Music Notation
Content:

In this section, a brief overview of music notation is reported. This overview is mainly focused on highlighting the structure of music from the point of view of its meanings for the executor, and the visual representation and syntax of the notation. In this context, only classical music is considered (e.g., Rossini, Bellini, Donizetti, Verdi, Vivaldi, Scarlatti, Puccini, Bach, Beethoven, etc.), modern and antique music should be separately considered. In modern music (e.g., Berio, Corghi, Donatoni, Grisey, Guarnieri, Huber, Maderna, Manzoni, Nono, Nunes, Pennisi, Sciarrino, Vacchi, etc.), several other symbols have to be added with respect to those of classical music. On the other hand, the proliferation of symbols is mainly due to the fantasy of composers rather than to real needs; since, in most cases, the new symbols are proposed for expressing effects that can be described even with the classical notation. Publishers tend to limit the adoption of new symbols to those that are adopted by at least a group of composers since the current trend of composers is to create several personal new symbols for each new composition. For these reasons to consider only classical symbols is not a limitation. On the other hand, from the point of view of publishers, schools of music, and theaters the music notation is that is published, taught and executed in front of large stalls.

Figures and their Attributes

The basic element of music notation is the figure. The figure can be a note or a rest. The sound is associated with notes, while a rest is a pause in the sound. The figures are read from left to right. Before to discuss about the organization of music figures in the music score a more detailed description of the basic elements related to figures is needed.

The concept of note in the music notation is not directly connected to that of pitch in sound, since the sound of a note can be deduced from its representation on the basis of:

Confidentially, the high of a note in the staff represents its sound in a certain context. Please note that the example in Fig. 2.1, it is strongly exasperate and thus the position of the symbols above and below the note could be performed by following other rules. The rules used in critical cases depend on experience and they are not reported on any book, neither in those mentioned as the handbooks for music engraving (especially for fingering and instrumental symbols which are discussed in the following). This knowledge is verbally inherited and strictly maintained by publishers.
Musical Symbols
The note, its main components and some related symbols.

 

The duration of a note is conventionally represented by a relative value to the beat -- e.g., a note of an eighth (8th), a note of a quarter (4th), etc. The number of beats is stated on the basis of indications of tempo. The effective value of duration depends on:

Moreover, the real duration of a note has to be evaluated considering these aspects and the context in which the note is inserted since the tempo (stating the absolute reference of the execution rate), can be different. Visually the form and the position of the notehead and the direction of the stem (if any) of the note follows well defined rules. The position of other symbols around the note frequently depends on the orientation of the stem.

For the duration of rests similar but simpler rules are applied. The tempo of a musician performance is described by a textual specification -- i.e., grave, largo, larghetto lento, adagio, andante, andantino, moderato, allegretto, allegro, allegro assai, vivace, presto, prestissimo (often called agogic indications), etc. This specification symbols change the context of the music execution. These indications are often accompanied by adjectives or attributes to better describes the general trend such as solenne, sostenuto, maestoso, marziale, grazioso, scherzando, giocoso, con fuoco, dolce, tranquillo, impetuoso, agitato, appassionato, deciso, con moto (sometime are translated in the other languages). In general, these specifications are subjected to interpretation, when an absolute precise vale is required a metronomic indication can be used, fixing in this way the number of beats per minute) remain valid until a different indication is given.

Along the score other indications -- e.g., rallentando (rall.), allargando (allarg.) -- are relative changes totally subjective in their realization. These indications are frequently given by means of special graphic symbols -- e.g., an arrow -> or a wave for rall.

A note may have ornaments (abbellimenti) such as: appoggiatura, grace notes, mordent, trill, glissando, turn, backturn, tremolo. These symbols are associated with the note in order to ornate its sound adding in this way a specific expression to the music phrase. For instance, the trill may consist in to alternate the sound of the note with a sound closely higher. Typically, these symbols produce an effect only on the note in which are added. The graphical representation of some of these symbols can be very useful for expressing duration of the effect such as for the trill. It states with length the point in which the effect starts and ends.

A note may have accents (even called articulations) to specify the expression of the note: such as martellato, staccato dot (truncated), accent, tenuto (legato, smooth), sforzato. The sequence and the relative position of the accents follow a set of well-defined visual rules. In general, the accents affect the duration and in some case also the dynamics. For instance, martellato is represented by using a small filled wedge towards the notehead specifying that the sound must be as that of a hammer (martello); staccato is represented with a dot over above the note and reduces the note duration of about one half. These accents can be put up or below the note. The position depends on the position of the notehead on the staff; usually on the opposite side of the stem, if any. Each note (in classical music) may present several of these accents at the same time -- e.g., staccato tenuto sforzato. Even in this case the visual representation and symbol position give a direct idea of the desired effect. Moreover, many other accents have been recently defined in the modern music.

