music theory online : notes & rests lesson 2
Dr. Brian Blood


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Most people rather think of music as an art. But, in reality music partakes of both art and science ...
every time a printed score is brought to life it has to be re-created through different sound machines called musical instruments.
Edgar Varèse (1883-1965) French-American composer

Duration :: Anatomy of a Note Sign :: Chart of Note & Rest Signs :: Dotting & Double-Dotting :: Beams & Beaming :: Ties :: Origin of Music Notation
Additional Notes on the History of Music Notation
supplement :: Links about Music Notation

Important: To see and hear our 'live' music examples you will need to install the free Scorch plug-in for PC and MAC systems.

Duration :: top

Key words:
time value
duration
proportional notation
mensural notation
1

Duration

Where the vertical position of a note on a staff or stave determines its pitch, its relative time value or duration is denoted by the particular sign chosen to represent it. This is the essence of proportional or mensural notation, first developed in the eleventh century and about which more information is given in the section below entitled Origin of Music Notation.

The coin & paper money you use to pay for goods & services are good examples of relative value. While in England 100 pence = 1 pound and in the United States the cent and dollar are similarly related (100 cents = 1 dollar) in neither case do you know the 'absolute' value of a currency or of its 'denominations'; for example, how many dollars = 1 pound. So it is with musical 'denominations'. The signs do not give duration in units of time, minutes or seconds. That must be given in ways we discuss in lesson 5.

The Anatomy of a Note Sign :: top

Key words:
notehead
flag
hook
stem
tail
1

The Anatomy of a Note Sign

In music the denomination of 'coinage' is the note or note sign. One can use either term. Each note sign is a construct of three distinct parts. The notehead, whose position on the stave actually sets its pitch, can be open (white) or closed (black). For all notes except the breve (double whole note) and semibreve (whole note), each note has a stem or tail and, for the notes of shorter time-value, a hook or flag, one for a quaver (eighth note), two for a semiquaver (sixteenth note), and so on). The stem can rise from the notehead, in which case it lies on the right-hand side of the notehead, or fall from the notehead, in which case it lies on the left hand side of the notehead (see the two crotchets or quarter notes).

In either case, the flag or hook lies on the right-hand side of the stem (see the two quavers (eighth notes)).


EnglishItalianFrenchGermanSpanish
note (sign) figure de noteNotenzeichen 
rest (sign) figure de silencePausenzeichen 
notenotanoteNotenota
noteheadtesta, testina, capocchiatête de la noteNotenkopfoval
stem, tailasta, gambaqueueNotenhals, Halsplica
flag, hookcoda uncinata, bandieracrochetFahne, Fähnchencorchete

When placed on the stave, a note sign will be placed either on a line or on a space between the lines. The position indicates the relative pitch of the note. If the note lies above or below the stave then it will lie on, above or below auxiliary lines called leger or ledger lines. This is illustrated below. Notice how the position of the note on the stave generally determines whether the stem 'rises' or 'falls' from the notehead.

Chart of Note and Rest Signs :: top

Key words:
chart of notes
chart of rests
1

Chart of Note and Rest Signs

If the notes are listed in decreasing time value, longest to shortest, each is half the duration of the one immediately before it. The table of 'denominations' below shows the note with the longest duration at the top and that with the shortest duration at the bottom.

Sign
number equal to
1 semibreve
English American Italian French German Spanish Catalan
1/2 breve
or
brevis
double-whole
note
breve (f.) carrée (f.)
or
brevis
or
double-ronde (f.)
(meaning square)
Doppeltakt (m.) cuadrada (f.)
or
breve
or
doble redonda
quadrada (f.)
or
breu (f.)
1 semibreve whole note semibreve (f.)
intero (m.)
semi-brève
or
ronde (f.)
(meaning round)
ganze Takt (m.)
or
Ganze (f.)
redonda (f.)
or
semibreve (f.)
rodona (f.)
2 minim half note minima (f.)
or
metà (f.)
or
bianca (f.)
blanche (f.)
(meaning white)
Halbe (f.)
or
halbe Takt (m.)
blanca (f.)
or
mínima (f.)
blanca (f.)
4 crotchet quarter note semiminima (f.)
or
nera (f.)
or
quarto (m.)
noire (f.)
(meaning black)
Viertel (f.) negra (f.) negra (f.)
8 quaver eighth note croma (f.)
or
ottavo (m.)
croche (f.)
(meaning hook)
Achtel (f.) corchea (f.)
or
croma (f.)
corxera (f.)
16 semiquaver sixteenth note semicroma (f.)
or
sedicesimo (m.)
double croche (f.)
(meaning double hook)
Sechzehntel (f.) semicorchea (f.) semicorxera (f.)
32 demisemiquaver thirty-second note biscroma (f.)
or
trentaduesimo (m.)
triple croche (f.)
(meaning triple hook)
Zweiunddreissigstel (f.) fusa (f.) fusa (f.)
64 hemidemisemiquaver sixty-fourth note semibiscroma (f.)
or
sessantaquattresimo (m.)
quadruple croche (f.)
(meaning quadruple hook)
Vierundsechzigstel (f.) semifusa (f.) semifusa (f.)
128 semihemidemisemiquaver
or
quasihemidemisemiquaver
one hundred and twenty-eighth note centoventottavo (nota) cent-vingt-huitième
or
quintuple croche
Hundertundachtundzwanzigstel(note) garrapatea (f.)
or
cuartifusa (f.)
 

