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Musical notation

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Hand-written musical notation by J. S. Bach: beginning of the Prelude from the Suite for Lute in G minor BWV 995 (transcription of Cello Suite No. 5, BWV 1011) BR Bruxelles II. 4805.

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

Contents

Western history

The earliest form of musical notation can be found in a cuneiform tablet that was created at Nippur, Iraq in about 2000 B.C. 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.[1] A tablet from about 1250 B.C. shows a more developed form of notation.[2] 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.[3] Although they were fragmentary, these tablets represent the earliest recorded melodies found anywhere in the world.[3]

Ancient Greece

Photograph of the original stone at Delphi containing the second of the two hymns to Apollo. The music notation is the line of occasional symbols above the main, uninterrupted line of Greek lettering.

Ancient Greek musical notation was capable of representing pitch and note-duration, and to a limited extent, harmony.[citation needed] 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 Decline of the Roman Empire.

Byzantine Empire

Byzantine music notation style in a Romanian "Book of Hymns at the Lord's Resurrection", 1823

Byzantine music is vocal religious music, based on the monodic modal singing of Ancient Greece and the pre-islamic Near East. The notation developed for it is similar in principle to subsequent Western notation, in that it is ordered left to right, and separated into measures. The main difference is that notation symbols are differential rather than absolute, i.e. they indicate pitch change (rise or fall), and the musician has to deduce correctly, from the score and the note they are singing presently, which note comes next. The pitch symbols themselves resemble brush strokes and are colloquially called gántzoi ("hooks") in Modern Greek. Notes themselves are represented in written form only between measures, as an optional reminder, along with modal and tempo directions if needed. Additional signs are used to indicate embellishments and microtones (pitch changes smaller than a semitone), both essential in Byzantine chant (see Romanian anastasimatarion picture, left).

The seven standard note names in Byzantine "solfege" are: pá, vú, ghá, dhē, ké, zō, nē, corresponding to Western re, mi, fa, sol, la, si, do. Byzantine music uses the eight natural, non-tempered scales called Ēkhoi, "sounds", exclusively, and therefore the absolute pitch of each note may slightly vary each time, depending on the particular Ēkhos used. Byzantine notation is still used in many Orthodox Churches. Better cantors can also use standard Western notation while adding non-notatable embellishment material from memory and "sliding" into the natural scales from experience.

Arab world

In 1252, Safi al-Din developed a form of musical notation, where rhythms were represented by geometric representation. Many subsequent scholars of rhythm have sought to develop graphical geometrical representations. For example, a similar geometric system was published in 1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph.[4]

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.[5]

The ancestors of modern symbolic music notation originated in the Roman Catholic Church, as monks developed methods to put plainchant (sacred songs) to parchment. 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.[citation needed]

Early Music Notation

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. 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,[6] an Italian Benedictine monk who lived from 995–1050.Guido D'Arezzo's achievements paved the way for the modern form of written music, music books, and the modern concept of a composer.[6] He named musical notes based on an ancient hymn dedicated to Saint John the Baptist, called Ut Queant Laxis, written by the lombard historian Paul the deacon. The first stanza is:

  1. Ut queant laxis
  2. resonare fibris,
  3. Mira gestorum
  4. famuli tuorum,
  5. Solve polluti
  6. labii reatum,
  7. Sancte Iohannes.

Guido used the first letters of each verse to name the Solfège syllables: Ut, Re, Mi Fa, Sol, La, and Si (the exception being Si, which has the S of Sancte and the I of Iohannes - it also helps in that if two adjacent notes had the same vowel, verbal communication errors would become more likely). In the 17th century, Ut was changed in most countries except France to the easily singable, "open" syllable Do, said to have been taken from the name of the Italian theorist Giovanni Battista Doni.[7]

Modern notation

An example of modern musical notation: Prelude, Op. 28, No. 7, by Frederic Chopin

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 (or stave, in British English) of written music generally begins with a clef, which indicates the position of one particular note on the staff. The treble or G clef was originally a letter G and it identifies the second line up on the five line staff as the note G above middle C. The bass or F clef shows the position of the note F below middle C. 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 groups 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. For short pauses (breaths), retakes (looks like ') are added.

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 from a complete set of parts and vice versa. The process can be laborious but computer software offers a more convenient and flexible method.

