musical notation, symbols used to make a written record of musical sounds.

Two different systems of letters were used to write down the instrumental and the vocal music of ancient Greece. In his five textbooks on music theory Boethius (c.A.D. 470-A.D. 525) applied the first 15 letters of the alphabet to the notes in use at the end of the Roman period. Notation of Gregorian chant was by means of neumes, which are thought to have been derived from symbols used in the Greek language to indicate pitch inflection. Neumes were certainly in use by the 6th cent., although the earliest extant manuscripts containing them are fragmentary ones from the 8th cent. These neumes indicated only the grouping of sounds in a given melody, evidently to recall to a singer the approximate shape of a melody already learned by ear.

Heighted neumes, arranged above and below a line, made the intervals of a melody more discernible in 10th-century notation, and by the end of the 12th cent. the staff perfected by Guido d'Arezzo was in use. Guido placed letters on certain lines to indicate their pitch, and thereby the pitch of the remaining lines and spaces. The letters evolved into the clef signs used today. Guido also invented a system of naming scale degrees using the initial syllables of the lines of a Latin hymn (ut, re, mi, fa, sol, la). Originally used for teaching sight singing, these or their derivatives are also used in some languages for naming absolute pitches.

A staff of five lines for vocal music was adopted in France and one of six lines in Italy. Instrumental music employed staves of varying numbers of lines until the 16th cent., when the five-line staff became the standard. Signs for chromatic alteration of tones appear almost from the beginning and had assumed their present shapes by the end of the 17th cent. The essential problems in pitch notation, the use of both lines and spaces to indicate successive scale degrees and the use of extra symbols to indicate raising or lowering a tone by a half step, were solved comparatively rapidly.

However, the evolution of the rhythmic notation used today took much longer than that for pitch. Mensural notation, in which each note has a specific time value, became a necessity with the development of polyphony. At first, certain patternings of neumes were used to represent the various rhythmic modes; later, in his Ars cantus mensurabilis (c.1280), Franco of Cologne created a clear indication for each note of its exact rhythmic length and selected certain neumes to represent tones of long and short duration. In his system, the long value was in principle equal to three of the short values.

In the 14th cent. Philippe de Vitry, author of Ars nova, which expands the system of Franco, codified the ready availability of duple divisions of the long and short notes. At the various rhythmic levels of a given piece either a 2:1 or a 3:1 relationship was implied, and a system of signs and colored notes developed for indicating which relationships were in force or were being temporarily altered.

In the 15th cent. numbers with the appearance of fractions indicated that one proportionality of rhythmic values was temporarily being substituted for another. Modern signatures evolved from these numbers. Bar lines, expression signs, and Italian terms to indicate tempo and dynamics came into use in the 17th cent. With the adoption of equal temperament and the major and minor modes, signatures indicating a major key or its relative minor became conventional. They assumed their present form during the baroque period.

The advent of aleatory music has produced notation systems, varying from piece to piece, indicating only approximate pitch, duration, and dynamic relations. Notation for electronic music is still not standardized but generally uses traditional reference symbols (staff and clef signs) in conjunction with specially adapted pitch and rhythm notation.

For a system of notation of lute and keyboard music, see tablature. See also score.

Written, printed, or other visual representation of music. There are two basic approaches to notating music. Tablature (such as guitar chord diagrams) depicts the actions a performer is to take (in particular, showing where to put the fingers to produce a given sound). Symbolic notation describes the sounds themselves and includes methods that vary from assigning pitches different letters of the alphabet to representing a given combination of notes by a graphic sign. The Western notation system combines rhythmic notation (the appearance of a note indicates its duration) with pitch notation (the line or space on a staff where a note is placed indicates its pitch). Thus, a single symbol shows both pitch and duration, and a string of these symbols notates both melody and rhythm.

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Music notation or musical notation is any system which represents aurally perceived music through the use of written symbols.

History

It has been suggested that the earliest form of musical notation can be found in a cuneiform tablet that was created at Nippur in about 2000 B.C. Apparently the tablet represents fragmentary instructions for performing music, that the music was composed in harmonies of thirds, and that it was written using a diatonic scale. A tablet from about 1250 B.C. shows a more developed form of notation. Although the interpretation of the notation system is still controversial, it is clear that the notation indicates the names of strings on a lyre, the tuning of which is described in other tablets. Although they were fragmentary, these tablets represent the earliest recorded melodies found anywhere in the world.