Rests, periods of silence, are shown in the table below.

Rest
number equal to 1 semibreve
English American Italian French German Spanish Catalan
1/2 breve rest double-whole
rest
pausa di breve (f.) bâton (m.)
or
pause de brève (f.)
or
silence de brève (m.)
doppel Pause (f.) silencio de cuadrada (m.)
or
pausa de cuadrada (f.)
or
silencio de breve (m.)
or
pausa de breve (f.)
doble pausa (f.)
or
pausa de quadrada (f.)
1 semibreve rest whole rest pausa di semibreve (f.) pause (f.) ganze Pause (f.) silencio de redonda (m.)
or
pausa de redonda (f.)
or
silencio de semibreve (m.)
or
pausa de semibreve (f.)
pausa (f.)
or
pausa de rodona (f.)
2 minim rest half rest pausa di minima (f.) demi-pause (f.) halbe Pause (f.) media pausa (f.)
or
silencio de blanca (m.)
or
pausa de blanca (f.)
mitja pausa (f.)
or
pausa de blanca (f.)
 or 
4 crotchet rest quarter rest pausa di semiminima (f.) soupir (m.) Viertelpause (f.) silencio de negra (m.)
or
pausa de negra (f.)
or
silencio de semiminima (m.)
or
pausa de semiminima (f.)
quart de pausa (m.)
or
pausa de negra (f.)
8 quaver rest eighth rest pausa di croma (f.) demi-soupir (m.) Achtelpause (f.) silencio de corchea (m.)
or
pausa de corchea (f.)
vuitè de pausa (m.)
or
pausa de corxera (f.)
16 semiquaver rest sixteenth rest pausa di semicroma (f.) quart de soupir (m.) Sechzehntelpause (f.) silencio de semicorchea (m.)
or
pausa de semicorchea (f.)
setzè de pausa (m.)
or
pausa de semicorxera (f.)
32 demisemiquaver rest thirty-second rest pausa di biscroma (f.) huitième de soupir (m.) Zweiunddreißigstelpause (f.) silencio de fusa (m.)
or
pausa de fusa (f.)
trenta-dosè de pausa (m.)
or
pausa de fusa (f.)
64 hemidemisemiquaver rest sixty-fourth rest pausa di semibiscroma (f.) seizième de soupir (m.) Vierundsechzigstelpause (f.) silencio de semifusa (m.)
or
pausa de semifusa (f.)
seixanta-quatrè de pausa (m.)
or
pausa de semifusa (f.)
128 semihemidemisemiquaver rest one hundred and twenty-eighth rest pausa di centoventottavo (f.) cent-vingt-huitième de soupir (m.) Hundertundachtundzwanzigstelpause (f.) silencio de garrapatea (m.)
or
pausa de garrapatea (f.)
 

Each line in the example below is a single bar (we meet bars in the next lesson ), with the same total time value of notes as every other line.

note tree

Each line in the example below is a single bar (we meet bars in the next lesson ), with the same total time value of rests as every other line.

rest tree

Dotting and Double-Dotting :: top

Key words:
dot
augmentation dot
double-dotting
triple-dotting
1

Dotting and Double-Dotting

A dot, placed to the immediate right of the notehead, increases its time-value by half; thus a minim (half note) (which is equivalent to two crotchets (quarter notes)) followed by a dot (which in this case is equivalent to a further crotchet (quarter note)) is equivalent to three crotchets (quarter notes), while a dotted crotchet (dotted quarter note) is equivalent to three quavers (eighth notes) and a dotted quaver (dotted eighth note) is equivalent to three semiquavers (sixteenth notes)). If the notehead is located in a space, the dot is placed in that same space. If the notehead is on a line, the dot is placed in the space just above the line. Exceptions sometimes have to be made if several dotted notes share a single stem. A dot placed after a rest or note is called an augmentation dot.