The ynamics is a relative concept to specify the loudness of the sound. For example different gradations of, soft: (e.g., pianissississississimo) pppppp, ppppp, pppp, ppp or pp; loud: f, ff, fff, ffff, fffff or ffffff and middle way values: halfsoft mp, halfloud mf, and many others: sf, fp, fz, ffz, etc.). The symbols of dynamics are typically placed below the staff. The dynamics is a relative specification since it depends on the context. The same dynamics have a different meaning if it is applied to a solo or to an orchestra; since in an orchestra the loudness is combined with those of the other instruments. These symbols change the context of the interpretation and remain valid until a different indication is stated. Moreover, the general dynamics can be changed on the basis of relative and local indications for increasing (crescendo) or decreasing the dynamics (diminuendo). These can be formally stated by either textual (e.g., dimin.) or graphical symbols Graphical symbols are much more effective since they have an immediate interpretation. Their direction states if the dynamic has to be increased or decreased, while the application points (starting and ending note) state exactly the range of application. On these bases, with graphical symbols instead of using textual versions other more sophisticated affects can be stated -- e.g., a crescendo smoothly connected with a diminuendo: <>.

Aggregations of Symbols

According to the music notation there are five main types of mechanisms on the basis of which the figures are grouped or group of figures are represented. Their meaning is strongly different:

 

Musical Figures
 
 
Chords, voices, repeated symbols and groups can be considered figures as well. On the other hand, each note in these structures can have all the above mentioned features.

The Structure of Music Scores

According to the music notation, the figures are organized in measures limited by bars, sometime the bar and measure are used as synonyms. Please see the score reported in the previous figure, it presents three measures.

Each measure is comprised of a defined number of beats depending on the meter (e.g., 4/4, 2/4, 6/8). The numerator of the meter represents the number of beats. For instance 3/4 means that one can needs 3 notes of a 1/4th for filling the measure. Therefore, the measure has to be consistent in terms of figure durations that it contains.

The ordered collection of measures represents a score. It may contain references to jump from a point to another, from a measure to another for repeating parts (e.g., ritornelli), etc. Some special kinds of barlines are defined for marking the start and end of ritornelli. In some cases, characters are used for labeling points from which the orchestra has to restart during rehearsals -- for instance, for studying the most difficult pieces of music.

Typically, if the score is for a group of instruments/musicians there exists a score (a part) for each instrument and these are aligned each other being aligned the respective measures. When an instrument has to be quite, it has rests as the 3rd measure of the violin in Fig. 2.3.

Therefore, in orchestras, the director reads the main score observing the measures of all instruments on the same column; while the musician can see only their respective part. In the main score, similar instruments are collected by using a graph or squared parenthesis. The placement of figures on aligned measures depends on the measure length and on the value of the figures.

At the beginning of a score, and when is needed, the clef has to be declared -- for example: G, F, baritone, tenor, alto, mezzo-soprano, soprano clef. Each clef has to be placed in well specific position on the staff, and not everywhere as allowed by several computer-based music-editors. The clef specifies the current interpretation of the lines and holes of the staff, this interpretation is fixed until a new clef or key signature is placed. The clef may present a key signature (e.g., a group of sharp or flat) for stating changes on the meaning of notes placed on the staff. A new clef, for changing the current one, can be used in instant along the measures, even in the middle.

Moreover, the music observed by the director on the main score is typically formatted differently with respect to that observed by musicians. In fact, it is different since:

Some Musical Parts

 

Main score and parts (produced by using Finale).
    1. Horizontal Music Notation Symbols
Up to now, only simple relationships among symbols have been described.

Please note that some of the components of music notation are typically referred to a couple of points along the staff. These points can belong to different measures and in some cases to different scores, for instruments reading music on more than one score:

Please note that this kind of information is totally asynchronous with respect to the sequence of measures. This can be noted by observing the previous figure and the next one.
Horizontal Symbols
Horizontal and other additional symbols.

General and Instrumental Symbols

In effectively executed music several other symbols are typically added. These symbols can be classified in two main categories:

Most symbols of this last set assume different graphical or textual representations on the basis of the instrument for which they are used. For example the inserting and the removing of the mute can be graphically represented by using a horizontal "E"' for strings, or with a "+" (plus, to insert the mute) or a "-" (minus, to remove the mute) for brass, or with a textual indication: con sordina, via sordina. The latter are frequently written in the language used by the musician that is playing. Some of these symbols change the context of the interpretation/execution. For example, with mute means to insert the mute and in some place will be written remove mute.

On the other hand, several interpretation symbols, which are typically neglected in computer music editor, are really relevant during the actual execution of music in theatres and during lessons in schools of music.

Discussion

According to the above presentation, it can be stated that the music notation is a visual language witch presents several rules along both horizontal and vertical directions. Several accompanying symbols strictly related to the notes have been discussed. The presence of more than one of these symbols around the figures changes their order, orientation and positions. For instance, the accents have to be placed on the opposite part of the stem (if any). In the case of a slur on the same note, they have to leave the space close to the note at the slur, thus they have to placed more far from the notehead then usually.

Please note that, in general, the position of accompanying symbols with respect to the note assumes a particular relevance since:

Moreover, according to the music notation the same meaning can be obtained by using different representations. In the traditional computer-based music editor, the problems have been addressed by considering only the visual representation of music. This means that in most of them every symbol can be place in any position on the score without constraining the organization of the graphical symbols according to the visual syntax of the music notation. Only few automatic mechanisms are established and they present a lot of situation in which the chosen position is unsuitable. 
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