Ancient Greece

Ancient Greek musical notation was capable of representing pitch and note-duration, and to a limited extent, harmony. It was in use from at least the 6th century BC until approximately the 4th century AD; several complete compositions and fragments of compositions using this notation survive. The notation consists of symbols placed above text syllables. An example of a complete composition is the Seikilos epitaph, which has been variously dated between the 2nd century BC to the 1st century AD. Three hymns by Mesomedes of Crete exist in manuscript. The Delphic Hymns, dated to the 2nd century BC, also use this notation, but they are not completely preserved. Ancient Greek notation appears to have fallen out of use around the time of the fall of the Roman empire.

Arab world

Al-Kindi (801–873 AD) was the first great theoretician of Arabic music. He proposed adding a fifth string to the 'ud and discussed the cosmological connotations of music. He surpassed the achievement of the Greek musicians in using the alphabetical annotation for one eighth. He published fifteen treatises on music theory, but only five have survived. Al-Farabi (872-950) wrote a notable book on music theory entitled Kitab al-Musiqa (The Book of Music). His pure Arabian tone system is still used in Arabic music.

Arabic maqam is the system of melodic modes used in traditional Arabic music, which is mainly melodic. The word maqam in Arabic means place, location or rank. The Arabic maqam is a melody type. Each maqam is built on a scale, and carries a tradition that defines its habitual phrases, important notes, melodic development and modulation. Both compositions and improvisations in traditional Arabic music are based on the maqam system. Maqams can be realized with either vocal or instrumental music, and do not include a rhythmic component.

A theory on the origins of the Western solfège musical notation suggests that it may have had Arabic origins. It has been argued that the solfège syllables (do, re, mi, fa, sol, la, ti) may have been derived from the syllables of the Arabic solmization system Durr-i-Mufassal ("Separated Pearls") (dal, ra, mim, fa, sad, lam). This origin theory was first proposed by Meninski in his Thesaurus Linguarum Orientalum (1680) and then by Laborde in his Essai sur la Musique Ancienne et Moderne (1780).

Early Europe

Scholar and music theorist Isidore of Seville, writing in the early 7th century, remarked that it was impossible to notate music. By the middle of the 9th century, however, a form of notation began to develop in monasteries in Europe for Gregorian chant, using symbols known as neumes; the earliest surviving musical notation of this type is in the Musica disciplina of Aurelian of Réôme, from about 850. There are scattered survivals from the Iberian peninsula before this time of a type of notation known as Visigothic neumes, but its few surviving fragments have not yet been deciphered.

The ancestors of modern symbolic music notation originated in the Roman Catholic Church, as monks developed methods to put plainchant (sacred songs) to paper. The earliest of these ancestral systems, from the 8th century, did not originally utilise a staff, and used neum (or neuma or pneuma), a system of dots and strokes that were placed above the text. Although capable of expressing considerable musical complexity, they could not exactly express pitch or time and served mainly as a reminder to one who already knew the tune, rather than a means by which one who had never heard the tune could sing it exactly at sight.

To address the issue of exact pitch, a staff was introduced consisting originally of a single horizontal line, but this was progressively extended until a system of four parallel, horizontal lines was standardized. The vertical positions of each mark on the staff indicated which pitch or pitches it represented (pitches were derived from a musical mode, or key). Although the four-line staff has remained in use until the present day for plainchant, for other types of music, staffs with differing numbers of lines have been used at various times and places for various instruments. The modern five-line staff was first adopted in France and became almost universal by the 16th century (although the use of staffs with other numbers of lines was still widespread well into the 17th century).

Because the neum system arose from the need to notate songs, exact timing was initially not a particular issue because the music would generally follow the natural rhythms of the Latin language. However, by the 10th century a system of representing up to four note lengths had been developed. These lengths were relative rather than absolute and depended on the duration of the neighbouring notes. It was not until the 14th century that something like the present system of fixed note lengths arose. Starting in the 15th century, vertical bar lines were used to divide the staff into sections. These did not initially divide the music into measures (bars) of equal length (as most music then featured far fewer regular rhythmic patterns than in later periods), but appear to have been introduced as an aid to the eye for "lining up" notes on different staves that were to be played or sung at the same time. The use of regular measures (bars) became commonplace by the end of the 17th century.

The founder of what is now considered the standard music stave was Guido d'Arezzo, an Italian Benedictine monk who lived from 995–1050 His revolutionary method—combining a four-line stave with the first form of notes known as 'neumes'—was the precursor to the five-line stave, which was introduced in the 14th century and is still in use today. Guido D'Arezzo's achievements paved the way for the modern form of written music, music books, and the modern concept of a composer.