 

A second dot, placed to the immediate right of the first dot, increases the original undotted time-value by a further quarter. Another way of thinking about the second dot is that it adds the note equivalent to half the note added by the first dot. So, for example, a minim (half note) (equivalent to four quavers (eighth notes)) followed by one dot (equivalent to two quavers (eighth notes)) followed by a second dot (equivalent to one quaver (eighth note)) is equivalent, in total, to seven quavers (eighth notes).

A triple-dotted note is a note with three dots written after it; its duration is 1 7/8 times (1 + 1/2 + 1/4 + 1/8) its basic note value. Use of a triple-dotted note value is not common in the Baroque and Classical periods, but quite common in the music of Richard Wagner and Anton Bruckner, especially in their brass parts

Dots after rests increase their time-value in the same way as dots after notes.

Beams and Beaming :: top

Key words:
beams
1

Beams and Beaming

When notes with flags lie together in groups they are often linked by one or more lines called beams. The number of beams reflect the number of flags each would have had when an individual note.

The beam that is furthest from the noteheads, and remains unbroken, and connects a group of notes is called a primary beam. Any beam other than than the primary beam is a secondary beam and may be broken, often dividing the grouping into smaller units for easier reading.

We illustrate below:

a group of four semiquavers (sixteenth notes), first unbeamed and then beamed

a group of two quavers (eighth notes), first unbeamed and then beamed

a group of one quaver (eighth note) and two semiquavers (sixteenth notes), first unbeamed and then beamed. Notice the use of primary and secondary beams in this example

Notice how the beaming reflects the time value of each note. Where a beam does not join a group of notes, for example a beam joining a dotted quaver (eighth note) to a semiquaver (sixteenth note), the secondary beam attached to the semiquaver (sixteenth note) is called a fractional beam.

Ties :: top

Key words:
ties
1

Ties

There are occasions when the duration of a note may not be easily notated using one of the note signs given above. If the duration of a note is longer than a breve (double whole note) or when the addition of dots cannot provide the required duration, groups of notes can be linked by one or more ties. Tied notes are treated as a single unbroken note whose duration is given by the duration of the notes under the tie taken successively. This is illustrated in the example given below where a crotchet (quarter note) tied to a quaver (eighth note) is equivalent to the dotted crotchet (dotted quarter note) that follows. Note that the tie is always written so as to join the noteheads of two notes. The beginning and end of the tie are on the same horizontal level, and the tie is placed between the noteheads (without touching them). Rests are never tied.

Origin of Music Notation :: top

Key word:
early notation
1

Origin of Music Notation

by the late John Howell

When Guido d'Arezzo invented chant notation on a staff in about 1025, the notes were drawn fully black. I imagine that the scribes cut their pens so as to give a broad stroke in one direction and a very narrow stroke in the other, because that's exactly what the manuscripts look like. (Twentieth-century music pens - both nibs and fountain pens - were designed exactly the same way.)

When late twelfth-early thirteenth century musicians at Notre Dame in Paris needed a way to indicate rhythmic values, they came up with the six rhythmic modes. They used existing chant notation (all black notes) with only two note values, short and long (or breve and longa), but in practice also needed a note value equal to a breve plus a longa. The rhythms were indicated not by the appearance of the notes, but by the way they were joined together in multi-note ligatures.

When Franco of Cologne, about 50 years later, proposed a system of mensural notation ("measured" notation), his biggest innovation was to assign specific values to specific note shapes. (The notes were still black.) The longa was a square black note with a descending tail on the right. The breve was a square black note with no tail. He added a new note value, the semibreve, which was a square note turned 45 degrees (which is to say a diamond-shaped note). He also added a new longer note, the double longa, which was a rectangular note about twice the width of a longa with a descending tail on the right.

