Musical Notes

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

Two notes of which the frequencies have a ratio that is any power of two (e.g. half, twice, or four times) will sound very similar. Because of that all notes with these kinds of relations can be grouped under the same pitch class. In traditional music theory pitch classes are represented by the first seven letters of the Latin alphabet (A, B, C, D, E, F, and G) and various modifications added to these letters (more on this below). The span of notes between one pitch and another that is twice (or half) its frequency is called an octave. In order to differentiate two notes that have the same pitch class but fall into different octaves, a complete note name consists in both its pitch class and also a designation of which unique octave it falls into. For example, the now-standard tuning pitch for most Western music, 440 Hz, is named A4. The A an octave above it will be named A5, the one above that A6, and so on to infinity; similarly the A an octave below A4 will be A3, etc. Traditionally, octave numberings begin with the note C and end with B - so for example, the D above C4 will be D4, but the B below C4 will be B3 (as it is in a different octave)

A musical scale or tone row is a collection of any series of pitches that fall within the space of an octave. So for example, a major scale beginning on the pitch class C would run in ascending order as C D E F G A B. A second C having twice the frequency of the first appears above the B, however including this second C in the set of notes for this scale is redundant because it is in the same pitch class as the first. A second identical scale at twice the frequency can be constructed on this second C, however all of the pitch classes will be the same as the previous one.

Although many scales may be constructed out of the set of original lettered pitches (A, B, C, D, E, F, G), a more diverse collection may be created by modifying these tones. The two most common modifiers, or accidentals, are sharps and flats. These accidentals will respectively raise or lower a pitch by a semitone or half-step, which in modern tuning will multiply or divide the frequency of the original note by an amount of 1.0594.... The sharp symbol is ♯ (similar to the pound symbol, #), the flat symbol is ♭ (similar to a lower-case italic b). They are written after the note name: so, for example, F♯ represents F sharp, B♭ is B flat. Other accidentals, such as double-sharps and double-flats (which will raise or lower the frequency by two semitones), are also possible in traditional music theory. Assuming enharmonicity, it is possible that use of accidentals will create equivalences between pitches that are written differently. For instance, raising the note B to B♯ will duplicate the note C. Assuming the elimination of all such equivalences, however, the complete chromatic scale adds five additional pitch classes to the original seven lettered notes for a total of 12, each separated by a half-step.

In musical notation, alterations to the seven lettered pitches in the scale are indicated by placing an accidental immediately before the note symbol, or by use of a key signature. The natural symbol (♮), can be inserted before a note to cancel a previously indicated flat or sharp.

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 labels the pitch class here represented by B, and the letter B replaces B♭.

This is a complete chart of a chromatic scale built on the note C4, or "middle C":

The table of each octave and the frequencies for every note of pitch class A is shown below. The traditional system centers on 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 (help·info) 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,

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

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) → A♭ — (2) → G — (3) → G♭ — (4) → F

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

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).

The distance of an equally tempered semitone is divided into 100 cents. So 1200 cents are equal to one octave — a frequency ratio of 2:1 — and. This means that a cent is precisely equal to the 1200th root of 2, which is approximately 1.0005777895

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

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).

See also

• 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.

External links

• Tonalsoft Encyclopaedia of Tuning
• Note Learning Flashcards
• List of Frequencies of musical notes