Modern notation

Modern music notation originated in European classical music and is now used by musicians of many different genres throughout the world.

The system uses a five-line staff. Pitch is shown by placement of notes on the staff (sometimes modified by accidentals), and duration is shown with different note values and additional symbols such as dots and ties. Notation is read from left to right, which makes setting music for right-to-left scripts difficult.

A staff of written music generally begins with a clef, which indicates the particular range of pitches encompassed by the staff. Notes representing a pitch outside of the scope of the five line staff can be represented using ledger lines, which provide a single note with additional lines and spaces.

Following the clef, the key signature on a staff indicates the key of the piece by specifying certain notes to be flat or sharp throughout the piece, unless otherwise indicated.

Following the key signature is the time signature. Measures (bars) divide the piece into regular groupings of beats, and the time signatures specify those groupings.

Directions to the player regarding matters such as tempo and dynamics are added above or below the staff. For vocal music, lyrics are written.

In music for ensembles, a "score" shows music for all players together, while "parts" contain only the music played by an individual musician. A score can be constructed (laboriously) from a complete set of parts and vice versa.

Variations

• Percussion notation conventions are varied because of the wide range of percussion instruments. Percussion instruments are generally grouped into two categories: pitched and non-pitched. The notation of non-pitched percussion instruments is the more problematic and less standardized.
• Figured bass notation originated in baroque basso continuo parts. It is also used extensively in accordion notation. The bass notes of the music are conventionally notated, along with numbers and other signs which determine the chords to be played. It does not, however, specify the exact pitches of the harmony, leaving that for the performer to improvise.
• A lead sheet specifies only the melody, lyrics and harmony, using one staff with chord symbols placed above and lyrics below. It is used to capture the essential elements of a popular song without specifying how the song should be arranged or performed.
• A chord chart or "chart" contains little or no melodic information at all but provides detailed harmonic and rhythmic information, using slash notation and rhythmic notation. This is the most common kind of written music used by professional session musicians playing jazz or other forms of popular music and is intended primarily for the rhythm section (usually containing piano, guitar, bass and drums).
• The shape note system is found in some church hymnals, sheet music, and song books, especially in the American south. Instead of the customary elliptical note head, note heads of various shapes are used to show the position of the note on the major scale. Sacred Harp is one of the most popular tune books using shape notes.

Notation in various countries

India

The Indian scholar and musical theorist Pingala (c. 200 B.C.), in his Chanda Sutra, used marks indicating long and short syllables to indicate meters in Sanskrit poetry.

In the notation of Indian rāga, a solfege-like system called sargam is used. As in Western solfege, there are names for the seven basic pitches of a major scale (Shadja, Rishabh, Gandhar, Madhyam, Pancham, Dhaivat and Nishad, usually shortened Sa Re Ga ma Pa Dha Ni). The tonic of any scale is named Sa, and the dominant Pa. Sa is fixed in any scale, and Pa is fixed at a fifth above it (a Pythagorean fifth rather than an equal-tempered fifth). These two notes are known as achala swar ('fixed notes'). Each of the other five notes, Re, Ga, ma, Dha and Ni, can take a 'regular' (shuddha) pitch, which is equivalent to its pitch in a standard major scale (thus, shuddha Re, the second degree of the scale, is a whole-step higher than Sa), or an altered pitch, either a half-step above or half-step below the shuddha pitch. Re, Ga, Dha and Ni all have altered partners that are a half-step lower (Komal-"flat") (thus, komal Re is a half-step higher than Sa). Ma has an altered partner that is a half-step higher (teevra-"sharp") (thus, tivra Ma is an augmented fourth above Sa). Re, Ga, ma, Dha and Ni are called vikrut swar ('movable notes'). In the written system of Indian notation devised by Ravi Shankar, the pitches are represented by Western letters. Capital letters are used for the achala swar, and for the higher variety of all the vikrut swar. Lowercase letters are used for the lower variety of the vikrut swar.

Other systems exist for non-twelve-tone equal temperament and non-Western music, such as the Indian svar lippi. New systems that remove handicaps in existing systems are also being developed like Ome Swarlipi

Russia

In ancient Byzantium and Russia, sacred music was notated with special 'hooks and banners' (see znamennoe singing).