Since notation always seems to lag behind what musicians are actually doing and wanting to write down, what happened in the next 150 years was that shorter and shorter note values were introduced to facilitate notating fast passages. As a result the original breve became slower and slower in practice, and the original longa slower still. The notes were still black (except when they were red, but that's another discussion entirely!). By the early sixteenth century the longa is seldom seen except as the final note of a piece, which is better notated in modern notation as a fermata rather than a note 16 bars long!

During the fifteenth century a major technological innovation came into use. Paper was invented. Or if not invented, it became available at reasonable prices. Instead of the painstaking and labor-intensive business of preparing animal skin (vellum) for manuscript use, paper could be made relatively inexpensively or even bought ready made. Only one problem for the music scribes. Since paper is made of fibers, apparently the ink had a tendency to spread out along those fibers and look like a blob instead of the nice, clean square note shape people were used to. That's when scribes started using outline notes (white notation) instead of solid black notes.

Throughout the sixteenth century, when the first methods for printing music were being worked out, the same white notation using the same square note shapes continued in use in the printed music. As a broad generalization I would guess that the rounded note shapes we are used to did not come into use until the seventeenth century, when engraving music on copper plates began to replace printing from movable type.

Additional Notes on The History of Music Notation :: top

Key word:
early notation
1

Additional Notes on The History of Music Notation

by Dr. Brian Blood

About the alphabet (the discovery of which is attributed to Palamedes, the mythical inventor of the joke, the lighthouse, dice, and a number of other essentials of human civilization), Socrates, in Phaedrus, warned:

"this discovery will create forgetfulness in the learner’s souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves. The specific which you have discovered is an aid not to memory but to recollection, and gives only a semblance of truth; they will hear much and learn nothing; they will appear to know much and will generally know nothing; they will be tiresome company, for they will seem wise without being wise."

Of course, the same reservations may be directed at musical notation - that traditions become immutable, that the musicians read but neither do they think nor do they understand, that their memories weaken, that improvisation is discouraged. However, at the time when our modern notational system was developing, there were pressing practical reasons for wanting to record certain aspects of a musical line accurately. These included the systemisation of the performance of religious music in a centrally organised Roman Catholic church, and, later, a desire to fix an intrinsically plastic medium, the better to apply to it the reflections of philosophers and critics.

Richard Restall writes, in his The Notation of Western Music (2nd ed. 1998, Leeds University Press), "the story of musical notation in Western Europe is one of innovations, changes and disappearances."

It appears that the Egyptians from the 3rd millennium BC practiced some kind of musical notation and that various systems were in use in the Orient in ancient times. A Hittite (or Hurrian) love-song, from about 1800 BC is the earliest example of musical notation we have. In the ancient Greek, Oriental and Jewish traditions, ekphonetic notation, a system of grammatical accents indicating inflections in language or liturgical texts, was in use as early as c. 200 BC. The invention of the Greek system of prosodic signs, from which both ekphonetic and neumatic notation are derived, is generally attributed to the grammarian Aristophanes of Byzantium (257-180 BC). Although many fragments have survived from this period, the Greek Seikilos epitaph, a find that has been dated variously from around 200 BC to around AD 100, is the oldest surviving example of a complete musical composition, including musical notation, from anywhere in the Western world.

Greek instrumental and vocal music was notated using two different systems of letters, but, by the time Boethius (c. 470-525) was writing his five books on music theory, the Romans were using a single system based on the first 15 letters of the alphabet. Neumes, themselves derived from Greek ekphonetic notation, were introduced into Gregorian chant probably as early as the sixth century. Although the scholar and music theorist Isidore of Seville, writing in the early seventh century, famously remarked that it was impossible to notate music, fragmentary evidence indicates that staffless neumes were certainly in use by the eighth century where they appear to have been used primarily to jog the memories of singers who would have learned the chants by ear. In their earliest form, neumes were purely adiastematic, that is, they only told the singer whether the pitch went up or down.

Louis W. G. Barton, in his essay entitled The Neume Notation Project explains that neumes are 'symbolic characters'. Each character is a literal (not pictorial) representation of a note or group of notes, in an analogous way to letters of the alphabet standing for sounds of speech. There is nothing inherent in the shape of the letter 'A' that would lead one to think that it stands for the sound 'ah', and so 'A' is symbolic, not iconic. For this reason the exact form that neumes could take varied from region to region.

