music, it will be studied, dissected and, eventually, become a part of the human cultural heritage that will be treasured by educated adults and analyzed by intellectuals[2] while some new musical form captures the young hearts and minds of the world.

Perhaps the only certain outcome of the revolution currently underway in popular music is the last of these, as scholars who have been raised nearly exclusively on popular music begin to gain influence in academia, and turn their minds toward the music they love most.  This scholarly study will lend further legitimacy to discussions of popular music in elementary and high schools, and as the educational system, one of whose purposes is to impart culture to the young, presents, say, hip-hop as an acceptable, even admirable, means of music-making, the prejudices which have so far kept the public from comparing Beethoven and Mozart to 50 Cent and the Wu Tang Clan will begin to dissolve.  In this way, the popular music of today will become the folk and art music of tomorrow.

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[1] Kenney, Caitlin.  “Album Sales Hit Record Lows.  Again.”  http://www.npr.org/blogs/money/2010/08/25/129428450/album-sales-hit-record-lows, Accessed August 27, 2010.  The year 2010 appeared no better, with fewer than five million albums (including digital copies) sold by the industry during the first week of August, the lowest weekly return since 1991.  These figures reflect a trend that neatly parallels the developing abilities of consumers to buy, sell, record and share music via personal computers and the Internet.[2] This has already occurred for jazz, and is beginning to take place for later popular styles in the realms of music theory, musicology, ethnomusicology and popular culture studies.  The 2008 joint conference of the American Musicological Society and the Society for Music Theory, meeting in Nashville, featured at least one session dedicated to twentieth-century popular music in every portion of the four-day conference, including a plenary session entitled “Popular Music and the Canon.”  The number of papers and sessions on popular music was such that scheduling dictated that a scholar of popular music would not have been able to attend every session in his field.

A portion from the first chapter of my forthcoming book, Music:  Notation and Practice in Past and Present, published by National Social Science Press.

Before discussing the seven elements [of music] in detail, it is important to think about just what constitutes a piece of music.  We are all aware of the existence of songs that have been recorded multiple times by different artists, or even by the same artists.  These “covers” may hold very closely to the original or may be completely different, even falling into a separate style.  Are all these versions separate pieces, or species of the same piece?  With a painting or a sculpture, it is possible to point to a specific object—perhaps even to pick it up and consider its physical properties.  Similarly, a book or a poem has a specific text that is the work of literature, and while there may be variant editions, there is a core sense of being to a book that keeps even different versions of the same story somehow separated from each other.  No one would dare suggest that a novel, its abridgement and its translation into a foreign language are all the same book, although we may study the similarities and differences.

A piece of music, though, seems somehow more mutable.  Without the physical objects of the painting, the sculpture or the book, there is no art, but music can be completely without any sort of tangible representation.  Even musical notation, one of the great inventions of European civilization, is not, of itself, the actual music, but rather relates to the experience of music in the way that a recipe in a cookbook is representative of actual food.  Cookbooks, of course, are extremely useful, interesting and often inspiring, but they cannot sustain, cannot satisfy, cannot taste the way that even the plainest tofu or simplest piece of fruit can.  A musical score is much the same.  It instructs, it reminds, it inspires, it describes, and it communicates at far removes of time and space, but it is not the music itself.

The technology of sound recording, first developed in the late 19^th century and advanced and marketed in ever more complexity and availability since then, also bears consideration.  When a consumer purchases a recording, whether in a physical or digital format, she tends to feel that she “owns” whatever music is in the recording.  But to what extent is this really the case?  Recordings may have very high fidelity, but does the experience of listening to a recording equate to the experience of listening to a live performance?  Listening to a recording lacks the human interaction of live performance—seeing the expressions on the faces of performers and the potential for performers to react to unique events in the audience that no recording, audio or video, can replicate.

The only conclusion, then, is that the actual existence of a piece of music lies not in written notation or in recorded performance.  Music somehow has an existence beyond all these things.  It is beyond notation and recording.  It exists first in the human mind, and perhaps most purely there, and like a map that inevitably has to overlook some details, music cannot be fully represented except in live performance, and perhaps not then.