China

The earliest known examples of text referring to music in China are inscriptions on musical instruments found in the Tomb of Marquis Ye of Zeng (d. 433 B.C.E.). Sets of 41 chimestones and 65 bells bore lengthy inscriptions concerning pitches, scales, and transposition. The bells still sound the pitches that their inscriptions refer to. Although no notated musical compositions were found, the inscriptions indicate that the system was sufficiently advanced to allow for musical notation. Two systems of pitch nomenclature existed, one for relative pitch and one for absolute pitch. For relative pitch, a solmization system was used.

The tablature of the guqin is unique and complex; the older form is composed of written words describing how to play a melody step-by-step using the plain language of the time, i.e. Descriptive Notation (Classical Chinese); the newer form, composed of bits of Chinese characters put together to indicate the method of play is called Prescriptive Notation. Rhythm is only vaguely indicated in terms of phrasing. Tablatures for the qin are collected in what is called qinpu.

The jianpu system of notation (an adaptation of a French Galin-Paris-Cheve system) had gained widespread acceptance by 1900 C.E. In this system, notes of the scale are numbered. For a typical Pentatonic Scale, the numbers 1,2,3,5,6 would be used. Dots above or below the notes would indicate a higher or lower octaves. Time values are indicated by dots and dashes following each number. Key signatures, barlines, and time signatures are also employed. The system also makes use of many symbols from the standard notation, such as bar lines, time signatures, accidentals, tie and slur, and the expression markings. In the present-day jianpu system, only the melody is notated. Harmonic and rhythmic elements are left to the discretion of the performers.

Japan

Japanese music is highly diversified, and therefore requires various systems of notation. In Japanese shakuhachi music, for example, glissandos and timbres are often more significant than distinct pitches (see Shakuhachi musical notation), whereas as taiko notation focuses on discrete strokes.

Indonesia

Notation plays a relatively minor role in the oral traditions of Indonesia. However, in Java and Bali, several systems were devised beginning at the end of the 19th century, initially for archival purposes. Today the most widespread are cipher notations ("not angka" in the broadest sense) in which the pitches are represented with some subset of the numbers 1 to 7, with 1 corresponding to either highest note of a particular octave, as in Sundanese gamelan, or lowest, as in the kepatihan notation of Javanese gamelan. Notes in the ranges outside the central octave are represented with one or more dots above or below the each number. For the most part, these cipher notations are mainly used to notate the skeletal melody (the balungan) and vocal parts (gerongan), although transcriptions of the elaborating instrument variations are sometimes used for analysis and teaching. Drum parts are notated with a system of symbols largely based on letters representing the vocables used to learn and remember drumming patterns; these symbols are typically laid out in a grid underneath the skeletal melody for a specific or generic piece. The symbols used for drum notation (as well as the vocables represented) are highly variable from place to place and performer to performer. In addition to these current systems, two older notations used a kind of staff: the Solonese script could capture the flexible rhythms of the pesinden with a squiggle on a horizontal staff, while in Yogyakarta a ladder-like vertical staff allowed notation of the balungan by dots and also included important drum strokes. In Bali there are a few books published of gender wayang pieces employing alphabetical notation in the old Balinese script.

Composers and scholars both Indonesian and foreign have also mapped the slendro and pelog tuning systems of gamelan onto the western staff, with and without various symbols for microtones. The Dutch composer Ton de Leeuw also invented a three line staff for his composition Gending. However, these systems do not enjoy widespread use.

In the second half of the twentieth century, Indonesian musicians and scholars extended cipher notation to other oral traditions, and a diatonic scale cipher notation has become common for notating western-related genres (church hymns, popular songs, and so forth). Unlike the cipher notation for gamelan music, which uses a "fixed Do" (that is, 1 always corresponds to the same pitch, within the natural variability of gamelan tuning), Indonesian diatonic cipher notation is "moveable-Do" notation, so scores must indicate which pitch corresponds to the number 1 (for example, "1=C."

Other systems and practices

Cipher notation

In many cultures, including Chinese (jianpu or gongche), Indonesian (kepatihan), and Indian (sargam), the "sheet music" consists primarily of the numbers, letters or native characters representing notes in order. Those different systems are collectively known as cipher notations. The numbered notation is an example, so are letter notation and Solfège if written in musical sequence.