Reference:

  • Neumatic Notation part of Medieval Liturgy in the Low Countries

    Black letter styles were a feature of most late Mediaeval hand-scribed manuscripts. Thick nibs scratching away on parchment could not produce light airy forms; rather, and to avoid raising the pen too often from the page, the hand was crowded, filled with numerous ligatures, often close to illegible and very black. This sense of overcrowding persisted even after a further refinement, heightened neumes arranged above and below a line (which appeared sometime towards the end of the tenth century), made the intervals of the melody somewhat clearer.

    Neumatic Notation through History
    (this notation was not standardised - there would have been considerable local variation)
    Neume names 9th-10th centuries 11th-13th centuries modern notation
    Neumes
    virga (or virgula)
    (single note)
    tractulus
    punctus/punctum
    the earlier gravis was generally converted into a short horizontal line (tractulus) or a dot, or something similar (hence punctum or punctus)
    podatus
    pes
    combination of the earlier gravis and acutus, lower and higher notes, an ascending group of two notes
    clivis (more properly clinis)
    virga flexa (an earlier name)
    combination of the earlier acutus and gravis, a higher note followed by a lower one, a descending group of two notes
    scandicus
    virga præpunctis
    (group of three notes)
    climacus
    virga subpunctis
    (group of three notes)
    torculus
    pes flexus
    combination of the earlier gravis, acutus, gravis, a group of three notes of which the second is the hightest
    porrectus
    flexus resupinus
    combination of the earlier acutus, gravis, acutus, a group of three notes of which the second is the lowest
    Compound neumes
    scandicus flexus
    clivis præpunctis
    (group of four notes)
    porrectus flexus
    (group of four notes)
    torculus respinus
    (group of four notes)
    pes subpunctis
    podatus subpunctis
    (group of four notes)
    quilisma - it occurs invariably as the middle note in an ascending group and seems to indicate a glide of the voice, being accompanied by a sustaining of the note or group of notes preceding it
    strophicus - one group of hook form signs shaped like a comma - singly it is called apostropha, when doubled, distropha; when trebled, tristropha. The apostropha is generally found at the end of another neum, or followed by a distropha at a higher pitch; it is never used as a single note over a syllable
    oriscus - apostropha and oriscus are sometimes interchanged in different manuscripts. In a few instances the oriscus, however, is found as the single sign over a syllable
    Latin Glossary: virga, virgula (from the Latin virga, rod) - punctus or punctum (Latin, point, dot) - tractulus (Latin, little stroke) - pes, podatus (from the Latin, pes, foot) - torculus (Latin, twisted - from torquere, to twist, from its broken form) - clivis (more properly clinis) (Latin, bend) - porrectus (Latin, extended - from porrigere, to extend, from the extended form of its lines) - climacus (from the Latin climax, stair, ladder) - scandicus (Latin, climber - from scandere, to rise) - salicus (from the Latin, salire, to jump) - flexus (Latin, 'bent' - the addition of a lower note to a group ending with a higher note) - resupinus (Latin, 'bent back' - the addition of a higher note to a group ending with a lower note) - præpunctis (the placing of several puncta before a sign) - compunctis (addition of puncta before and after a group of notes) - subpunctis (the placing of several puncta after a sign)

    Ashenafi Kebede, in Music in Black Jewish and Christian Communities, describes the 'dual' system introduced in the sixteenth century that featured in Ethiopic chant notation. It employed both milikitoch (neumatic signs: curves, dots, dashes, etc.) and siraye (letter notation taken from the Ethiopian Ge'ez alphabet). To keep the two systems apart, the siraye was often placed above, while the milikit was placed below the text of the manuscripts. The siraye consisted of small letters usually written in red ink; the milikitoch were easily recognizable by their distinct shapes, and they were often written in black ink. Although neither the signs nor the letters indicated individual pitches, they clearly reminded the knowledgeable cantor of melodic passages, each with its own relative pitches, each passage being both melodically and textually meaningful. The duration of each pitch, silence, and volume was also measured according to their importance within each passage and the entire chant as a whole.

    We would recommend the reference below for further information about the development of neumatic notation.

    Reference:

  • Gregorian Notation - examples showing the development of the notation

    In modern printing of medieval chant usually four line staffs are employed. In medieval manuscripts, however, there might be no staff line, or anything from one to six lines per staff, where each line signified a different voice.