Specialized notation conventions

  • 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
  • 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
  • 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).
  • Simpler chord charts for songs may contain only the chord changes, placed above the lyrics where they occur. Such charts depend on prior knowledge of the melody, and are used as reminders in performance or informal group singing.
  • The shape note system is found in some church hymnals, sheet music, and song books, especially in the Southern United States. 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

Indian music, early 20th century

The Indian scholar and musical theorist Pingala (c. 200 BC), 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 Byzantium and Russia, sacred music was notated with special 'hooks and banners'.

China

Chinese Guqin notation, 1425

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.). 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.[8]

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.

Gongche notation used Chinese characters for the names of the scale.

The jianpu system of notation (probably an adaptation of a French Galin-Paris-Cheve system) had gained widespread acceptance by 1900. It uses a movable do system, with the numbers 1,2,3,4,5,6,7 standing for do, re, mi, fa, sol, la, si. Dots above or below a numeral indicate the octave of the note it represents. Key signatures, barlines, and time signatures are also employed. Many symbols from Western standard notation, such as bar lines, time signatures, accidentals, tie and slur, and the expression markings are also used. The number of dashes following a numeral represents the number of crotchets (quarter notes) by which the note extends. The number of underlines is analogous to the number of flags or beams on notes or rests in standard notation.

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, whereas 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 Gamelan 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, or numerical 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 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 Ni, while the 'bilinear music notation' system offers a fully chromatic method.[citation needed] See also: solfège, sargam, Kodály Hand Signs. In China Xi is used instead of Ti.

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.

In Northern Europe, a similar letter system ranging from A to H is used, and instead of the sharp and flat symbols, the syllables "is" (for sharp) or "es" (for flat) are used; e.g. the note a semitone above C is either Cis or Des. H stands for the English B, while Northern European B stands for English B.

Tablature

Tablature was first used in the Middle Ages for organ music and later in the Renaissance for lute music.[9] In most lute tablatures, a staff is used, but instead of pitch values, the lines of the staff represent the strings of the instrument. The frets to be fingered are written on each line, indicated by letters or numbers. Rhythm is written separately with one or another variation of standard note values indicating the duration of the slowest moving part. Few seem to have remarked on the fact that tablature combines in one notation system both the physical and technical requirements of play (the lines and symbols on them and in relation to each other representing the actual performance actions) with the unfolding of the music itself (the lines of tablature taken horizontally represent the actual temporal unfolding of the music). 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, Jacques-Daniel Rochat's Dodeka system, 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.[citation needed] 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.

Simplified Music Notation

Simplified Music Notation is an alternative form of musical notation designed to make sight-reading easier. It is based on classical staff notation, but sharps and flats are incorporated into the shape of the noteheads. Notes such as double sharps and double flats are written at the pitch at which they are actually played, but preceded by symbols called 'History Signs' to show that they have been transposed. The notation was designed to help people who struggle with sight-reading, including those who suffer from working memory impairments, dyslexia and other learning difficulties.

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.

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 technique, serial, or otherwise atonal music.

Turntablist transcription methodology

Music notation on computer

Many computer programs have been developed for creating music notation (called scorewriters or music notation software). Music may also be stored in various digital file formats for purposes other than graphic notation output.

Perspectives of musical notation in composition and musical performance

According to Philip Tagg and Richard Middleton, musicology and to a degree European-influenced musical practice suffer from a 'notational centricity', a methodology slanted by the characteristics of notation.[10]

Notation-centric training induces particular forms of listening, and these then tend to be applied to all sorts of music, appropriately or not.[citation needed] 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.[citation needed] 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.[citation needed]

Patents

Recent US patent 6987220  on a new color based musical notation scheme

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, U.S. Patent 1,383 was published in 1839.

See also

Notes

  1. ^ Kilmer & Civil 1986,[page needed].
  2. ^ Kilmer 1965,[page needed].
  3. ^ a b West 1994,[page needed].
  4. ^ Toussaint 2004, 3.
  5. ^ Zapke 2007,[page needed]
  6. ^ a b Otten 1910.
  7. ^ McNaught 1893, 43.
  8. ^ Bagley 2004.
  9. ^ Apel 1961, xxiii and 22.
  10. ^ Tagg 1979, 28–32; Middleton 1990, 104–6.

