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Note

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In music, the term note has two primary meanings: 1) a sign used in musical notation to represent the relative duration and pitch of a sound; and 2) a pitched sound itself. Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis (Nattiez 1990, p.81n9).

The term "note" can be used in both generic and specific senses: one might say either "the piece Happy Birthday to You begins with two notes having the same pitch," or "the piece begins with two repetitions of the same note." In the former case, one uses "note" to refer to a specific musical event; in the latter, one uses the term to refer to a class of events sharing the same pitch.

Note name

Two notes with fundamental frequencies in a ratio of 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) (some countries use other names as in the table 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, the system of scientific pitch notation combines a letter name with an Arabic numeral designating a specific octave. For example, the now-standard tuning pitch for most Western music, 440 Hz, is named a′ or A4. There are two formal ways to define each note and octave, the Helmholtz system and the Scientific pitch notation.

Accidentals

Letter names are modified by the accidentals - sharp (similar to the symbol #) and flat (similar to the letter b). These symbols respectively raise or lower a pitch by a semitone or half-step, which in modern tuning will multiply or divide (respectively) the frequency of the original note by

sqrt[12]{2}

, approximately 1.059. 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: avoiding sharps/flats in the key signature, "C" yields D, when D's sharp is in the signature. 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 is equal to 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.

Notes that belong to the diatonic scale relevant in the context are sometimes called diatonic notes; notes that do not meet that criterion are then sometimes called chromatic notes.

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 (so as "F" an F-sharp would become simply F).

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, Ges for G, Es for E. This system first arose in Germany and is used in almost all European countries whose main language is not English or a Romance language.

In most countries using this system, the letter H is used to represent what is B natural in English, the letter B represents the B, and Heses represents the B (not Bes, which would also have fit into the system). Belgium and the Netherlands use the same suffixes, but applied throughout to the notes A to G, so that B is Bes. Denmark also uses H, but uses bes instead of heses for B.

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

Name	prime		second		third	fourth		fifth		sixth		seventh
Natural (English)	C		D		E	F		G		A		B
Sharp (symbol)		C		D			F		G		A
Flat (symbol)		D		E			G		A		B
Sharp (English name)		C sharp		D sharp			F sharp		G sharp		A sharp
Flat (English name)		D flat		E flat			G flat		A flat		B flat
Natural (Scandinavian after 1990s)	C		D		E	F		G		A		B
Sharp (Northern European)		Cis		Dis			Fis		Gis		Ais
Flat (Northern European)		Des		Es			Ges		As		Bes
Natural (Northern European, and Scandinavian before 1990s)	C		D		E	F		G		A		H
Flat (Nothern European, and Scandinavian before 1990s)		Des		Es			Ges		As		B
Southern European	Do		Re		Mi	Fa		Sol		La		Si
Variant names	Ut		-		-	-		So		-		Ti
Indian style	Sa	Re Komal	Re	Ga Komal	Ga	Ma	Ma Teevra	Pa	Dha Komal	Dha	Ni Komal	Ni
Korean style	Da		La		Ma	Ba		Sa		Ga		Na
Approx. Frequency [Hz]	262	277	294	311	330	349	370	392	415	440	466	494
MIDI note number	60	61	62	63	64	65	66	67	68	69	70	71

Note designation in accordance with octave name

The table of each octave and the frequencies for every note of pitch class A is shown below. The traditional (Helmholtz) system centers on the great octave (with capital letters) and small octave (with lower case letters). Lower octaves are named "contra" (with primes before), higher ones "lined" (with primes after). Another system (scientific) 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.

Octave naming systems				frequency of A (Hz)
traditional	shorthand	numbered	MIDI nr	frequency of A (Hz)
subsubcontra	Cˌˌˌ – Bˌˌˌ	C-1 – B-1	0 – 11	13.75
sub-contra	Cˌˌ – Bˌˌ	C0 – B0	12 – 23	27.5
contra	Cˌ – Bˌ	C1 – B1	24 – 35	55
great	C – B	C2 – B2	36 – 47	110
small	c – b	C3 – B3	48 – 59	220
one-lined	c′ – b′	C4 – B4	60 – 71	440
two-lined	c′′ – b′′	C5 – B5	72 – 83	880
three-lined	c′′′ – b′′′	C6 – B6	84 – 95	1760
four-lined	c′′′′ – b′′′′	C7 – B7	96 – 107	3520
five-lined	c′′′′′ – b′′′′′	C8 – B8	108 – 119	7040
six-lined	c′′′′′′ – b′′′′′′	C9 – G9	120 – 127	14080

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 to know at a glance the proper pitch to play on his instrument for each note-head marked on the page.

The staff above shows the notes C, D, E, F, G, A, B, C 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 modern "concert pitch" for this note is 440 Hz, although this varies in actual practice (see History of pitch standards).

The note-naming convention specifies a letter, any accidentals (sharps/flats), and an octave number. Any note is an integer of half-steps away from middle A (A4). Let this distance be denoted n. If the note is above A4, then n is positive; if it is below A4, then n is negative. The frequency of the note (f) (assuming equal temperament) is then:

f = 2^n/12 × 440 Hz

For example, one can find the frequency of C5, the first C above A4. There are 3 half-steps between A4 and C5 (A4 → A4 → B4 → C5), and the note is above A4, so n = +3. The note's frequency is:

f = 2^3/12 × 440 Hz ≈ 523.2511 Hz.

To find the frequency of a note below A4, the value of n is negative. For example, the F below A4 is F4. There are 4 half-steps (A4 → A4 → G4 → G4 → F4), and the note is below A4, so n = −4. The note's frequency is:

f = 2^−4/12 × 440 Hz ≈ 349.2290 Hz.

Finally, it can be seen from this formula that octaves automatically yield factors of two times the original frequency, since n is therefore a multiple of 12 (12k, where k is the number of octaves up or down), and so the formula reduces to:

f = 2^12k/12 × 440 Hz = 2^k × 440 Hz,

yielding a factor of 2. In fact, this is the means by which this formula is derived, 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. 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:

p = 69 + 12 × log₂ (f / (440 Hz))

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 tritone 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, Poland and Russia, 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, Portuguese, Greek, French, Russian, Flemish, Romanian, Spanish, Hebrew and Turkish notation the notes of scales are given also 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 (most likely from the beginning of Dominus, Lord), though "Ut" is still used in some places. "Si" or "Ti" was added as the seventh degree (from Sancte Johannes, St. John, to which the hymn is dedicated).

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.