    Odo, abbot of the great abbey of Cluny from 927 to 942, actively fostered choral music both in his own abbey, where a hundred or more psalms were being sung daily, and in his travels to other monasteries, inspecting their music and instructing their choirs. From documents of the period, we know both of his teaching methods and of the importance attached to music at Cluny. His great innovation was to arrange the notes of the scale into an orderly progression from A to G, in this way developing the earliest effective system of Western musical notation. To aid the pitching the notes in the various Gregorian modes he associated them with string lengths on the monochord. Reproducibility replaced unreliable 'learning by rote'.

    The failure of the neume system to maintain consistency in the performance of religious chant, inspired Guido d'Arezzo, in about 1025, to extend Odo's methods, and perfect his new staff-based system of music notation.

    Reference:

  • Graduale [ref: Fol. 236. St. Gall, 1512. Wurttembergische Landesbibliothek, Cod. mus. I.] - an example of early sixteenth-century notation.

    Sometime during the tenth century, a red line, traced horizontally above the text, gave the singer a fixed note (F=fa), and so helped him to approximate the intervals. A second line in yellow (for C=ut) was added later. The staff arose from the addition of further black lines. It should be emphasised that these developments varied from place to place and that a remarkable range of notations coexisted at any one period. These experiments would result in the assignment of a four-lined staff to sacred music and of a five-lined staff to secular music. The yellow and red colours were later replaced by Guido who indicated the pitch of certain lines on the stave using letters. From one assigned pitch, the pitch of the remaining lines and spaces followed. By the time Petrucci's 1501 Harmonice musices odhecaton appeared, the first book of music printed from moveable type, bass and alto clefs identifying the note F and the note C respectively, symbols virtually identical to those found in earlier manuscript, had become standard. Only in the case where the cantus line was preceded by a C clef marking the bottom line of the stave, would we use today a treble clef marking G on the second line from the bottom of the stave. We illustrate the C and F clef signs below:

    Gregorian chant clefs: C and F

    An example of the Petrucci 'style' may be found on page 160 of A History of Western Music by Grout and Palisca (published by W.W. Norton).

    As we have noted above, Guido also named the degrees of the scale 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. However, the term 'absolute pitch' when referring to medieval music should be handled with care.

    Reference:

  • Pitch, Temperament & Timbre

    first line of Sumer Is Icumen In

    While a staff of five lines was adopted in France for vocal music, one of six lines was used in Italy and, as the example illustrates, in the Reading Abbey manuscript in which the Reading rota (entitled Sumer Is Icumen In) appears. Instrumental music employed staves of varying numbers of lines until the sixteenth century when the five-line staff became the standard. Accidental notation derives from variations of the letter B, particularly, the sharp and natural from the square B quadratum, and the flat from the B rotundum. In the earliest European music notation, 4-line staff Gregorian chant manuscripts, only B needed to be altered. It could be flattened, so altering from its position in the hexachordum durum ('hard hexachord' - hard because of the 'hard b': G-A-B-C-D-E) where it is natural, to that in the hexachordum molle ('soft hexachord' - soft because of the 'soft b': F-G-A-Bb-C-D) where it is flat. B is absent from the third hexachord, hexachordum naturale ('natural hexachord' - natural because it is neither hard nor soft: C-D-E-F-G-A).

    This use of B as the only altered note explains some modern notational peculiarities. The flat sign actually derives from a round B (b), to signify the B of the soft hexachord, that is B flat (hence the name of the flat sign in French bémol from medieval French bé mol — modern French bé mou — or 'soft b') and originally meant only the altered B, Bb. The natural sign derives from a square B (), to indicate the B of the 'hard hexachord', that is, B natural (hence the name of the natural sign in French bécarre from medieval French bé carre, earlier bé quarre — modern French bé carré — or 'square b') and originally meant only the unaltered B, B natural. For the same reason, in the German notation the letter B only designates the B flat while the letter H, which is actually a deformation of a square B designates the B natural. As polyphonic harmony developed more alterations were required. The first sharp in use was F#, then came the second flat Eb, then C#, as so on. By the sixteenth century Bb, Eb, Db, Ab, Gb and F#, C#, G#, D# and A# were all in use.

    The opposition of the 'soft b' (B flat) and the 'hard b' (B natural) went beyond the fact that they are present in different hexachords: the rules of polyphony stated that they could not be sung together or even consecutively either in the same part or in different parts. The segregation of the 'hard b' (which in the medieval hexachordal system bore the name 'b mi') from the 'soft b' (which in the medieval hexachordal system bore the name 'b fa') was extended in polyphonic music to the rule of 'mi contra fa', whereby the tritone, the medieval 'diabolo in musica' was a forbidden melodic and vertical interval and had to be corrected to a perfect fourth or fifth.