Solfège

Solfège is a way of assigning syllables to names of the musical scale. In order, they are today: Do, Re, Mi, Fa, Sol, La, Ti, and Do (for the octave). The classic variation is: Do, Re, Mi, Fa, Sol, La, Si, Do. These functional names of the musical notes were introduced by Guido of Arezzo (c.991 – after 1033) using the beginning syllables of the first six musical lines of the Latin hymn Ut queant laxis. The original sequence was Ut, Re, Mi, Fa, Sol, La, where each verse would start a note higher. "Ut" later became "Do". The equivalent syllables used in Indian music are: Sa, Ri, Ga, Ma, Pa, Dha, and Ni, while the 'bilinear music notation' system offers a chromatic method: Li, (Je), Ja, (Bo), Baw, Zu, (Zer or Fer), Fee, (De), Da, (Go), and Gaw. See also: solfège, sargam, Kodály Hand Signs. In China Qi is used instead of Ti (Qi for 七, Chinese 7).

Tonic Sol-fa is a type of notation using the initial letters of solfège.

Letter notation

The notes of the 12-tone scale can be written by their letter names A-G, possibly with a trailing sharp or flat symbol, such as A or B. This is the most common way of specifying a note in English speech or written text.

Tablature

Tablature was first used in the Renaissance for lute music. A staff is used, but instead of pitch values, the fret or frets to be fingered are written instead. Rhythm is written separately and durations are relative and indicated by horizontal space between notes. In later periods, lute and guitar music was written with standard notation. Tablature caught interest again in the late 20th century for popular guitar music and other fretted instruments, being easy to transcribe and share over the internet in ASCII format. Websites like OLGA.net (currently off-line pending legal disputes) have archives of text-based popular music tablature.

Klavar notation

Klavar notation (or "klavarskribo") is a chromatic system of notation geared mainly towards keyboard instruments, which transposes the usual "graph" of music. The pitches are indicated horizontally, with "staff" lines in twos and threes like the keyboard, and the sequence of music is read vertically from top to bottom. A considerable body of repertoire has been transcribed into Klavar notation. Klavar notation eliminates the need of accidentals and key signatures, and its advocates claim that this facilitates music-reading.

12-note non-equal temperament

Sometimes the pitches of music written in just intonation are notated with the frequency ratios, while Ben Johnston has devised a system for representing just intonation with traditional western notation and the addition of accidentals which indicate the cents a pitch is to be lowered or raised.

Chromatic staff notations

Over the past three centuries, hundreds of music notation systems have been proposed as alternatives to traditional western music notation. Many of these systems seek to improve upon traditional notation by using a "chromatic staff" in which each of the 12 pitch classes has its own unique place on the staff. Examples are the Ailler-Brennink notation, Tom Reed's Twinline notation, John Keller's Express Stave, and José A. Sotorrio's Bilinear Music Notation. These notation systems do not require the use of standard key signatures, accidentals, or clef signs. They also represent interval relationships more consistently and accurately than traditional notation. The Music Notation Project (formerly known as the Music Notation Modernization Association) has a website with information on many of these notation systems.

Graphic notation

The term 'graphic notation' refers to the contemporary use of non-traditional symbols and text to convey information about the performance of a piece of music. It is used for experimental music, which in many cases is difficult to transcribe in standard notation. Practitioners include Christian Wolff, Earle Brown, John Cage, Morton Feldman, Krzysztof Penderecki, Cornelius Cardew, and Roger Reynolds. See Notations, edited by John Cage and Alison Knowles, ISBN 0-685-14864-5.

Parsons code

Parsons code is used to encode music so that it can be easily searched. This style is designed to be used by individuals without any musical background.

Braille music

Braille music is a complete, well developed, and internationally accepted musical notation system that has symbols and notational conventions quite independent of print music notation. It is linear in nature, similar to a printed language and different from the two-dimensional nature of standard printed music notation. To a degree Braille music resembles musical markup languages such as XML for Music or NIFF. See Braille music.

Integer notation

In integer notation, or the integer model of pitch, all pitch classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone, serial, or otherwise atonal music.

Turntablist transcription methodology

Computer musical notation

Beside notations developed for human readers and performers, there are also many computer oriented representations of music designed to either be turned into conventional notation, or read directly by the computer.

There are a great many software programs designed to produce musical notation. These are called musical notation software, or sometimes Scorewriters. In addition to this software, there are many file formats used to store musical information that this software and other programs can convert into notation, sound, or into some other usable form. In a sense, these file formats are a "notation" for computers.

The most common musical file format is probably the MIDI file format, which stores pitch and timing information about music (as well as velocity, volume, pitch bend, and modulation) and can be used to control a MIDI instrument which will produce the specified sound.