References

  • Apel, Willi (1961). The Notation of Polyphonic Music, 900-1600, 5th edition, revised and with commentary. Publications of the Mediaeval Academy of America, no. 38. Cambridge, Mass.: Mediaeval Academy of America.
  • Bagley, Robert (2004). "The Prehistory of Chinese Music Theory". Elsley Zeitlyn Lecture on Chinese Archaeology and Culture. (Tuesday 26 October) British Academy's Autumn 2004 Lecture Programme. London: British Academy. Abstract. (Accessed 30 May 2010)
  • Kilmer, Anne Draffkorn (1965). "The Strings of Musical Instruments: Their Names, Numbers, and Significance", in Studies in Honor of Benno Landsberger on His Seventy-fifth Birthday, April 21, 1965, Assyriological Studies 16, edited by Hans G. Güterbock and Thorkild Jacobsen, 261–68. Chicago, University of Chicago Press.
  • Kilmer, Anne Draffkorn, and Miguel Civil (1986). "Old Babylonian Musical Instructions Relating to Hymnody". Journal of Cuneiform Studies 38, no. 1:94–98.
  • McNaught, W. G. (1893). "The History and Uses of the Sol-fa Syllables". Proceedings of the Musical Association (London: Novello, Ewer and Co.) 19: 35–51. ISSN 0958-8442. http://books.google.com/?id=nNYPAAAAYAAJ&pg=PA35. Retrieved 2010-04-23. 
  • Middleton, Richard (1990/2002). Studying Popular Music. Philadelphia: Open University Press. ISBN 0-335-15275-9.
  • Otten, J. (1910). "Guido of Arezzo". The Catholic Encyclopedia. New York: Robert Appleton Company. Retrieved May 30, 2010 from New Advent.
  • Saoud, Rabah (2004). "The Arab Contribution to the Music of the Western World". Manchester: Foundation for Science, Technology, and Civilisation, Limited.
  • Schneider, Albrecht (1987). "Musik, Sound, Sprache, Schrift: Transkription und Notation in der Vergleichenden Musikwissenschaft und Musikethnologie". Zeitschrift für Semiotik 9, nos. 3–4:317–43.
  • Sotorrio, José A (1997). Bilinear Music Notation –A New Notation System for the Modern Musician. Spectral Music, ISBN 978-0-9548498-2-5.
  • Tagg, Philip (1979). Kojak—50 Seconds of Television Music: Toward the Analysis of Affect in Popular Music. Skrifter från Musikvetenskapliga Institutionen, Göteborg 2. Göteborg: Musikvetenskapliga Institutionen, Göteborgs Universitet. ISBN 9172222352 (Rev. translation of "Kojak—50 sekunders tv-musik")
  • Touma, Habib Hassan (1996). The Music of the Arabs, new expanded edition, translated by Laurie Schwartz. With accompanying CD recording. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8
  • Toussaint, Godfried (2004). "A Comparison of Rhythmic Similarity Measures". Technical Report SOCS-TR-2004.6. Montréal: School of Computer Science, McGill University.
  • West, M. L. (1994). "The Babylonian Musical Notation and the Hurrian Melodic Texts". Music & Letters 75, no. 2. (May): 161–179
  • Williams, Charles Francis Abdy (1903). "The Story of Notation." New York: Charles Scribner's Sons.
  • Zapke, Susana (ed.) (2007). Hispania Vetus: Musical-Liturgical Manuscripts from Visigothic Origins to the Franco-Roman Transition (9th–12th Centuries), with a foreword by Anscario M Mundó. Bilbao: Fundación BBVA. ISBN 9788496515505

Further reading

  • Hall, Rachael (2005). Math for Poets and Drummers. Saint Joseph's University.
  • Gayou, Évelyne. “Transcrire les musiques électroacoustiques.” eContact! 12.4 — Perspectives on the Electroacoustic Work / Perspectives sur l’œuvre électroacoustique (August 2010). Montréal: CEC. (French)
  • Lieberman, David (2006). Game Enhanced Music Manuscript. In GRAPHITE '06: Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, Kuala Lumpur (Malaysia), 29 November–2 December 2006, edited by Y Tina Lee, Siti Mariyam Shamsuddin, Diego Gutierrez, and Norhaida Mohd Suaib, 245–50. New York: ACM Press. ISBN 1595935649
  • 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



This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Musical notation". Allthough most Wikipedia articles provide accurate information accuracy can not be guaranteed.


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