    References:

  • Hexachord
  • Tritone

    After a period during which printers sought to replicate features of handwritten manuscript in their choice of print face, a process of standardisation took place and when new ideas in letter form design were adopted in one country, they became commonplace elsewhere.

    Those interested in the history of design and form in early printing, much of it unrelated to notation of music, may like to read The Alphabet Abecedarium by Richard A. Firmage published in 2000 by Bloomsbury (ISBN 0 7475 4757 2) - an earlier edition appeared in 1993 published by David R. Godine, Boston, MA, USA.

    The evolution of rhythmic notation took much longer than that for pitch. It would appear that prior to mensural notation the length of notes would be determined by the ancient rules of proportional rhythm applied to the words accompanying the melody (prosodic feet and proportions). By the tenth century, notation was beginning to develop its own rules. We find, in the anonymous Commemoratio brevis, some striking observations on the relative lengths of different notes.

    "Breves must not be slower than is fitting for Breves; nor may Longs be distorted in erratic haste and be faster than is appropriate for Longs .... All notes which are long must correspond rhythmically with those which are not long through their proper inherent durations ... for the longer values consist of the shorter, and the shorter subsist in the longer, and in such a fashion that one has always twice the duration of the other, neither more nor less ... for without question all music should be strictly measured in the manner of prosody"

    Even so, it remains a problem when classifying and analysing the music of the troubadour, associated with Southern France between 1100 and 1300, as to whether the lyrics or the melody form the foundation for interpretation and performance. There is a complete absence of any mensural notation. Mensural or 'measured-time' notation would emerge only slowly and the golden era of the troubadours was a time of evolution.

    Mensural notation became a necessity as polyphony and, in particular, the motet developed. Time could no longer be elastic. A single invariable time-unit became essential. At first, rhythmic modes were represented by certain patternings of neumes; later, in his Ars cantus mensurabilis (c.1280), Franco of Cologne clearly indicated, for each note, its exact rhythmic length and represented notes of long and short duration by particular specific neumes. In his system, the longer value was in principle equal to three of the shorter values. Indeed, the essence of mensuration was the relationships between two sets of note durations specifically, the ratio of breves to semibreves (called tempus), and of semibreves to minims (called prolatio).

    In the fourteenth century, Philippe de Vitry, author of Ars nova, expanded Franco's 3:1 system to allow duple divisions of the long and short notes, i.e. a 2:1 system. At the various rhythmic levels of a given piece, either relationship was implied, and a system of signs and coloured notes was used to identify which relationship was currently being used or being temporarily set aside.

    Mensural notation had become, then, a system of rhythmic notation where distinct note-shapes (from about 1260, maxima, longa, brevis and semibrevis - from the fourteenth century, minima - from the fifteenth century, semiminima, fusa and semifusa) indicated the relative lengths of different notes.

    Groups of notes could be 'bound' together to form ligatures. This notational system was distinct both from that of rhythmic modes in which the context of the musical line limited any rhythmic flexibity, and unmeasured music which was entirely free from any set rhythmic values.

    The ternary ratio (3:1) applied to the tempus (ratio of breves to semibreves), was called perfect, and was represented by a complete circle; applied to the prolatio (ratio of semibreves to minims), it was called major and was represented by a dot in the middle of the sign. The binary ratio (2:1) applied to the tempus was called imperfect, and was represented by an incomplete circle; applied to prolatio, it was called minor and was represented by the lack of an internal dot.

    This system was extended to the ratio of longer note values, in particular, of maxima to longa (called modus maximorum, modus major or maximodus) and of longa to breve (called modus longarum, modus minor or simply modus).

    The mensural notation system remained in use until about 1600.

    We thank Ken Moore for his help in clarifying this section on mensuration.