There are also hybrid formats, such as ABC notation, Lilypond, and MusicXML that are text files that can be read and edited by a capable human, but can also be manipulated by the computer. One notable system is the NEUMES standard, which is being used to form a computerized catalog of Medieval plainchant that can be searched by melody, text, or any encoded aspect of the music. Similarly the Mutopia project maintains a library of scores available in such formats (though they are not searchable by content).

Finally there are notational forms that are not intended to be processed by computer, but are nonetheless commonly used to transmit information via computer, such as text file guitar tablature which has become extremely popular following the growth of the World Wide Web.

Perspectives of musical notation in composition and musical performance

According to Richard Middleton (1990, p.104-6), and also Philip Tagg (1979, p.28-32), musicology and to a degree European-influenced musical practice suffer from a 'notational centricity'; a methodology slanted by the characteristics of notation. Notation-centric training induces particular forms of listening, and these then tend to be applied to all sorts of music, appropriately or not. Musicological methods tend to foreground those musical parameters which can be easily notated...they tend to neglect or have difficulty with widened parameters which are not easily notated. Examples include the unique vocal style of Joni Mitchell and the String Quartets of Elliott Sharp. Because of the limitations of conventional musical notation, many present-day composers of various genres prefer to compose music which is either not notated, or notated only through the computer language of digital recording.

A further perspective on musical notation is provided in the "Composer's Note" from Fredrick Pritchard's "Brushed With Blue", Op. 55 "(No. 2, performed by Fredrick Pritchard)", pub. Effel Publications, 2002:

"The written language of music is at once indispensable yet hopelessly inadequate in conveying every detail of a musical concept. While musical scores are static, music itself is a living art, and as such requires the freedom to change, not only from bar to bar but from day to day and from year to year, the elements of experience and spontaneity unleashing the various potentials of a given work. The composer therefore entrusts the performer as co-creator of his art."

Patents

In some countries, new musical notations can be patented. In the United States, for example, about 90 patents have been issued on new notation systems. The earliest patent, was published in 1839.

See also

• Modern musical symbols
• Music engraving
• Guido of Arezzo, inventor of modern musical notation
• Znamennoe singing
• Time unit box system, a notation system useful for polyrhythms
• Tongan music notation, a subset of standard music notation
• Eye movement in music reading
• Music OCR

Notes

References

• Middleton, Richard (1990/2002). Studying Popular Music. Philadelphia: Open University Press. ISBN 0-335-15275-9.
• Tagg, Philip (1979). Cited in Middleton, Richard (1990/2002). Studying Popular Music. Philadelphia: Open University Press. ISBN 0-335-15275-9.
• Albrecht Schneider: Music, sound, language, writing. Transcription and notation in comparative musicology and music ethnology, in: Zeitschrift für Semiotik, 1987, Volume: 9, Number: 3-4.
• Sotorrio, José A (1997). Bilinear Music Notation –A New Notation System for the Modern Musician, Spectral Music, ISBN 978-0-9548498-2-5.
• Kilmer, Anne Draffkorn (1965). The Strings of Musical Instruments: their Names, Numbers, and Significance, ''Studies in Honor of Benno Landsberger = Assyriological Studies, xvi, 261-8
• Kilmer, Anne Draffkorn (1986). Journal of Cuneiform Studies, xxxviii, 94-98
• West, M. L., The Babylonian Musical Notation and the Hurrian Melodic Texts, Music & Letters, Vol. 75, No. 2. (May, 1994), pp. 161-179

Further reading

• Hall, Rachael (2005). Math for Poets and Drummers. Saint Joseph's University.
• Read, Gardner (1978). Modern Rhythmic Notation. Victor Gollance Ltd.
• Read, Gardner (1987). Source Book of Proposed Music Notation Reforms. Greenwood Press.
• Stone, Kurt (1980). Music Notation in the Twentieth Century: A Practical Guidebook. W. W. Norton & Company.

External links

• Contains a Guide to Byzantine Music Notation (neumes)
• On-line activity that counts musical notes!
• Glossary of U.S. and British English musical terms
• A collection of interactive lessons and trainers that can be downloaded for offline use
• Extremes of Conventional Musical Notation
• Information on Stanford University Course on music representation. Links page shows examples of different notations
• Abstracts on Musical Notation from Zeitschrift für Semiotik
• Collection of lessons covering Rhythmic Musical Notation for drummers
• Potato print - examples of musical symbols from the 16th and 17th century
• The Music Notation Project - alternative music notation systems that use chromatic staves
• Ensemble Kerylos, who has reconstructed ancient instruments and plays Ancient Greek melodies.