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MUSICAL NOTATION
http://en.wikipedia.org/wiki/Note

All text is available under the terms of the GNU Free Documentation License: http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License

# Note

A note is a sign used in music to represent the relative duration and pitch of sound. The word note is also used for the graphic representation of that pitch in a notation system (and sometimes its duration) or a specific instance of either.

The general and specific meanings are freely mixed by musicians, although they can be initially confusing: one can speak of "the second note of Happy Birthday to You" for example. The first two notes of Happy Birthday to You are the same note, meaning, "the first two sounds of Happy Birthday to You have the same pitch." A note is a discretization of musical or sound phenomena and thus facilitates musical analysis (Nattiez 1990, p.81n9).

## Note name

A note with doubled frequency as another sounds very similar, and is commonly given the same name, called pitch class. The span of notes within this doubling is called an octave. The complete name of a note consists of its pitch class and the octave it lies in. The pitch class uses the first seven letters of the latin alphabet: A, B, C, D, E, F, and G (in order of rising pitch). The letter names repeat, so that the note above G is A (an octave higher than the first A) and the sequence continues indefinitely. Notes are used together as a musical scale or tone row.

Because there are actually 12 notes needed by diatonic music, the 7 letter names can also be given a modifier. The two main modifiers are sharps and flats which respectively raise or lower the pitch of a note by a semitone. These are used to create the additional five notes necessary to complete the chromatic scale. The sharp symbol is ♯ (similar to the pound symbol, #), the flat symbol is ♭ (similar to a lower-case italic b). These accidentals are written after the note name; for example F♯ represents the note F sharp, B♭ is B flat.

In music notation the symbols are placed before the note symbol or at the beginning of the line as a key signature. The natural symbol (♮), can be inserted before a note to cancel a flat or sharp in the signature.

Sharps can also be applied to notes B and E creating notes that are equal to C and F respectively (in modern western musical practice). Similarly flats applied to C and F are other names for B and E. Pushing this further, double-sharps and double-flats are used to indicate raised sharps and lowered flats. For example B♭♭ is another name for A.

Another style of notation, rarely used in English, uses the suffix "is" to indicate a sharp and "es" (only "s" after A and E) for a flat, e.g. Fis for F♯, Bes for B♭, Es for E♭. In parts of Europe, the letter H is sometimes used instead of B, in which case B represents B♭.

The octaves of doubled frequency are indicated in various ways as shown in the table below. Octaves count from C upwards to B. The traditional system starts from the great octave (with capital letters) and small octave (with minuscule letters). Lower octaves are named "contra" (with primes before), higher ones "lined" (with primes after). Another system suffixes a number (starting with 0, or sometimes -1). In this system A4 is nowadays standardised to 440 Hz, lying in the octave containing notes from C4 (middle C) to B4. The lowest note on most pianos is A0, the highest C8. The MIDI system for electronic musical instruments and computers uses a straight count starting with note 0 for C-1 at 8.1758 Hz up to note 127 for G9 at 12,544 Hz.

## Written notes

A written note can also have a note value, a code which determines the note's relative duration. These note values include quarter notes (crotchets), eighth notes (quavers), and so on.

When notes are written out in a score, each note is assigned a specific vertical position on a staff position (a line or a space) on the staff, as determined by the clef. Each line or space is assigned a note name, these names are memorized by the musician and allows him or her to know at a glance the proper pitch to play on his or her instrument for each note-head marked on the page.

The staff above shows the notes C, D, E, F, G, A, B, C listen  and then in reverse order, with no key signature or accidentals.

## Note frequency (hertz)

In all technicality, music can be composed of notes at any arbitrary frequency. Since the physical causes of music are vibrations of mechanical systems, they are often measured in hertz (Hz), with 1 Hz = 1 complete vibration per second. For historical and other reasons especially in Western music, only twelve notes of fixed frequencies are used. These fixed frequencies are mathematically related to each other, and are defined around the central note, A4. The current "standard pitch" or "concert pitch" for this note is 440 Hz. Actual practice may vary. In the past there has been a rising tendency.

The note naming convention specifies a letter, any sharp/flat, and an octave number. Any note is exactly an integer number of half-steps away from central A (A4). Let this distance be denoted n. Then,

$\mathrm{Frequency} = 440 \times 2^{n/12} \ \mbox{Hz}$

For example, let's find the frequency of the C above Middle A (C5). There are +3 half-steps between A4 and C5

• A — (1) → A♯— (2) → B — (3) → C
$f = 440 \times 2^{3/12} \approx 523.2511 \ \mbox{Hz}$

It is important to keep the sign of n in mind. For example, the F below Middle A is F4. There are -4 half-steps:

• A — (1) → Ab — (2) → G — (3) → Gb — (4) → F

... each of these is descending the scale. Thus:

$f = 440 \times 2^{-4/12} \approx 349.2290 \ \mbox{Hz}$

Finally, it can be seen from this formula that octaves automatically yield factors of two times the original frequency (in fact this is the means to derive the formula, combined with the notion of equally-spaced intervals).

For use with the MIDI (Musical Instrument Digital Interface) standard, a frequency mapping is defined by:

$p = 69 + 12\times\log_2 {(\frac {f}{440})}$

For notes in an A440 equal temperament, this formula delivers the standard MIDI note number. Any other frequencies fill the space between the whole numbers evenly. This allows MIDI instruments to be tuned very accurately in any microtuning scale, including non-western traditional tunings.

## History of note names

Music notation systems have used letters of the alphabet for centuries. The 6th century philosopher Boethius is known to have used the first fifteen letters of the alphabet to signify the notes of the two-octave range that was in use at the time. Though it is not known whether this was his devising or common usage at the time, this is nonetheless called Boethian notation.

Following this, the system of repeating letters A-G in each octave was introduced, these being written as minuscules for the second octave and double minuscules for the third. When the compass of used notes was extended down by one note, to a G, it was given the Greek G (Γ), gamma. (It is from this that the French word for scale, gamme is derived, and the English word gamut, from "Gamma-Ut", the lowest note in Medieval music notation.)

The remaining five notes of the chromatic scale (the black keys on a piano keyboard) were added gradually; the first being B which was flattened in certain modes to avoid the dissonant augmented fourth interval. This change was not always shown in notation, but when written, B♭ (B flat) was written as a Latin, round "b", and B♮ (B natural) a Gothic b. These evolved into the modern flat and natural symbols respectively. The sharp symbol arose from a barred b, called the "cancelled b".

In parts of Europe, including Germany, the natural symbol transformed into the letter H: in German music notation, H is B♮ (B natural) and B is B♭ (B flat).

In Italian notation the notes of scales are given in terms of Do - Re - Mi - Fa - Sol - La - Si rather than C - D - E - F - G - A - B. These names follow the original names reputedly given by Guido d'Arezzo, who had taken them from the first syllables of the first six musical phrases of a Gregorian Chant melody Ut queant laxis, which began on the appropriate scale degrees. These became the basis of the solfege system. "Do" later replaced the original "Ut" for ease of singing, though "Ut" is still used in some places. "Si" or "Ti" was added as the seventh degree (which is not from a word in the chant).

• Pensato
• Solfege
• grace note
• ghost notes

## Source

• Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate (1990). ISBN 0-691-02714-5.