    Pre-Mensural Notation Symbols

    Ekphonetic
    Notation

     

    accentus acutus or acutus

    the acutus, being drawn upwards, from left to right, indicates a rise in the melody, a higher note

    accentus gravis or gravis

    the gravis, being drawn downwards, from left to right, indicates a fall in the melody, a lower note

     

    Neumatic
    Notation

    6th to 13th
    centuries

     

    Virga

    virga jacens
    (Latin, literally 'thrown rod')

     

     

    punctus or punctum

    Mensural Notation Symbols

    Mensural
    Notation
     

    maxima
    (duplex long)

    longa
    (long)

    brevis
    (breve)

    semibrevis
    (semibreve)

    minima
    (minim)

    semiminima

    fusa

    semifusa

    13th century

     

    14th century

     

    15th to 17th centuries

    Modern
    Notation

    from the 17th century

     

    breve
    (double whole note)

    semibreve
    (whole note)

    minim
    (half note)

    crotchet
    (quarter note)

    quaver
    (eighth note)

    semiquaver
    (sixteenth note)

    References:

    We thank Christian Mondrup for recommending and providing information about two of these links

    By the fifteenth century, numbers appeared in the form of fractions, which in time developed into our time signatures, to mark when one proportionality of rhythmic values was temporarily being substituted for by another. Bar lines, expression signs, and, by the seventeenth century, Italian became the standard language for indicating the tempo (e.g. allegro, andante, largo). It should be mentioned that indications of the character of a piece had been used as far back as the Musica Enchiriadis (ninth century) employing the Latin words morosus (sadly) and cum celeritate (fast).

    Nicola Vicentino (1511-1575/76) was one of the first theorists to mention volume as an expressive parameter. In his treatise L'antica musica ridotta alla moderna prattica (1555) he mentioned that the strength of singing must respect carefully the text and passage being sung and Giovanni Gabrieli's Sacrae Symphoniae (1597) is an early example where we find dynamic markings (i.e. piano, forte, pianissimo, fortissimo) used in their abbreviated form. German, French and English composers sometimes indicated, at the top of the page, the mood or speed of a piece in their own language while employing titles drawn from a wide range of languages.

    With the adoption of equal temperament and the major and minor modes, key signatures indicating a major key or its relative minor became conventional and assumed their present form during the baroque period.

    Even so there could be the odd example where composers modified standard notation to meet specific needs.

    This is a portion of the first movement of Partita VII from Biber's collection of scordatura trios, Harmonia artificiosa-ariosa diversimode accordata, a work in 7 movements for two violas d'amore and basso continuo, originally published in 1696; this is a facsimile from the 1712 reprint. The tuning given is for 6 strings. The 9 line stave is Biber's way of extending the fingerings of the ordinary 4 string viola to the viola d'amore. There is one other example of this 9 line stave notation surviving.

    To those interested in hearing this Partitia by Biber we recommend the superb recording of the complete Harmonia Artificioso Ariosa by The Rare Fruits Council on Auvidis France E 8572.

    The Auvidis label is now part of Naive Classique.
    Naive Classique
    148 rue du Faubourg Poissonnière
    75010 Paris
    France

    Tel: +33 (0)1 44 91 64 00
    Fax: +33 (0)1 44 91 64 02
    Email: info@naive.fr

    In the example below, taken from the Lilypond music processor web site, the arrangement of stems in the second half of the first bar, the whole of the second bar and the first half of the third bar, reflects the fact that the left hand melody line has been written on both staves for clarity. In order to make readable multiple voices on an individual staff, the engraver combines notes and rests so that the player can follow easily the disposition of the individual voices from beat to beat, bar to bar.

    multiple voices on one staff

    The advent of aleatory music has produced new notational 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. Proportionate (proportional) Notation, a graphic method of indicating durations, where instead of traditional notation, the horizontal spacing of symbols represents the intended length of durations has been introduced to handle pulseless music and music in which different and often complicated rhythms progress simultaneously at different speeds.

    Sagittal is a microtonal notation system by George D. Secor and David C. Keenan. George Secor began development of the Sagittal (pronounced “SAJ-i-tl”) notation system in August 2001. In January 2002 he presented what he had developed to the Yahoo group tuning and offered to consider suggestions for improvements. At that stage the system could notate the equal temperaments with 17, 19, 22, 29, 31, 41, and 72 divisions per octave. Little did he know that he had provided a unifying symbolic principle which would ultimately be developed into a system capable of notating almost any conceivable microtonal tuning.

    References:

  • A downloadable pdf format file entitled The Written Notation of Medieval Music by Nigel Horne
  • Sumer Is Icumen In from which the Reading rota illustration has been taken
  • Graphical scores [link recommended by Brandon Hendrix]
  • The History of Mechanical Musical Instruments and Musical Notation
  • Sagittal - A Microtonal Notation System

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